MATH40006 137 ability units
English review edition prepared on 4 October 2026 from a preserved source copy. It is a later presentation, not the historical study interface. Source checks and difficulty judgements describe the original material author's own process; they do not indicate Imperial College London endorsement.
Source SHA-256: 91f028ce01a29c59a8b503406fb27b33f7b3c4260ac1b6603ca9b7b097544377Source date: 2026-08-06
Source page 1
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 1 page
English passage 2 (6% down the source page)
MATH40006 Complete competency inventory from verifiable official materials
English passage 3 (11% down the source page)
137 subquestion-level competency units; five documents, not a purported complete seven-year database
English passage 4 (16% down the source page)
Encoded fields include year and question number, marks, topic, question type, recognition cues, first key step and course / Official method sequence, tools, combinations, computational workload and abstraction
English passage 5 (17% down the source page)
level, integration level, normal completion time, official solution length, whether it appeared in the main examination, and earlier / New coverage status .
Source page 2
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 2 page
English passage 2 (9% down the source page)
AU001 Q1(a) [4 marks ;official] LCM Algorithm counts and complexity
English passage 3 (12% down the source page)
Knowledge point
Test design and boundary cases; Function interfaces, return values and docstrings
English passage 4 (14% down the source page)
question type
Design function tests covering coprime, non-coprime and boundary cases
English passage 5 (15% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 6 (16% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 7 (18% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 8 (19% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 9 (21% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 10 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 11 (25% down the source page)
AU002 Q1(b) [3 marks ;official] LCM Algorithm counts and complexity
English passage 12 (28% down the source page)
Knowledge point
Algorithm counters and experimental measurement; Greatest common divisor / Least common multiple and Euclid algorithm; Loops, conditions and comprehensions
English passage 13 (29% down the source page)
question type
as repeated addition LCM Add comparison counters to the algorithm
English passage 14 (31% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 15 (32% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 16 (33% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 17 (35% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 18 (36% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (38% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 20 (41% down the source page)
AU003 Q1(c) [3 marks ;official] LCM Algorithm counts and complexity
English passage 21 (43% down the source page)
Knowledge point
Algorithm counters and experimental measurement; Greatest common divisor / Least common multiple and Euclid algorithm; Loops, conditions and comprehensions
English passage 22 (45% down the source page)
question type
is Euclid LCM Add comparison counters to the algorithm
English passage 23 (46% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 24 (48% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 25 (49% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 26 (51% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 27 (52% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 28 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 29 (56% down the source page)
AU004 Q1(d) [3 marks ;official] LCM Algorithm counts and complexity
English passage 30 (59% down the source page)
Knowledge point
Loops, conditions and comprehensions; Algorithm counters and experimental measurement; Greatest common divisor / Least common multiple and Euclid algorithm
English passage 31 (60% down the source page)
question type
Use exhaustive experiments to find fixed a worst-case input when
English passage 32 (62% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 33 (63% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 34 (65% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 35 (66% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 36 (68% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 37 (69% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 38 (72% down the source page)
AU005 Q1(e) [3 marks ;official] LCM Algorithm counts and complexity
English passage 39 (75% down the source page)
Knowledge point
Greatest common divisor / Least common multiple and Euclid algorithm; Asymptotic complexity O/Omega/Theta
English passage 40 (76% down the source page)
question type
Derive the exact comparison count of the repeated-addition algorithm
English passage 41 (77% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 42 (79% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 43 (80% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 44 (82% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 45 (83% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 46 (85% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 47 (87% down the source page)
AU006 Q1(f) [2 marks ;official] LCM Algorithm counts and complexity
English passage 48 (90% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Greatest common divisor / Least common multiple and Euclid algorithm
Source page 3
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 3 page
English passage 2 (6% down the source page)
question type
Obtain from the worst-case input lcm1 asymptotic complexity of
English passage 3 (7% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 4 (9% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 5 (10% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 6 (12% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 7 (13% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 8 (15% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 9 (17% down the source page)
AU007 Q1(g) [3 marks ;official] LCM Algorithm counts and complexity
English passage 10 (20% down the source page)
Knowledge point
Loops, conditions and comprehensions; Algorithm counters and experimental measurement; Greatest common divisor / Least common multiple and Euclid algorithm
English passage 11 (22% down the source page)
question type
Find experimentally Euclid Algorithm worst case b
English passage 12 (23% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 13 (24% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 14 (26% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 15 (27% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 16 (29% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 17 (30% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 18 (33% down the source page)
AU008 Q1(h) [4 marks ;official] LCM Algorithm counts and complexity
English passage 19 (36% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Greatest common divisor / Least common multiple and Euclid algorithm
English passage 20 (37% down the source page)
question type
use Fibonacci Proof of the asymptotic formula Euclid Worst-case complexity
English passage 21 (39% down the source page)
Recognition signal
two LCM Implementation, comparison counts, worst-case inputs and asymptotic complexity
English passage 22 (40% down the source page)
first key step
Count from 1 starting from, including the final unsuccessful while determine .
English passage 23 (42% down the source page)
Complete method sequence
Multiple test categories -> Counters for both algorithms -> fixed a scan -> exact / Worst-case count -> O(a) and O(log a)
English passage 24 (43% down the source page)
theorem / formula / tools
Repeated addition , Euclid, Counting, worst-case inputs and asymptotic analysis
English passage 25 (44% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 26 (46% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 27 (49% down the source page)
AU009 Q2(a) [4 marks ;official] Escape time for complex iteration
English passage 28 (51% down the source page)
Knowledge point
NumPy Array creation , dtype and shape;meshgrid and two-dimensional / Complex grid
English passage 29 (53% down the source page)
question type
Construct a two-dimensional grid in the complex plane
English passage 30 (54% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 31 (56% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 32 (57% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 33 (59% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 34 (60% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 35 (61% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 36 (64% down the source page)
AU010 Q2(b) [4 marks ;official] Escape time for complex iteration
English passage 37 (67% down the source page)
Knowledge point
NumPy Array creation , dtype and shape; Boolean masks and vectorised updates; Scalar-field visualisation (imshow/contour/origin/extent)
English passage 38 (68% down the source page)
question type
Mark initial escape points with a Boolean array and display them
English passage 39 (70% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 40 (71% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 41 (73% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 42 (74% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 43 (76% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 44 (77% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 45 (80% down the source page)
AU011 Q2(c) [4 marks ;official] Escape time for complex iteration
English passage 46 (83% down the source page)
Knowledge point
NumPy Indexing, slicing and step sizes; Boolean masks and vectorised updates; Complex iteration, escape time and stability; Scalar-field visualisation (imshow/contour/origin/extent)
English passage 47 (84% down the source page)
question type
Perform one complex iteration and record the 1 th escape
English passage 48 (86% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 49 (87% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 50 (88% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 51 (90% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 52 (91% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
Source page 4
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 4 page
English passage 2 (6% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 3 (9% down the source page)
AU012 Q2(d) [7 marks ;official] Escape time for complex iteration
English passage 4 (11% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Boolean masks and vectorised updates; Complex iteration, escape time and stability
English passage 5 (13% down the source page)
question type
Wrap the two-dimensional escape-time algorithm in a function
English passage 6 (14% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 7 (16% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 8 (17% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 9 (19% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 10 (20% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 8 minutes; official solution: long (multiple code sections / Derive )
English passage 11 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 12 (24% down the source page)
AU013 Q2(e) [3 marks ;official] Escape time for complex iteration
English passage 13 (27% down the source page)
Knowledge point
Test design and boundary cases; Scalar-field visualisation (imshow/contour/origin/extent); Complex iteration, escape time and stability
English passage 14 (28% down the source page)
question type
Test the escape-time plot with parameters varying over the grid
English passage 15 (30% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 16 (31% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 17 (33% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 18 (34% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 19 (36% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 20 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 21 (40% down the source page)
AU014 Q2(f) [3 marks ;official] Escape time for complex iteration
English passage 22 (43% down the source page)
Knowledge point
Test design and boundary cases ;NumPy Array creation , dtype and shape; Scalar-field visualisation (imshow/contour/origin/extent); Complex iteration, escape time and stability
English passage 23 (44% down the source page)
question type
Test fixed c of Julia type plot
English passage 24 (46% down the source page)
Recognition signal
z<-z^2+c, abs(z)>=2, Two-dimensional state array
English passage 25 (47% down the source page)
first key step
Copy inside the function z0 and initialise unresolved flags .
