MATH40006 Seven-year coverage matrix

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: 65ae294c5f6d72cd3594ad2fb7b2036d5fbf750a412a11707735a9b85430f905
Source 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 (93% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials ) number 1 page

English passage 2 (8% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials )

English passage 3 (14% down the source page) A = direct question-type coverage; B = method coverage with transfer to unfamiliar formulations; C = label-only coverage; D = not covered. Effective coverage counts A+B only.

English passage 4 (26% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 5 (28% down the source page) AU001 Q1(a) 4 LCM Algorithm counts and complexity Design function tests covering coprime, non-coprime and boundary cases D D D A D D A

English passage 6 (30% down the source page) AU002 Q1(b) 3 LCM Algorithm counts and complexity as repeated addition LCM Add comparison counters to the algorithm D D D A D D A

English passage 7 (33% down the source page) AU003 Q1(c) 3 LCM Algorithm counts and complexity is Euclid LCM Add comparison counters to the algorithm D D D A D D A

English passage 8 (35% down the source page) AU004 Q1(d) 3 LCM Algorithm counts and complexity Use exhaustive experiments to find fixed a worst-case input when D D D A D D A

English passage 9 (37% down the source page) AU005 Q1(e) 3 LCM Algorithm counts and complexity Derive the exact comparison count of the repeated-addition algorithm D D D A D D A

English passage 10 (39% down the source page) AU006 Q1(f) 2 LCM Algorithm counts and complexity Obtain from the worst-case input lcm1 asymptotic complexity of D D D A D D A

English passage 11 (41% down the source page) AU007 Q1(g) 3 LCM Algorithm counts and complexity Find experimentally Euclid Algorithm worst case b D D D A D D A

English passage 12 (43% down the source page) AU008 Q1(h) 4 LCM Algorithm counts and complexity use Fibonacci Proof of the asymptotic formula Euclid Worst-case complexity D D D A D D A

English passage 13 (45% down the source page) AU009 Q2(a) 4 Escape time for complex iteration Construct a two-dimensional grid in the complex plane D D D D A D A

English passage 14 (47% down the source page) AU010 Q2(b) 4 Escape time for complex iteration Mark initial escape points with a Boolean array and display them D D D D A D A

English passage 15 (49% down the source page) AU011 Q2(c) 4 Escape time for complex iteration Perform one complex iteration and record the 1 th escape D D D D A D A

English passage 16 (51% down the source page) AU012 Q2(d) 7 Escape time for complex iteration Wrap the two-dimensional escape-time algorithm in a function D D D D A D A

English passage 17 (53% down the source page) AU013 Q2(e) 3 Escape time for complex iteration Test the escape-time plot with parameters varying over the grid D D D D A D A

English passage 18 (55% down the source page) AU014 Q2(f) 3 Escape time for complex iteration Test fixed c of Julia type plot D D D D A D A

English passage 19 (57% down the source page) AU015 Q3(a) 2 Symbolic analysis of dynamical-system stability Find fixed points of the complex quadratic mapping symbolically D D D D A D A

English passage 20 (59% down the source page) AU016 Q3(b) 1 Symbolic analysis of dynamical-system stability Find the derivative of the mapping D D D D A D A

English passage 21 (61% down the source page) AU017 Q3(c) 2 Symbolic analysis of dynamical-system stability Compute the squared modulus of the derivative at each fixed point D D D D A D A

English passage 22 (63% down the source page) AU018 Q3(d) 3 Symbolic analysis of dynamical-system stability Convert the two stability expressions into NumPy function D D D D A D A

English passage 23 (65% down the source page) AU019 Q3(e) 4 Symbolic analysis of dynamical-system stability Plot stability-boundary contours D D D D A D A

English passage 24 (67% down the source page) AU020 Q3(f) 3 Symbolic analysis of dynamical-system stability Construct and expand the composite mapping ff D D D D A D A

English passage 25 (69% down the source page) AU021 Q3(g) 8 Symbolic analysis of dynamical-system stability Repeat the fixed-point analysis for the composite mapping - stability - Complete contour-plot workflow D D D D A D A

English passage 26 (71% down the source page) AU022 Q3(h) 1 Symbolic analysis of dynamical-system stability Explain the relationship between stability curves and the boundary of the non-escaping set D D D D A D A

English passage 27 (74% down the source page) AU023 Q4(a) 1 Word-substitution encoding Check the vocabulary read from the external file D D D D D A A

English passage 28 (76% down the source page) AU024 Q4(b) 4 Word-substitution encoding Copy and shuffle the vocabulary without changing the original D D D D D A A