English passage 26 (48% down the source page)
Complete method sequence
Complex grid -> -1 Status -> Initial escape mask -> Update only positions that have not escaped -> Wrap the loop in a function -> Fill in values for non-escaped points -> Logarithmic colour map
English passage 27 (50% down the source page)
theorem / formula / tools
Complex grids, Boolean masks and state iteration , imshow
English passage 28 (51% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 29 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 30 (55% down the source page)
AU015 Q3(a) [2 marks ;official] Symbolic analysis of dynamical-system stability
English passage 31 (58% down the source page)
Knowledge point
SymPy Symbolic modelling and algebraic simplification; Symbolic equations, differentiation and substitution; Complex iteration, escape time and stability
English passage 32 (60% down the source page)
question type
Find fixed points of the complex quadratic mapping symbolically
English passage 33 (61% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 34 (63% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 35 (64% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 36 (66% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 37 (67% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 38 (68% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 39 (71% down the source page)
AU016 Q3(b) [1 marks ;official] Symbolic analysis of dynamical-system stability
English passage 40 (74% down the source page)
Knowledge point
Symbolic equations, differentiation and substitution
English passage 41 (75% down the source page)
question type
Find the derivative of the mapping
English passage 42 (77% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 43 (78% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 44 (80% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 45 (81% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 46 (83% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 47 (84% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 48 (87% down the source page)
AU017 Q3(c) [2 marks ;official] Symbolic analysis of dynamical-system stability
English passage 49 (90% down the source page)
Knowledge point
Symbolic equations, differentiation and substitution; tuples , zip and list combinations; Complex iteration, escape time and stability
English passage 50 (91% down the source page)
question type
Compute the squared modulus of the derivative at each fixed point
Source page 5
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 5 page
English passage 2 (6% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 3 (7% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 4 (9% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 5 (10% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 6 (12% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 2 minutes; official solution: short (single step / test )
English passage 7 (13% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 8 (16% down the source page)
AU018 Q3(d) [3 marks ;official] Symbolic analysis of dynamical-system stability
English passage 9 (19% down the source page)
Knowledge point
lambdify Symbol - Numerical conversion; Complex iteration, escape time and stability
English passage 10 (20% down the source page)
question type
Convert the two stability expressions into NumPy function
English passage 11 (22% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 12 (23% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 13 (24% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 14 (26% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 15 (27% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 16 (29% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 17 (31% down the source page)
AU019 Q3(e) [4 marks ;official] Symbolic analysis of dynamical-system stability
English passage 18 (34% down the source page)
Knowledge point
meshgrid and two-dimensional / Complex grid; Scalar-field visualisation (imshow/contour/origin/extent);lambdify Symbol - Numerical conversion; Complex iteration, escape time and stability
English passage 19 (36% down the source page)
question type
Plot stability-boundary contours
English passage 20 (37% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 21 (39% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 22 (40% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 23 (42% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 24 (43% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 25 (44% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 26 (47% down the source page)
AU020 Q3(f) [3 marks ;official] Symbolic analysis of dynamical-system stability
English passage 27 (50% down the source page)
Knowledge point
SymPy Symbolic modelling and algebraic simplification; Symbolic equations, differentiation and substitution; Complex iteration, escape time and stability
English passage 28 (51% down the source page)
question type
Construct and expand the composite mapping ff
English passage 29 (53% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 30 (54% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 31 (56% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 32 (57% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 33 (59% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 34 (60% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 35 (63% down the source page)
AU021 Q3(g) [8 marks ;official] Symbolic analysis of dynamical-system stability
English passage 36 (66% down the source page)
Knowledge point
SymPy Symbolic modelling and algebraic simplification; Symbolic equations, differentiation and substitution ;lambdify Symbol - Numerical conversion; Scalar-field visualisation (imshow/contour/origin/extent); Complex iteration, escape time and stability
English passage 37 (67% down the source page)
question type
Repeat the fixed-point analysis for the composite mapping - stability - Complete contour-plot workflow
English passage 38 (68% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 39 (70% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 40 (71% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 41 (73% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 42 (74% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 10 minutes; official solution: long (multiple code sections / Derive )
English passage 43 (76% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
English passage 44 (78% down the source page)
AU022 Q3(h) [1 marks ;official] Symbolic analysis of dynamical-system stability
English passage 45 (81% down the source page)
Knowledge point
Complex iteration, escape time and stability
English passage 46 (83% down the source page)
question type
Explain the relationship between stability curves and the boundary of the non-escaping set
English passage 47 (84% down the source page)
Recognition signal
fixed points / Periodic points and | derivative |=1 Stability boundary
English passage 48 (86% down the source page)
first key step
First solve f(z)=z, Then substitute the roots into the derivative .
English passage 49 (87% down the source page)
Complete method sequence
solve fixed points -> diff -> re/im Squared modulus -> lambdify -> level=1 -> Composite mapping / Exclude fixed points -> Stability boundaries of periodic points
English passage 50 (88% down the source page)
theorem / formula / tools
fixed points / Periodic points and derivative modulus , lambdify, Contours
English passage 51 (90% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 52 (91% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 5
Source page 6
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 6 page
English passage 2 (7% down the source page)
AU023 Q4(a) [1 marks ;official] Word-substitution encoding
English passage 3 (10% down the source page)
Knowledge point
Text-file reading and parsing; Test design and boundary cases
English passage 4 (11% down the source page)
question type
Check the vocabulary read from the external file
English passage 5 (13% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 6 (14% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 7 (16% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 8 (17% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 9 (19% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 10 (20% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 11 (23% down the source page)
AU024 Q4(b) [4 marks ;official] Word-substitution encoding
English passage 12 (26% down the source page)
Knowledge point
Mutable objects, in-place modification and copying / aliasing; Randomisation and random data; tuples , zip and list combinations
English passage 13 (27% down the source page)
question type
Copy and shuffle the vocabulary without changing the original
English passage 14 (28% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 15 (30% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 16 (31% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 17 (33% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 18 (34% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (36% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 20 (38% down the source page)
AU025 Q4(c) [2 marks ;official] Word-substitution encoding
English passage 21 (41% down the source page)
Knowledge point
tuples , zip and list combinations; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 22 (43% down the source page)
question type
Pair the two lists into a list of pairs
English passage 23 (44% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 24 (46% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 25 (47% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 26 (48% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 27 (50% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 28 (51% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 29 (54% down the source page)
AU026 Q4(d) [3 marks ;official] Word-substitution encoding
English passage 30 (57% down the source page)
Knowledge point
Dictionary mappings and hash lookup ;pandas Series/DataFrame; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 31 (58% down the source page)
question type
Construct from paired data dict and Series
English passage 32 (60% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 33 (61% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 34 (63% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 35 (64% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 36 (66% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 37 (67% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 38 (70% down the source page)
AU027 Q4(e) [2 marks ;official] Word-substitution encoding
English passage 39 (72% down the source page)
Knowledge point
Dictionary mappings and hash lookup; String tokenisation , join and substitution encoding
English passage 40 (74% down the source page)
question type
Encode word by word using a dictionary
English passage 41 (75% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 42 (77% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 43 (78% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 44 (80% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 45 (81% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 46 (83% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 47 (85% down the source page)
AU028 Q4(f) [2 marks ;official] Word-substitution encoding
English passage 48 (88% down the source page)
Knowledge point
pandas Series/DataFrame; String tokenisation , join and substitution encoding
English passage 49 (90% down the source page)
question type
use Series Complete word-by-word encoding
English passage 50 (91% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
Source page 7
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 7 page
English passage 2 (6% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 3 (7% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 4 (9% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 5 (10% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 6 (12% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version C; target Mock 6
English passage 7 (14% down the source page)
AU029 Q4(g) [4 marks ;official] Word-substitution encoding
English passage 8 (17% down the source page)
Knowledge point
Dictionary mappings and hash lookup; tuples , zip and list combinations; String tokenisation , join and substitution encoding; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 9 (19% down the source page)
question type
Invert the mapping and decode
English passage 10 (20% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 11 (22% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 12 (23% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 13 (24% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 14 (26% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 15 (27% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 6
English passage 16 (30% down the source page)
AU030 Q4(h) [6 marks ;official] Word-substitution encoding
English passage 17 (33% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Recursive design and efficiency; binary search
English passage 18 (34% down the source page)
question type
Implement and test recursive binary search on a sorted list of pairs
English passage 19 (36% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 20 (37% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 21 (39% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 22 (40% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 23 (42% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 7 minutes; official solution: long (multiple code sections / Derive )
English passage 24 (43% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 6
English passage 25 (46% down the source page)
AU031 Q4(i) [2 marks ;official] Word-substitution encoding
English passage 26 (48% down the source page)
Knowledge point
binary search; String tokenisation , join and substitution encoding
English passage 27 (50% down the source page)
question type
Encode word by word using the binary-search function
English passage 28 (51% down the source page)
Recognition signal
Shuffle a copy of the vocabulary, preserving the original; construct the mapping and encode / decoding
English passage 29 (53% down the source page)
first key step
Copy before shuffling, keeping the plaintext key list sorted .
English passage 30 (54% down the source page)
Complete method sequence
Copy and shuffle -> zip pairs -> dict/Series -> split/lookup/join code -> Decode using the inverse mapping -> sorted pairs binary search
English passage 31 (56% down the source page)
theorem / formula / tools
Copy and shuffle , zip/dict/Series, Encoding, decoding and binary search
English passage 32 (57% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 33 (59% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 6
Source page 8
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 8 page
English passage 2 (9% down the source page)
AU032 Q1(a) [3 marks ;official] Legendre Recurrence and Gauss integral
English passage 3 (12% down the source page)
Knowledge point
Test design and boundary cases ;SymPy Symbolic modelling and algebraic simplification; Recurrence relations and sequences / Polynomial generation
English passage 4 (14% down the source page)
question type
Verify the given Legendre Recurrence implementation
English passage 5 (15% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 6 (16% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 7 (18% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 8 (19% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 9 (21% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 10 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 11 (25% down the source page)
AU033 Q1(b) [5 marks ;official] Legendre Recurrence and Gauss integral
English passage 12 (28% down the source page)
Knowledge point
Two-dimensional curves and scatter plots ;SymPy Symbolic modelling and algebraic simplification ;lambdify Symbol - Numerical conversion; Recurrence relations and sequences / Polynomial generation
English passage 13 (29% down the source page)
question type
generate P5, lambdify and plot
English passage 14 (31% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 15 (32% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 16 (33% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 17 (35% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 18 (36% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (38% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 20 (41% down the source page)
AU034 Q1(c) [5 marks ;official] Legendre Recurrence and Gauss integral
English passage 21 (43% down the source page)
Knowledge point
Loops, conditions and comprehensions; Two-dimensional curves and scatter plots ;SymPy Symbolic modelling and algebraic simplification ;lambdify Symbol - Numerical conversion; Recurrence relations and sequences / Polynomial generation
English passage 22 (45% down the source page)
question type
Plot on the same axes P1-P10
English passage 23 (46% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 24 (48% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 25 (49% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 26 (51% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 27 (52% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 28 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 29 (56% down the source page)
AU035 Q1(d) [8 marks ;official] Legendre Recurrence and Gauss integral
English passage 30 (59% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Recursive design and efficiency ;SymPy Symbolic modelling and algebraic simplification; Recurrence relations and sequences / Polynomial generation
English passage 31 (60% down the source page)
question type
Design an efficient recursive version Legendre function
English passage 32 (62% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 33 (63% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 34 (65% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 35 (66% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 36 (68% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 10 minutes; official solution: long (multiple code sections / Derive )
English passage 37 (69% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 38 (72% down the source page)
AU036 Q1(e) [6 marks ;official] Legendre Recurrence and Gauss integral
English passage 39 (75% down the source page)
Knowledge point
SymPy Symbolic modelling and algebraic simplification; Symbolic equations, differentiation and substitution; Recurrence relations and sequences / Polynomial generation; Consistency checks between symbolic and numerical results
English passage 40 (76% down the source page)
question type
find P5 Roots, derivatives and Gauss weights
English passage 41 (77% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 42 (79% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 43 (80% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 44 (82% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 45 (83% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 7 minutes; official solution: long (multiple code sections / Derive )
English passage 46 (85% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 47 (87% down the source page)
AU037 Q1(f) [8 marks ;official] Legendre Recurrence and Gauss integral
English passage 48 (90% down the source page)
Knowledge point
Symbolic equations, differentiation and substitution; Numerical integration and Gaussian quadrature; Consistency checks between symbolic and numerical results
Source page 9
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 9 page
English passage 2 (6% down the source page)
question type
Using five points Gauss-Legendre Approximate the integral and assess the error
English passage 3 (7% down the source page)
Recognition signal
Three-term polynomial recurrence and symbolic roots / derivative / Weights and numerical integration
English passage 4 (9% down the source page)
first key step
Maintain a pair of consecutive-order polynomials to avoid repeated recursive computation .
English passage 5 (10% down the source page)
Complete method sequence
Iterative recurrence -> lambdify/ plotting -> Design using one recursive call -> Roots and weights -> Interval mapping -> Gauss Sum / error
English passage 6 (12% down the source page)
theorem / formula / tools
Symbolic recurrence , lambdify, Recursion, roots and weights, and integration
English passage 7 (13% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 10 minutes; official solution: long (multiple code sections / Derive )
English passage 8 (15% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best C; best in the revised version A; target Mock 4
English passage 9 (17% down the source page)
AU038 Q2(a) [2 marks ;official] bit shifts and bit_length
English passage 10 (20% down the source page)
Knowledge point
Test design and boundary cases; Integer arithmetic (floor division, remainder and bit shifts , bit_length)
English passage 11 (22% down the source page)
question type
Verify experimentally that a left shift is equivalent to multiplication by 2^r
English passage 12 (23% down the source page)
Recognition signal
<<, >> or bit_length Experiment and infer the exact rule
English passage 13 (24% down the source page)
first key step
around 2 experiment with values on both sides of powers of .
English passage 14 (26% down the source page)
Complete method sequence
Multiple experiments -> 2 power boundaries of -> floor(log2 n) Exact formula
English passage 15 (27% down the source page)
theorem / formula / tools
Experimental inference, exact relationships and integer arithmetic
English passage 16 (29% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 17 (30% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 18 (33% down the source page)
AU039 Q2(b) [4 marks ;official] bit shifts and bit_length
English passage 19 (36% down the source page)
Knowledge point
Test design and boundary cases; Integer arithmetic (floor division, remainder and bit shifts , bit_length)
English passage 20 (37% down the source page)
question type
Experiment and define right shifts precisely
English passage 21 (39% down the source page)
Recognition signal
<<, >> or bit_length Experiment and infer the exact rule
English passage 22 (40% down the source page)
first key step
around 2 experiment with values on both sides of powers of .
English passage 23 (42% down the source page)
Complete method sequence
Multiple experiments -> 2 power boundaries of -> floor(log2 n) Exact formula
English passage 24 (43% down the source page)
theorem / formula / tools
Experimental inference, exact relationships and integer arithmetic
English passage 25 (44% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 26 (46% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 27 (49% down the source page)
AU040 Q2(c) [4 marks ;official] bit shifts and bit_length
English passage 28 (51% down the source page)
Knowledge point
Test design and boundary cases; Integer arithmetic (floor division, remainder and bit shifts , bit_length)
English passage 29 (53% down the source page)
question type
infer bit_length and log2 exact relationship of
English passage 30 (54% down the source page)
Recognition signal
<<, >> or bit_length Experiment and infer the exact rule
English passage 31 (56% down the source page)
first key step
around 2 experiment with values on both sides of powers of .
English passage 32 (57% down the source page)
Complete method sequence
Multiple experiments -> 2 power boundaries of -> floor(log2 n) Exact formula
English passage 33 (59% down the source page)
theorem / formula / tools
Experimental inference, exact relationships and integer arithmetic
English passage 34 (60% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 35 (61% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4
English passage 36 (64% down the source page)
AU041 Q3(a) [4 marks ;official] Integer square-root algorithms
English passage 37 (67% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Integer square-root algorithms
English passage 38 (68% down the source page)
question type
Implement an integer square root using a linear scan
English passage 39 (70% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 40 (71% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 41 (73% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 42 (74% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 43 (76% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 44 (77% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4, Mock 6
English passage 45 (80% down the source page)
AU042 Q3(b) [3 marks ;official] Integer square-root algorithms
English passage 46 (83% down the source page)
Knowledge point
Test design and boundary cases; Integer square-root algorithms
English passage 47 (84% down the source page)
question type
Systematically test the integer square-root invariant
English passage 48 (86% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 49 (87% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 50 (88% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 51 (90% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 52 (91% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
Source page 10
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 10 page
English passage 2 (6% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4, Mock 6
English passage 3 (9% down the source page)
AU043 Q3(c) [1 marks ;official] Integer square-root algorithms
English passage 4 (11% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Integer square-root algorithms
English passage 5 (13% down the source page)
question type
Give the iteration complexity of the linear scan
English passage 6 (14% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 7 (16% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 8 (17% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 9 (19% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 10 (20% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 11 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4, Mock 6
English passage 12 (24% down the source page)
AU044 Q3(d) [6 marks ;official] Integer square-root algorithms
English passage 13 (27% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Integer arithmetic (floor division, remainder and bit shifts , bit_length); Integer square-root algorithms
English passage 14 (28% down the source page)
question type
use bit_length Improve the initial value using a lower bound and test it
English passage 15 (30% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 16 (31% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 17 (33% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 18 (34% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 19 (36% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 7 minutes; official solution: long (multiple code sections / Derive )
English passage 20 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version A; target Mock 4, Mock 6
English passage 21 (40% down the source page)
AU045 Q3(e) [5 marks ;official] Integer square-root algorithms
English passage 22 (43% down the source page)
Knowledge point
Algorithm counters and experimental measurement; Asymptotic complexity O/Omega/Theta; Integer square-root algorithms
English passage 23 (44% down the source page)
question type
Derive exact iteration counts for two input families
English passage 24 (46% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 25 (47% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 26 (48% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 27 (50% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 28 (51% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 29 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version D; Target: none
English passage 30 (55% down the source page)
AU046 Q3(f) [1 marks ;official] Integer square-root algorithms
English passage 31 (58% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Integer square-root algorithms
English passage 32 (60% down the source page)
question type
Give the improved algorithm's best case / Worst-case bound
English passage 33 (61% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 34 (63% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 35 (64% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 36 (66% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 37 (67% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 38 (68% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version A; target Mock 4, Mock 6
English passage 39 (71% down the source page)
AU047 Q4(a) [7 marks ;official] Integer square-root algorithms
English passage 40 (74% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Integer arithmetic (floor division, remainder and bit shifts , bit_length); Integer square-root algorithms
English passage 41 (75% down the source page)
question type
Implement a bit-by-bit integer square root and test large integers
English passage 42 (77% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 43 (78% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 44 (80% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 45 (81% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 46 (83% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 8 minutes; official solution: long (multiple code sections / Derive )
English passage 47 (84% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 4, Mock 6
English passage 48 (87% down the source page)
AU048 Q4(b) [3 marks ;official] Integer square-root algorithms
English passage 49 (90% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Integer square-root algorithms
English passage 50 (91% down the source page)
question type
Prove the complexity of the bit-by-bit algorithm
Source page 11
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 11 page
English passage 2 (6% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 3 (7% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 4 (9% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 5 (10% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 6 (12% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 7 (13% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 4, Mock 6
English passage 8 (16% down the source page)
AU049 Q4(c) [5 marks ;official] Integer square-root algorithms
English passage 9 (19% down the source page)
Knowledge point
Integer arithmetic (floor division, remainder and bit shifts , bit_length); Integer square-root algorithms; Binary representation and run-length compression
English passage 10 (20% down the source page)
question type
Hand calculation n=120 and explain how the algorithm constructs binary digits
English passage 11 (22% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 12 (23% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 13 (24% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 14 (26% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 15 (27% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 16 (29% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version D; Target: none