English passage 29 (78% down the source page) AU025 Q4(c) 2 Word-substitution encoding Pair the two lists into a list of pairs D D D D D A A

English passage 30 (80% down the source page) AU026 Q4(d) 3 Word-substitution encoding Construct from paired data dict and Series D D D D D A A

English passage 31 (82% down the source page) AU027 Q4(e) 2 Word-substitution encoding Encode word by word using a dictionary D D D D D A A

English passage 32 (84% down the source page) AU028 Q4(f) 2 Word-substitution encoding use Series Complete word-by-word encoding D D D D D C C

English passage 33 (86% down the source page) AU029 Q4(g) 4 Word-substitution encoding Invert the mapping and decode D D D D D A A

English passage 34 (88% down the source page) AU030 Q4(h) 6 Word-substitution encoding Implement and test recursive binary search on a sorted list of pairs D D D D D A A

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 (93% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials ) number 2 page

English passage 2 (7% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 3 (10% down the source page) AU031 Q4(i) 2 Word-substitution encoding Encode word by word using the binary-search function D D D D D A A

English passage 4 (19% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 5 (21% down the source page) AU032 Q1(a) 3 Legendre Recurrence and Gauss integral Verify the given Legendre Recurrence implementation D D D A D D A

English passage 6 (23% down the source page) AU033 Q1(b) 5 Legendre Recurrence and Gauss integral generate P5, lambdify and plot D D D A D D A

English passage 7 (25% down the source page) AU034 Q1(c) 5 Legendre Recurrence and Gauss integral Plot on the same axes P1-P10 D D D A D D A

English passage 8 (27% down the source page) AU035 Q1(d) 8 Legendre Recurrence and Gauss integral Design an efficient recursive version Legendre function D D D A D D A

English passage 9 (29% down the source page) AU036 Q1(e) 6 Legendre Recurrence and Gauss integral find P5 Roots, derivatives and Gauss weights D D D A D D A

English passage 10 (31% down the source page) AU037 Q1(f) 8 Legendre Recurrence and Gauss integral Using five points Gauss-Legendre Approximate the integral and assess the error D D D A D D A

English passage 11 (33% down the source page) AU038 Q2(a) 2 bit shifts and bit_length Verify experimentally that a left shift is equivalent to multiplication by 2^r D D D A D D A

English passage 12 (35% down the source page) AU039 Q2(b) 4 bit shifts and bit_length Experiment and define right shifts precisely D D D A D D A

English passage 13 (37% down the source page) AU040 Q2(c) 4 bit shifts and bit_length infer bit_length and log2 exact relationship of D D D A D D A

English passage 14 (40% down the source page) AU041 Q3(a) 4 Integer square-root algorithms Implement an integer square root using a linear scan D D D A D B A

English passage 15 (42% down the source page) AU042 Q3(b) 3 Integer square-root algorithms Systematically test the integer square-root invariant D D D A D B A

English passage 16 (44% down the source page) AU043 Q3(c) 1 Integer square-root algorithms Give the iteration complexity of the linear scan D D D A D B A

English passage 17 (46% down the source page) AU044 Q3(d) 6 Integer square-root algorithms use bit_length Improve the initial value using a lower bound and test it D D D A D B A

English passage 18 (48% down the source page) AU045 Q3(e) 5 Integer square-root algorithms Derive exact iteration counts for two input families D D D D D D D

English passage 19 (50% down the source page) AU046 Q3(f) 1 Integer square-root algorithms Give the improved algorithm's best case / Worst-case bound D D D A D B A

English passage 20 (52% down the source page) AU047 Q4(a) 7 Integer square-root algorithms Implement a bit-by-bit integer square root and test large integers D D D A D B A

English passage 21 (54% down the source page) AU048 Q4(b) 3 Integer square-root algorithms Prove the complexity of the bit-by-bit algorithm D D D A D B A

English passage 22 (56% down the source page) AU049 Q4(c) 5 Integer square-root algorithms Hand calculation n=120 and explain how the algorithm constructs binary digits D D D D D D D

English passage 23 (58% down the source page) AU050 Q5(a) 7 Integer square-root algorithms Implement discrete Newton Integer square root and testing D D D A D B A

English passage 24 (60% down the source page) AU051 Q5(b) 3 Integer square-root algorithms statistics 2^1 to 2^30 of Newton Iteration count D D D A D B A

English passage 25 (62% down the source page) AU052 Q5(c) 1 Integer square-root algorithms Conjecture an initial version from the data Newton is Theta(log n) D D D A D B A

English passage 26 (64% down the source page) AU053 Q5(d) 5 Integer square-root algorithms Improve using an upper bound Newton initial value and test D D D A D B A