English passage 17 (31% down the source page)
AU050 Q5(a) [7 marks ;official] Integer square-root algorithms
English passage 18 (34% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Integer arithmetic (floor division, remainder and bit shifts , bit_length); Integer square-root algorithms ;Newton iteration
English passage 19 (36% down the source page)
question type
Implement discrete Newton Integer square root and testing
English passage 20 (37% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 21 (39% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 22 (40% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 23 (42% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 24 (43% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 8 minutes; official solution: long (multiple code sections / Derive )
English passage 25 (44% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4, Mock 6
English passage 26 (47% down the source page)
AU051 Q5(b) [3 marks ;official] Integer square-root algorithms
English passage 27 (50% down the source page)
Knowledge point
Algorithm counters and experimental measurement ;Newton iteration
English passage 28 (51% down the source page)
question type
statistics 2^1 to 2^30 of Newton Iteration count
English passage 29 (53% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 30 (54% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 31 (56% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 32 (57% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 33 (59% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 34 (60% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 4, Mock 6
English passage 35 (63% down the source page)
AU052 Q5(c) [1 marks ;official] Integer square-root algorithms
English passage 36 (66% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta;Newton iteration
English passage 37 (67% down the source page)
question type
Conjecture an initial version from the data Newton is Theta(log n)
English passage 38 (68% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 39 (70% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 40 (71% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 41 (73% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 42 (74% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 43 (76% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 4, Mock 6
English passage 44 (78% down the source page)
AU053 Q5(d) [5 marks ;official] Integer square-root algorithms
English passage 45 (81% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Integer arithmetic (floor division, remainder and bit shifts , bit_length); Integer square-root algorithms ;Newton iteration
English passage 46 (83% down the source page)
question type
Improve using an upper bound Newton initial value and test
English passage 47 (84% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 48 (86% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 49 (87% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 50 (88% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 51 (90% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 52 (91% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 4, Mock 6
Source page 12
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 12 page
English passage 2 (7% down the source page)
AU054 Q5(e) [4 marks ;official] Integer square-root algorithms
English passage 3 (10% down the source page)
Knowledge point
Algorithm counters and experimental measurement; Asymptotic complexity O/Omega/Theta;Newton iteration
English passage 4 (11% down the source page)
question type
Check using inputs with very large exponents Theta(log log n)
English passage 5 (13% down the source page)
Recognition signal
return floor(sqrt(n)) and both squared inequalities must be checked
English passage 6 (14% down the source page)
first key step
Use integer arithmetic throughout and use the defining inequalities as the test criterion .
English passage 7 (16% down the source page)
Complete method sequence
Reference algorithm -> Invariant testing -> bit_length initial value / Bit-by-bit algorithm -> Newton -> Iteration counting -> Asymptotic assessment
English passage 8 (17% down the source page)
theorem / formula / tools
linear / bit construction /Newton, Boundary tests and complexity
English passage 9 (19% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 10 (20% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 4, Mock 6
Source page 13
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 13 page
English passage 2 (9% down the source page)
AU055 Q1(a) [4 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 3 (12% down the source page)
Knowledge point
Test design and boundary cases ;NumPy Array creation , dtype and shape; Boolean masks and vectorised updates; Prime generation and sieves
English passage 4 (14% down the source page)
question type
Test the given Eratosthenes sieve
English passage 5 (15% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 6 (16% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 7 (18% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 8 (19% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 9 (21% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 10 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 11 (25% down the source page)
AU056 Q1(b) [5 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 12 (28% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Mutable objects, in-place modification and copying / aliasing; Loops, conditions and comprehensions; Prime generation and sieves
English passage 13 (29% down the source page)
question type
Implement conditional in-place appending of primes
English passage 14 (31% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 15 (32% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 16 (33% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 17 (35% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 18 (36% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (38% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 20 (41% down the source page)
AU057 Q1(c) [4 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 21 (43% down the source page)
Knowledge point
Test design and boundary cases; Mutable objects, in-place modification and copying / aliasing; Prime generation and sieves
English passage 22 (45% down the source page)
question type
Verify that composites are not appended and primes are appended
English passage 23 (46% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 24 (48% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 25 (49% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 26 (51% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 27 (52% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 28 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 29 (56% down the source page)
AU058 Q1(d) [4 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 30 (59% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Prime generation and sieves
English passage 31 (60% down the source page)
question type
use conditional_append Construct a prime list
English passage 32 (62% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 33 (63% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 34 (65% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 35 (66% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 36 (68% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 37 (69% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 38 (72% down the source page)
AU059 Q1(e) [4 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 39 (75% down the source page)
Knowledge point
Test design and boundary cases; Prime generation and sieves
English passage 40 (76% down the source page)
question type
Test the complete prime function
English passage 41 (77% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 42 (79% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 43 (80% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 44 (82% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 45 (83% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 46 (85% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 47 (87% down the source page)
AU060 Q1(f) [4 marks ;official] Eratosthenes and the incremental prime algorithm
English passage 48 (90% down the source page)
Knowledge point
Runtime benchmarking; Prime generation and sieves
Source page 14
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 14 page
English passage 2 (6% down the source page)
question type
Compare the running times of a vectorised sieve and trial division up to one million
English passage 3 (7% down the source page)
Recognition signal
A vectorised sieve is given; append primes one candidate at a time
English passage 4 (9% down the source page)
first key step
in conditional_append only tested up to q*q>p.
English passage 5 (10% down the source page)
Complete method sequence
Test the given sieve -> in place conditional_append -> Driven by odd-number candidates -> Cross-check the two algorithms -> Fair timing -> Interpret cautiously
English passage 6 (12% down the source page)
theorem / formula / tools
Boolean sieves, in-place appending, testing and timing
English passage 7 (13% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 8 (15% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3
English passage 9 (17% down the source page)
AU061 Q2(a) [5 marks ;official] Integer recursion and digits / Run-length representation
English passage 10 (20% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Recursive design and efficiency; Integer arithmetic (floor division, remainder and bit shifts , bit_length)
English passage 11 (22% down the source page)
question type
modulo 4 Implement the integer recursive function by cases
English passage 12 (23% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 13 (24% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 14 (26% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 15 (27% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 16 (29% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 17 (30% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 18 (33% down the source page)
AU062 Q2(b) [3 marks ;official] Integer recursion and digits / Run-length representation
English passage 19 (36% down the source page)
Knowledge point
Test design and boundary cases; Recursive design and efficiency
English passage 20 (37% down the source page)
question type
Check the three specified recursive values
English passage 21 (39% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 22 (40% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 23 (42% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 24 (43% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 25 (44% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 26 (46% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 27 (49% down the source page)
AU063 Q2(c) [4 marks ;official] Integer recursion and digits / Run-length representation
English passage 28 (51% down the source page)
Knowledge point
Loops, conditions and comprehensions; Two-dimensional curves and scatter plots
English passage 29 (53% down the source page)
question type
plot f(n) point plot of
English passage 30 (54% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 31 (56% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 32 (57% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 33 (59% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 34 (60% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 35 (61% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 36 (64% down the source page)
AU064 Q2(d) [3 marks ;official] Integer recursion and digits / Run-length representation
English passage 37 (67% down the source page)
Knowledge point
Loops, conditions and comprehensions
English passage 38 (68% down the source page)
question type
Filter all items that f(2024) equal n
English passage 39 (70% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 40 (71% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 41 (73% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 42 (74% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 43 (76% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 44 (77% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 45 (80% down the source page)
AU065 Q2(e) [4 marks ;official] Integer recursion and digits / Run-length representation
English passage 46 (83% down the source page)
Knowledge point
Loops, conditions and comprehensions; Integer arithmetic (floor division, remainder and bit shifts , bit_length); Recurrence relations and sequences / Polynomial generation
English passage 47 (84% down the source page)
question type
Experimental verification f(n)=n two families of closed-form conditions
English passage 48 (86% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 49 (87% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 50 (88% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 51 (90% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 52 (91% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
Source page 15
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 15 page
English passage 2 (6% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version D; Target: none
English passage 3 (9% down the source page)
AU066 Q2(f) [3 marks ;official] Integer recursion and digits / Run-length representation
English passage 4 (11% down the source page)
Knowledge point
Test design and boundary cases; Binary representation and run-length compression
English passage 5 (13% down the source page)
question type
Test that the binary conversion functions are mutual inverses
English passage 6 (14% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 7 (16% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 8 (17% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 9 (19% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 10 (20% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 11 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 12 (24% down the source page)
AU067 Q2(g) [6 marks ;official] Integer recursion and digits / Run-length representation
English passage 13 (27% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; tuples , zip and list combinations; Binary representation and run-length compression
English passage 14 (28% down the source page)
question type
Implement compression of consecutive identical elements
English passage 15 (30% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 16 (31% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 17 (33% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 18 (34% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 19 (36% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 7 minutes; official solution: long (multiple code sections / Derive )
English passage 20 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 21 (40% down the source page)
AU068 Q2(h) [4 marks ;official] Integer recursion and digits / Run-length representation
English passage 22 (43% down the source page)
Knowledge point
Test design and boundary cases; Binary representation and run-length compression
English passage 23 (44% down the source page)
question type
Verify recursion f Equals the run-length-compressed binary representation
English passage 24 (46% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 25 (47% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 26 (48% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 27 (50% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 28 (51% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 29 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 30 (55% down the source page)
AU069 Q2(i) [3 marks ;official] Integer recursion and digits / Run-length representation
English passage 31 (58% down the source page)
Knowledge point
Recursive design and efficiency; Asymptotic complexity O/Omega/Theta; Binary representation and run-length compression
English passage 32 (60% down the source page)
question type
using the number of binary digits m Analyse recursive complexity
English passage 33 (61% down the source page)
Recognition signal
Integer recursion by residues, also requiring an explanation in terms of digits or list structure
English passage 34 (63% down the source page)
first key step
Write the base case first and ensure each recursive call reduces the integer .
English passage 35 (64% down the source page)
Complete method sequence
Recursive implementation -> Tests at specified values -> Point plot / filter -> Digit conversion or list_crush -> Verify equivalence over a broad range -> Recursion depth
English passage 36 (66% down the source page)
theorem / formula / tools
Recursive branches, point plots, list compression and complexity
English passage 37 (67% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 38 (68% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best B; best in the revised version B; target Mock 3, Mock 6
English passage 39 (71% down the source page)
AU070 Q3(i-a) [3 marks ;official] Text data, search and container comparison
English passage 40 (74% down the source page)
Knowledge point
Text-file reading and parsing
English passage 41 (75% down the source page)
question type
Open, read and close the text file lexicon File
English passage 42 (77% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 43 (78% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 44 (80% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 45 (81% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 46 (83% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 47 (84% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 48 (87% down the source page)
AU071 Q3(i-b) [2 marks ;official] Text data, search and container comparison
English passage 49 (90% down the source page)
Knowledge point
Test design and boundary cases; Text-file reading and parsing; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 50 (91% down the source page)
question type
check eval then becomes a list of dictionaries
Source page 16
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 16 page
English passage 2 (6% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 3 (7% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 4 (9% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 5 (10% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 6 (12% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 7 (13% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 8 (16% down the source page)
AU072 Q3(i-c) [2 marks ;official] Text data, search and container comparison
English passage 9 (19% down the source page)
Knowledge point
tuples , zip and list combinations; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 10 (20% down the source page)
question type
Verify conversion from a list of dictionaries to a list of pairs
English passage 11 (22% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 12 (23% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 13 (24% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 14 (26% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 15 (27% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 16 (29% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 17 (31% down the source page)
AU073 Q3(i-d) [4 marks ;official] Text data, search and container comparison
English passage 18 (34% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; Sequential search
English passage 19 (36% down the source page)
question type
Implement sequential search and handle unsuccessful searches
English passage 20 (37% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 21 (39% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 22 (40% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 23 (42% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 24 (43% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 25 (44% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 26 (47% down the source page)
AU074 Q3(i-e) [2 marks ;official] Text data, search and container comparison
English passage 27 (50% down the source page)
Knowledge point
Test design and boundary cases; Sequential search
English passage 28 (51% down the source page)
question type
Test successful and unsuccessful searches
English passage 29 (53% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 30 (54% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 31 (56% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 32 (57% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 33 (59% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 34 (60% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 35 (63% down the source page)
AU075 Q3(i-f) [3 marks ;official] Text data, search and container comparison
English passage 36 (66% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Sequential search
English passage 37 (67% down the source page)
question type
Analyse the best case for sequential search / Worst-case complexity
English passage 38 (68% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 39 (70% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 40 (71% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 41 (73% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 42 (74% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 43 (76% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 44 (78% down the source page)
AU076 Q3(i-g) [5 marks ;official] Text data, search and container comparison
English passage 45 (81% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Recursive design and efficiency; binary search
English passage 46 (83% down the source page)
question type
Implement binary search on sorted keys and handle unsuccessful searches
English passage 47 (84% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 48 (86% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 49 (87% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 50 (88% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 51 (90% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 52 (91% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
Source page 17
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 17 page
English passage 2 (7% down the source page)
AU077 Q3(i-h) [2 marks ;official] Text data, search and container comparison
English passage 3 (10% down the source page)
Knowledge point
Test design and boundary cases; binary search
English passage 4 (11% down the source page)
question type
Test successful and unsuccessful binary searches
English passage 5 (13% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 6 (14% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 7 (16% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 8 (17% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 9 (19% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 10 (20% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 11 (23% down the source page)
AU078 Q3(i-i) [3 marks ;official] Text data, search and container comparison
English passage 12 (26% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; binary search
English passage 13 (27% down the source page)
question type
Analyse the best case for binary search / Worst-case complexity
English passage 14 (28% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 15 (30% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 16 (31% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 17 (33% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 18 (34% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (36% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 20 (38% down the source page)
AU079 Q3(ii-a) [2 marks ;official] Text data, search and container comparison
English passage 21 (41% down the source page)
Knowledge point
Dictionary mappings and hash lookup; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 22 (43% down the source page)
question type
Take lexicon convert to Python dictionary
English passage 23 (44% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 24 (46% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 25 (47% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 26 (48% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 27 (50% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 28 (51% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 29 (54% down the source page)
AU080 Q3(ii-b) [2 marks ;official] Text data, search and container comparison
English passage 30 (57% down the source page)
Knowledge point
Test design and boundary cases; Dictionary mappings and hash lookup
English passage 31 (58% down the source page)
question type
Test dictionary hits and KeyError failure
English passage 32 (60% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 33 (61% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 34 (63% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 35 (64% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 36 (66% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 37 (67% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 38 (70% down the source page)
AU081 Q3(ii-c) [2 marks ;official] Text data, search and container comparison
English passage 39 (72% down the source page)
Knowledge point
pandas Series/DataFrame; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 40 (74% down the source page)
question type
Convert the dictionary into pandas Series
English passage 41 (75% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 42 (77% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 43 (78% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 44 (80% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 45 (81% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 46 (83% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 47 (85% down the source page)
AU082 Q3(ii-d) [2 marks ;official] Text data, search and container comparison
English passage 48 (88% down the source page)
Knowledge point
Test design and boundary cases ;pandas Series/DataFrame
English passage 49 (90% down the source page)
question type
test Series Successful and unsuccessful searches
English passage 50 (91% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
Source page 18
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 18 page
English passage 2 (6% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 3 (7% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 4 (9% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 5 (10% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 6 (12% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
English passage 7 (14% down the source page)
AU083 Q3(ii-e) [6 marks ;official] Text data, search and container comparison
English passage 8 (17% down the source page)
Knowledge point
Runtime benchmarking; Sequential search; binary search; Dictionary mappings and hash lookup ;pandas Series/DataFrame
English passage 9 (19% down the source page)
question type
Compare and explain the running times of four search structures
English passage 10 (20% down the source page)
Recognition signal
The text file contains a list of dictionaries with sorted keys; multiple search structures are required
English passage 11 (22% down the source page)
first key step
First read / parse, then project into a sorted list of pairs .
English passage 12 (23% down the source page)
Complete method sequence
Text reading / worked solution -> List of dictionaries / pairs -> Sequential search -> binary search -> dict/Series -> successful search / failure -> Timing comparison
English passage 13 (24% down the source page)
theorem / formula / tools
File reading, pairs and sequential / bisection , dict/Series, timing
English passage 14 (26% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 7 minutes; official solution: long (multiple code sections / Derive )
English passage 15 (27% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 3, Mock 5, Mock 6
Source page 19
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 19 page
English passage 2 (9% down the source page)
AU084 Q1(a) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 3 (12% down the source page)
Knowledge point
NumPy Array creation , dtype and shape
English passage 4 (14% down the source page)
question type
Construct two high-resolution one-dimensional coordinate arrays
English passage 5 (15% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 6 (16% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 7 (18% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 8 (19% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 9 (21% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 10 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 11 (25% down the source page)
AU085 Q1(b) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 12 (28% down the source page)
Knowledge point
meshgrid and two-dimensional / Complex grid
English passage 13 (29% down the source page)
question type
Construct a two-dimensional grid
English passage 14 (31% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 15 (32% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 16 (33% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 17 (35% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 18 (36% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 19 (38% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 20 (41% down the source page)
AU086 Q1(c) [3 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 21 (43% down the source page)
Knowledge point
Scalar-field visualisation (imshow/contour/origin/extent)
English passage 22 (45% down the source page)
question type
Display the scalar-field colour map correctly
English passage 23 (46% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 24 (48% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 25 (49% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 26 (51% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 27 (52% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 28 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 29 (56% down the source page)
AU087 Q1(d) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 30 (59% down the source page)
Knowledge point
Scalar-field visualisation (imshow/contour/origin/extent)
English passage 31 (60% down the source page)
question type
Plot contours of the scalar field
English passage 32 (62% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 33 (63% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 34 (65% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 35 (66% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 36 (68% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 37 (69% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 38 (72% down the source page)
AU088 Q1(e) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 39 (75% down the source page)
Knowledge point
NumPy Array creation , dtype and shape
English passage 40 (76% down the source page)
question type
Construct a low-resolution coordinate array
English passage 41 (77% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 42 (79% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 43 (80% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 44 (82% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 45 (83% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 46 (85% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 47 (87% down the source page)
AU089 Q1(f) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 48 (90% down the source page)
Knowledge point
meshgrid and two-dimensional / Complex grid
Source page 20
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 20 page
English passage 2 (6% down the source page)
question type
Construct a low-resolution two-dimensional grid
English passage 3 (7% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 4 (9% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 5 (10% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 6 (12% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 7 (13% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 8 (15% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 9 (17% down the source page)
AU090 Q1(g) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 10 (20% down the source page)
Knowledge point
Vector field quiver and layer overlays
English passage 11 (22% down the source page)
question type
Plot the rotated-gradient vector field
English passage 12 (23% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 13 (24% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 14 (26% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 15 (27% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 16 (29% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 17 (30% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 18 (33% down the source page)
AU091 Q1(h) [2 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 19 (36% down the source page)
Knowledge point
Scalar-field visualisation (imshow/contour/origin/extent); Vector field quiver and layer overlays
English passage 20 (37% down the source page)
question type
Red contours overlaid on a blue vector field
English passage 21 (39% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 22 (40% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 23 (42% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 24 (43% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 25 (44% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 26 (46% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 27 (49% down the source page)
AU092 Q1(i) [3 marks ;official] Visualisation of two-dimensional scalar and vector fields
English passage 28 (51% down the source page)
Knowledge point
Three-dimensional surface / Wireframe plot
English passage 29 (53% down the source page)
question type
Plot a three-dimensional wireframe surface
English passage 30 (54% down the source page)
Recognition signal
Rectangular region and two grid resolutions , imshow/contour/quiver/wireframe
English passage 31 (56% down the source page)
first key step
First construct a one-dimensional coordinate array, then meshgrid; Do not write the plotting code first .
English passage 32 (57% down the source page)
Complete method sequence
linspace/arange -> meshgrid -> Array expression -> imshow/contour -> Coarse grid quiver -> overlay/wireframe
English passage 33 (59% down the source page)
theorem / formula / tools
One-dimensional coordinates /meshgrid/ Vectorised expression / Multiple plot layers
English passage 34 (60% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 35 (61% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 36 (64% down the source page)
AU093 Q2(a) [1 marks ;official] Pritchard sieve
English passage 37 (67% down the source page)
Knowledge point
Test design and boundary cases ;NumPy Structural transformation (tile/flatnonzero/append/riffle)
English passage 38 (68% down the source page)
question type
Describe experimentally tile
English passage 39 (70% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 40 (71% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 41 (73% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 42 (74% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 43 (76% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 44 (77% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 45 (80% down the source page)
AU094 Q2(b) [1 marks ;official] Pritchard sieve
English passage 46 (83% down the source page)
Knowledge point
Test design and boundary cases ;NumPy Structural transformation (tile/flatnonzero/append/riffle)
English passage 47 (84% down the source page)
question type
Describe experimentally flatnonzero
English passage 48 (86% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 49 (87% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 50 (88% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 51 (90% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 52 (91% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
Source page 21
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 21 page
English passage 2 (6% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 3 (9% down the source page)
AU095 Q2(c) [2 marks ;official] Pritchard sieve
English passage 4 (11% down the source page)
Knowledge point
NumPy Array creation , dtype and shape; Prime generation and sieves
English passage 5 (13% down the source page)
question type
initialisation Pritchard Sieve state
English passage 6 (14% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 7 (16% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 8 (17% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 9 (19% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 10 (20% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 11 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 12 (24% down the source page)
AU096 Q2(d) [1 marks ;official] Pritchard sieve
English passage 13 (27% down the source page)
Knowledge point
NumPy Array creation , dtype and shape; Prime generation and sieves
English passage 14 (28% down the source page)
question type
Create a Boolean array of discard flags
English passage 15 (30% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 16 (31% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 17 (33% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 18 (34% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 19 (36% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 20 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 21 (40% down the source page)
AU097 Q2(e) [1 marks ;official] Pritchard sieve
English passage 22 (43% down the source page)
Knowledge point
Integer arithmetic (floor division, remainder and bit shifts , bit_length); Prime generation and sieves
English passage 23 (44% down the source page)
question type
Initialise the algorithm's scalar state
English passage 24 (46% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 25 (47% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 26 (48% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 27 (50% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 28 (51% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 29 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 30 (55% down the source page)
AU098 Q2(f) [5 marks ;official] Pritchard sieve
English passage 31 (58% down the source page)
Knowledge point
Loops, conditions and comprehensions ;NumPy Indexing, slicing and step sizes ;NumPy Structural transformation (tile/flatnonzero/append/riffle); Prime generation and sieves
English passage 32 (60% down the source page)
question type
Execute step by step Pritchard sieve
English passage 33 (61% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 34 (63% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 35 (64% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 36 (66% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 37 (67% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 38 (68% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 39 (71% down the source page)
AU099 Q2(g) [2 marks ;official] Pritchard sieve
English passage 40 (74% down the source page)
Knowledge point
NumPy Indexing, slicing and step sizes ;NumPy Structural transformation (tile/flatnonzero/append/riffle); Prime generation and sieves
English passage 41 (75% down the source page)
question type
Extract primes from the two state arrays
English passage 42 (77% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 43 (78% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 44 (80% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 45 (81% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 46 (83% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 47 (84% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 48 (87% down the source page)
AU100 Q2(h) [5 marks ;official] Pritchard sieve
English passage 49 (90% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions ;NumPy Indexing, slicing and step sizes ;NumPy Structural transformation (tile/flatnonzero/append/riffle); Prime generation and sieves
English passage 50 (91% down the source page)
question type
Wrap a general implementation Pritchard Sieve function
Source page 22
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 22 page
English passage 2 (6% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 3 (7% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 4 (9% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 5 (10% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 6 (12% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 7 (13% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 8 (16% down the source page)
AU101 Q2(i) [2 marks ;official] Pritchard sieve
English passage 9 (19% down the source page)
Knowledge point
Test design and boundary cases; Prime generation and sieves
English passage 10 (20% down the source page)
question type
Test typical, boundary and five-digit inputs
English passage 11 (22% down the source page)
Recognition signal
tile, flatnonzero, Periodic Boolean arrays and stopping conditions
English passage 12 (23% down the source page)
first key step
Initialise accurately sieving_array, discards, l and p.
English passage 13 (24% down the source page)
Complete method sequence
initialisation -> flag p -> Extend the periodic array -> Remove multiples using slices -> flatnonzero Select the next p -> stop -> Combine the output -> Boundary tests
English passage 14 (26% down the source page)
theorem / formula / tools
tile Periodic array , flatnonzero, State loops, function wrapping and testing
English passage 15 (27% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 16 (29% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best C; best in the revised version A; target Mock 1
English passage 17 (31% down the source page)
AU102 Q3(a) [2 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 18 (34% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions; tuples , zip and list combinations
English passage 19 (36% down the source page)
question type
Implement the adjacent-sum list function
English passage 20 (37% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 21 (39% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 22 (40% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 23 (42% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 24 (43% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 25 (44% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 26 (47% down the source page)
AU103 Q3(b) [1 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 27 (50% down the source page)
Knowledge point
Test design and boundary cases; tuples , zip and list combinations
English passage 28 (51% down the source page)
question type
Check the adjacent-sum example
English passage 29 (53% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 30 (54% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 31 (56% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 32 (57% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 33 (59% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 34 (60% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 35 (63% down the source page)
AU104 Q3(c) [2 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 36 (66% down the source page)
Knowledge point
Function interfaces, return values and docstrings ;NumPy Structural transformation (tile/flatnonzero/append/riffle); tuples , zip and list combinations
English passage 37 (67% down the source page)
question type
Interleave the original list with adjacent sums
English passage 38 (68% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 39 (70% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 40 (71% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 41 (73% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 42 (74% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 43 (76% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 44 (78% down the source page)
AU105 Q3(d) [1 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 45 (81% down the source page)
Knowledge point
Test design and boundary cases; tuples , zip and list combinations
English passage 46 (83% down the source page)
question type
check riffled output
English passage 47 (84% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 48 (86% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 49 (87% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 50 (88% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 51 (90% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 52 (91% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
Source page 23
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 23 page
English passage 2 (7% down the source page)
AU106 Q3(e) [3 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 3 (10% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Loops, conditions and comprehensions ;NumPy Structural transformation (tile/flatnonzero/append/riffle); Recurrence relations and sequences / Polynomial generation ;Stern-Brocot/ Rational-number tree
and adjacent sums
English passage 4 (12% down the source page)
question type
Generate iteratively Stern-Brocot number n generation and convert Rational
English passage 5 (14% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 6 (15% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 7 (17% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 8 (18% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 9 (19% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 10 (21% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
English passage 11 (24% down the source page)
AU107 Q3(f) [1 marks ;official] Adjacent-entry operations and Stern-Brocot
English passage 12 (26% down the source page)
Knowledge point
Test design and boundary cases ;Stern-Brocot/ Rational-number trees and adjacent sums
English passage 13 (28% down the source page)
question type
Check the 3 generation rational-number list
English passage 14 (29% down the source page)
Recognition signal
Adjacent sums / Intermediate vectors, interleaved lists and iterative algebraic structures
English passage 15 (31% down the source page)
first key step
First write a shorter-length 1 adjacent-operation function of .
English passage 16 (32% down the source page)
Complete method sequence
Adjacent-entry operations -> riffle/interleave -> Repeated iteration -> Odd indices -> Rational -> Example verification
English passage 17 (34% down the source page)
theorem / formula / tools
Adjacent-entry list , riffle Interleaving and iteration , Rational
English passage 18 (35% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 19 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: yes; earlier version's best A; best in the revised version A; target Mock 1
Source page 24
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 24 page
English passage 2 (9% down the source page)
AU108 Q1(i-a) [1 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 3 (12% down the source page)
Knowledge point
Test design and boundary cases; Mutable objects, in-place modification and copying / aliasing; Elementary row operations
English passage 4 (14% down the source page)
question type
Test the given row_add In-place row replacement
English passage 5 (15% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 6 (16% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 7 (18% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 8 (19% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 9 (21% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 1 minutes; official solution: short (single step / test )
English passage 10 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 11 (25% down the source page)
AU109 Q1(i-b) [2 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 12 (28% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Mutable objects, in-place modification and copying / aliasing; Elementary row operations
English passage 13 (29% down the source page)
question type
Implement in-place scaling of a row
English passage 14 (31% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 15 (32% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 16 (33% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 17 (35% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 18 (36% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 19 (38% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 20 (41% down the source page)
AU110 Q1(i-c) [1 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 21 (43% down the source page)
Knowledge point
Test design and boundary cases; Elementary row operations
English passage 22 (45% down the source page)
question type
test row_multiply
English passage 23 (46% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 24 (48% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 25 (49% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 26 (51% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 27 (52% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 28 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 29 (56% down the source page)
AU111 Q1(i-e) [3 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 30 (59% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Mutable objects, in-place modification and copying / aliasing; Elementary row operations
English passage 31 (60% down the source page)
question type
Implement safe in-place row swapping
English passage 32 (62% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 33 (63% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 34 (65% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 35 (66% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 36 (68% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 37 (69% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 38 (72% down the source page)
AU112 Q1(i-f) [1 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 39 (75% down the source page)
Knowledge point
Test design and boundary cases; Elementary row operations
English passage 40 (76% down the source page)
question type
test row_swap
English passage 41 (77% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 42 (79% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 43 (80% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 44 (82% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 45 (83% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 46 (85% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 47 (87% down the source page)
AU113 Q1(ii-a) [2 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 48 (90% down the source page)
Knowledge point
Mutable objects, in-place modification and copying / aliasing; Loops, conditions and comprehensions; Elementary row operations; Row-echelon form and Gaussian elimination
Source page 25
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 25 page
English passage 2 (6% down the source page)
question type
for the 0 column: perform elimination and check
English passage 3 (7% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 4 (9% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 5 (10% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 6 (12% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 7 (13% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 8 (15% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 9 (17% down the source page)
AU114 Q1(ii-b) [2 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 10 (20% down the source page)
Knowledge point
Loops, conditions and comprehensions; Row-echelon form and Gaussian elimination
English passage 11 (22% down the source page)
question type
Sequence of consecutive pairs 1, 2 Use elimination to obtain upper-triangular form
English passage 12 (23% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 13 (24% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 14 (26% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 15 (27% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 16 (29% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 17 (30% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 18 (33% down the source page)
AU115 Q1(ii-c) [3 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 19 (36% down the source page)
Knowledge point
Determinants (elimination )
English passage 20 (37% down the source page)
question type
Obtain the determinant from the product of the upper-triangular diagonal entries
English passage 21 (39% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 22 (40% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 23 (42% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 24 (43% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 25 (44% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 26 (46% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 27 (49% down the source page)
AU116 Q1(ii-d) [2 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 28 (51% down the source page)
Knowledge point
Loops, conditions and comprehensions; Row-echelon form and Gaussian elimination
English passage 29 (53% down the source page)
question type
take 3x4 Reduce the matrix to row-echelon form
English passage 30 (54% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 31 (56% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 32 (57% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 33 (59% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 34 (60% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 35 (61% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 36 (64% down the source page)
AU117 Q1(ii-e) [2 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 37 (67% down the source page)
Knowledge point
Loops, conditions and comprehensions; Row-echelon form and Gaussian elimination
English passage 38 (68% down the source page)
question type
take 4x3 Reduce the matrix to row-echelon form
English passage 39 (70% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 40 (71% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 41 (73% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 42 (74% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 43 (76% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 44 (77% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 45 (80% down the source page)
AU118 Q1(ii-f) [3 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 46 (83% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Row-echelon form and Gaussian elimination
English passage 47 (84% down the source page)
question type
Derive m×n required zero_column degree
English passage 48 (86% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 49 (87% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 50 (88% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 51 (90% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 52 (91% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
Source page 26
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 26 page
English passage 2 (6% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version A; target Mock 2
English passage 3 (9% down the source page)
AU119 Q1(ii-g) [5 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 4 (11% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Mutable objects, in-place modification and copying / aliasing; Loops, conditions and comprehensions; Row-echelon form and Gaussian elimination
English passage 5 (13% down the source page)
question type
Wrap a general implementation that does not change its input row_echelon_form
English passage 6 (14% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 7 (16% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 8 (17% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 9 (19% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 10 (20% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 6 minutes; official solution: medium (function or multi-step explanation )
English passage 11 (22% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 12 (24% down the source page)
AU120 Q1(ii-h) [3 marks ;inferred_from_question_total_no_markscheme] Elementary row operations and row-echelon form
English passage 13 (27% down the source page)
Knowledge point
Test design and boundary cases; Row-echelon form and Gaussian elimination
English passage 14 (28% down the source page)
question type
Test matrices of three shapes REF function
English passage 15 (30% down the source page)
Recognition signal
In-place matrix row operations, pivot columns and row-echelon form
English passage 16 (31% down the source page)
first key step
Copy the entire row before swapping; ensure floating-point type before elimination .
English passage 17 (33% down the source page)
Complete method sequence
row_add/multiply/swap -> zero_column -> Loop over multiple pivots -> Copy the input -> method / wide / Tall-matrix tests
English passage 18 (34% down the source page)
theorem / formula / tools
In-place row operations, elimination, copying and matrix shapes
English passage 19 (36% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: low; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 20 (37% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 21 (40% down the source page)
AU121 Q2(i-a) [4 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 22 (43% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Row-echelon form and Gaussian elimination; Determinants (elimination )
English passage 23 (44% down the source page)
question type
Compute a square matrix's determinant using row-echelon form
English passage 24 (46% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 25 (47% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 26 (48% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 27 (50% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 28 (51% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 29 (53% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 30 (55% down the source page)
AU122 Q2(i-b1) [2 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 31 (58% down the source page)
Knowledge point
Test design and boundary cases; Determinants (elimination); Consistency checks between symbolic and numerical results
English passage 32 (60% down the source page)
question type
Numerically test the custom implementation determinant and numpy.det
English passage 33 (61% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 34 (63% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 35 (64% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 36 (66% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 37 (67% down the source page)
workload
Computational workload: low; abstraction: low; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 38 (68% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 39 (71% down the source page)
AU123 Q2(i-b2) [4 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 40 (74% down the source page)
Knowledge point
SymPy Symbolic modelling and algebraic simplification; Symbolic equations, differentiation and substitution; Determinants (recursive cofactor expansion); Consistency checks between symbolic and numerical results
English passage 41 (75% down the source page)
question type
Symbolically compare determinants by elimination and recursive cofactor expansion
English passage 42 (77% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 43 (78% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 44 (80% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 45 (81% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 46 (83% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 47 (84% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version D; Target: none
English passage 48 (87% down the source page)
AU124 Q2(i-c) [3 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 49 (90% down the source page)
Knowledge point
Asymptotic complexity O/Omega/Theta; Elementary row operations; Row-echelon form and Gaussian elimination; Determinants (elimination )
English passage 50 (91% down the source page)
question type
Derive elimination determinant of Theta(n^3)
Source page 27
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 27 page
English passage 2 (6% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 3 (7% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 4 (9% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 5 (10% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 6 (12% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 7 (13% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 8 (16% down the source page)
AU125 Q2(i-d) [3 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 9 (19% down the source page)
Knowledge point
Recursive design and efficiency; Asymptotic complexity O/Omega/Theta; Determinants (recursive cofactor expansion )
English passage 10 (20% down the source page)
question type
Derive the factorial complexity of recursive cofactor expansion
English passage 11 (22% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 12 (23% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 13 (24% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 14 (26% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 15 (27% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 16 (29% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best D; best in the revised version C; target Mock 2
English passage 17 (31% down the source page)
AU126 Q2(ii-a) [1 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 18 (34% down the source page)
Knowledge point
Test design and boundary cases ;NumPy Indexing, slicing and step sizes
English passage 19 (36% down the source page)
question type
Explain argmax Return the position of the maximum
English passage 20 (37% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 21 (39% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 22 (40% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 23 (42% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 24 (43% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 25 (44% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 26 (47% down the source page)
AU127 Q2(ii-b) [4 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 27 (50% down the source page)
Knowledge point
Mutable objects, in-place modification and copying / aliasing ;NumPy Indexing, slicing and step sizes; Elementary row operations; Pivot selection and numerical stability
English passage 28 (51% down the source page)
question type
is zero_column Add partial pivoting
English passage 29 (53% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 30 (54% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 31 (56% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 32 (57% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 33 (59% down the source page)
workload
Computational workload: high; abstraction: high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 34 (60% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 35 (63% down the source page)
AU128 Q2(ii-c) [1 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 36 (66% down the source page)
Knowledge point
Test design and boundary cases; Pivot selection and numerical stability
English passage 37 (67% down the source page)
question type
Test elimination with row swapping on a matrix whose first pivot is zero
English passage 38 (68% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 39 (70% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 40 (71% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 41 (73% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 42 (74% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 43 (76% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 44 (78% down the source page)
AU129 Q2(ii-d) [3 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 45 (81% down the source page)
Knowledge point
Function interfaces, return values and docstrings; Elementary row operations; Pivot selection and numerical stability
English passage 46 (83% down the source page)
question type
such that zero_column Return whether a row swap occurred
English passage 47 (84% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 48 (86% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 49 (87% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 50 (88% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 51 (90% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 52 (91% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
Source page 28
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 28 page
English passage 2 (7% down the source page)
AU130 Q2(ii-e) [1 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 3 (10% down the source page)
Knowledge point
Test design and boundary cases; Pivot selection and numerical stability
English passage 4 (11% down the source page)
question type
test swap flagged as True
English passage 5 (13% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 6 (14% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 7 (16% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 8 (17% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 9 (19% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 1 minutes; official solution: short (single step / test )
English passage 10 (20% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 11 (23% down the source page)
AU131 Q2(ii-f) [4 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 12 (26% down the source page)
Knowledge point
Mutable objects, in-place modification and copying / aliasing; Loops, conditions and comprehensions; Row-echelon form and Gaussian elimination; Pivot selection and numerical stability
English passage 13 (27% down the source page)
question type
REF Track the parity sign of row swaps at the same time
English passage 14 (28% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 15 (30% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 16 (31% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 17 (33% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 18 (34% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 19 (36% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 20 (38% down the source page)
AU132 Q2(ii-g) [3 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 21 (41% down the source page)
Knowledge point
Determinants (elimination); Pivot selection and numerical stability
English passage 22 (43% down the source page)
question type
in determinant correct the row-swap sign in
English passage 23 (44% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 24 (46% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 25 (47% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 26 (48% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 27 (50% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 4 minutes; official solution: medium (function or multi-step explanation )
English passage 28 (51% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 29 (54% down the source page)
AU133 Q2(ii-h) [2 marks ;inferred_from_question_total_no_markscheme] Determinants by elimination and pivot selection
English passage 30 (57% down the source page)
Knowledge point
Test design and boundary cases; Determinants (elimination); Pivot selection and numerical stability; Consistency checks between symbolic and numerical results
English passage 31 (58% down the source page)
question type
For a matrix with a zero first pivot, compare with numpy.det compare
English passage 32 (60% down the source page)
Recognition signal
Determinants by elimination, zero pivots and row-swap signs
English passage 33 (61% down the source page)
first key step
First take the local argmax Convert to an absolute row index and record it swap.
English passage 34 (63% down the source page)
Complete method sequence
REF -> Diagonal product -> Complexity -> Partial pivoting -> swap parity -> determinant Correction -> numerical / Singularity tests
English passage 35 (64% down the source page)
theorem / formula / tools
REF, Diagonal product, row-swap sign and complexity
English passage 36 (66% down the source page)
workload
Computational workload: low-medium; abstraction: medium; integration: medium; estimated 2 minutes; official solution: short (single step / test )
English passage 37 (67% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2
English passage 38 (70% down the source page)
AU134 Q3(a) [4 marks ;inferred_from_question_total_no_markscheme] Timing data structures and file export
English passage 39 (72% down the source page)
Knowledge point
Runtime benchmarking ;pandas Series/DataFrame; Randomisation and random data; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 40 (74% down the source page)
question type
construct three types of determinant Nested timing dictionary for the implementations
English passage 41 (75% down the source page)
Recognition signal
Algorithm timing results must be stored as a dictionary , pickle, DataFrame or CSV
English passage 42 (77% down the source page)
first key step
Time each algorithm on the same input in turn; save the original nested dictionary first .
English passage 43 (78% down the source page)
Complete method sequence
perf_counter/time -> Nested dictionary -> pickle.dump -> DataFrame -> to_csv -> File-existence check
English passage 44 (80% down the source page)
theorem / formula / tools
Nested dictionary , pickle, DataFrame, CSV
English passage 45 (81% down the source page)
workload
Computational workload: medium-high; abstraction: medium-high; integration: high; estimated 5 minutes; official solution: medium (function or multi-step explanation )
English passage 46 (83% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2, Mock 6
English passage 47 (85% down the source page)
AU135 Q3(b) [2 marks ;inferred_from_question_total_no_markscheme] Timing data structures and file export
English passage 48 (88% down the source page)
Knowledge point
File export and persistence (pickle/CSV)
English passage 49 (90% down the source page)
question type
use pickle.dump Export the timing dictionary
English passage 50 (91% down the source page)
Recognition signal
Algorithm timing results must be stored as a dictionary , pickle, DataFrame or CSV
Source page 29
Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.
English passage 1 (95% down the source page)
MATH40006 137 Competency unit
number 29 page
English passage 2 (6% down the source page)
first key step
Time each algorithm on the same input in turn; save the original nested dictionary first .
English passage 3 (7% down the source page)
Complete method sequence
perf_counter/time -> Nested dictionary -> pickle.dump -> DataFrame -> to_csv -> File-existence check
English passage 4 (9% down the source page)
theorem / formula / tools
Nested dictionary , pickle, DataFrame, CSV
English passage 5 (10% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 6 (12% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2, Mock 6
English passage 7 (14% down the source page)
AU136 Q3(c) [2 marks ;inferred_from_question_total_no_markscheme] Timing data structures and file export
English passage 8 (17% down the source page)
Knowledge point
pandas Series/DataFrame; Data-structure conversion (list/tuple/dict/Series/DataFrame)
English passage 9 (19% down the source page)
question type
Convert the nested dictionary into DataFrame
English passage 10 (20% down the source page)
Recognition signal
Algorithm timing results must be stored as a dictionary , pickle, DataFrame or CSV
English passage 11 (22% down the source page)
first key step
Time each algorithm on the same input in turn; save the original nested dictionary first .
English passage 12 (23% down the source page)
Complete method sequence
perf_counter/time -> Nested dictionary -> pickle.dump -> DataFrame -> to_csv -> File-existence check
English passage 13 (24% down the source page)
theorem / formula / tools
Nested dictionary , pickle, DataFrame, CSV
English passage 14 (26% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 15 (27% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2, Mock 6
English passage 16 (30% down the source page)
AU137 Q3(d) [2 marks ;inferred_from_question_total_no_markscheme] Timing data structures and file export
English passage 17 (33% down the source page)
Knowledge point
pandas Series/DataFrame; File export and persistence (pickle/CSV)
English passage 18 (34% down the source page)
question type
Take DataFrame export CSV
English passage 19 (36% down the source page)
Recognition signal
Algorithm timing results must be stored as a dictionary , pickle, DataFrame or CSV
English passage 20 (37% down the source page)
first key step
Time each algorithm on the same input in turn; save the original nested dictionary first .
English passage 21 (39% down the source page)
Complete method sequence
perf_counter/time -> Nested dictionary -> pickle.dump -> DataFrame -> to_csv -> File-existence check
English passage 22 (40% down the source page)
theorem / formula / tools
Nested dictionary , pickle, DataFrame, CSV
English passage 23 (42% down the source page)
workload
Computational workload: low; abstraction: low; integration: low; estimated 2 minutes; official solution: short (single step / test )
English passage 24 (43% down the source page)
Main examination / coverage
2025-26 Appears in the main examination: no; earlier version's best A; best in the revised version A; target Mock 2, Mock 6