English passage 27 (66% down the source page) AU054 Q5(e) 4 Integer square-root algorithms Check using inputs with very large exponents Theta(log log n) D D D A D B A

English passage 28 (75% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 29 (78% down the source page) AU055 Q1(a) 4 Eratosthenes and the incremental prime algorithm Test the given Eratosthenes sieve D D A D D D A

English passage 30 (80% down the source page) AU056 Q1(b) 5 Eratosthenes and the incremental prime algorithm Implement conditional in-place appending of primes D D A D D D A

English passage 31 (82% down the source page) AU057 Q1(c) 4 Eratosthenes and the incremental prime algorithm Verify that composites are not appended and primes are appended D D A D D D A

English passage 32 (84% down the source page) AU058 Q1(d) 4 Eratosthenes and the incremental prime algorithm use conditional_append Construct a prime list D D A D D D A

English passage 33 (86% down the source page) AU059 Q1(e) 4 Eratosthenes and the incremental prime algorithm Test the complete prime function D D A D D D A

English passage 34 (88% down the source page) AU060 Q1(f) 4 Eratosthenes and the incremental prime algorithm Compare the running times of a vectorised sieve and trial division up to one million D D A D D D A

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 (93% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials ) number 3 page

English passage 2 (7% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 3 (10% down the source page) AU061 Q2(a) 5 Integer recursion and digits / Run-length representation modulo 4 Implement the integer recursive function by cases D D B D D B B

English passage 4 (12% down the source page) AU062 Q2(b) 3 Integer recursion and digits / Run-length representation Check the three specified recursive values D D B D D B B

English passage 5 (14% down the source page) AU063 Q2(c) 4 Integer recursion and digits / Run-length representation plot f(n) point plot of D D B D D B B

English passage 6 (16% down the source page) AU064 Q2(d) 3 Integer recursion and digits / Run-length representation Filter all items that f(2024) equal n D D B D D B B

English passage 7 (18% down the source page) AU065 Q2(e) 4 Integer recursion and digits / Run-length representation Experimental verification f(n)=n two families of closed-form conditions D D D D D D D

English passage 8 (20% down the source page) AU066 Q2(f) 3 Integer recursion and digits / Run-length representation Test that the binary conversion functions are mutual inverses D D B D D B B

English passage 9 (22% down the source page) AU067 Q2(g) 6 Integer recursion and digits / Run-length representation Implement compression of consecutive identical elements D D B D D B B

English passage 10 (24% down the source page) AU068 Q2(h) 4 Integer recursion and digits / Run-length representation Verify recursion f Equals the run-length-compressed binary representation D D B D D B B

English passage 11 (26% down the source page) AU069 Q2(i) 3 Integer recursion and digits / Run-length representation using the number of binary digits m Analyse recursive complexity D D B D D B B

English passage 12 (28% down the source page) AU070 Q3(i-a) 3 Text data, search and container comparison Open, read and close the text file lexicon File D D A D A B A

English passage 13 (30% down the source page) AU071 Q3(i-b) 2 Text data, search and container comparison check eval then becomes a list of dictionaries D D A D A B A

English passage 14 (32% down the source page) AU072 Q3(i-c) 2 Text data, search and container comparison Verify conversion from a list of dictionaries to a list of pairs D D A D A B A

English passage 15 (34% down the source page) AU073 Q3(i-d) 4 Text data, search and container comparison Implement sequential search and handle unsuccessful searches D D A D A B A

English passage 16 (36% down the source page) AU074 Q3(i-e) 2 Text data, search and container comparison Test successful and unsuccessful searches D D A D A B A

English passage 17 (38% down the source page) AU075 Q3(i-f) 3 Text data, search and container comparison Analyse the best case for sequential search / Worst-case complexity D D A D A B A

English passage 18 (40% down the source page) AU076 Q3(i-g) 5 Text data, search and container comparison Implement binary search on sorted keys and handle unsuccessful searches D D A D A B A

English passage 19 (42% down the source page) AU077 Q3(i-h) 2 Text data, search and container comparison Test successful and unsuccessful binary searches D D A D A B A

English passage 20 (44% down the source page) AU078 Q3(i-i) 3 Text data, search and container comparison Analyse the best case for binary search / Worst-case complexity D D A D A B A

English passage 21 (46% down the source page) AU079 Q3(ii-a) 2 Text data, search and container comparison Take lexicon convert to Python dictionary D D A D A B A

English passage 22 (49% down the source page) AU080 Q3(ii-b) 2 Text data, search and container comparison Test dictionary hits and KeyError failure D D A D A B A

English passage 23 (51% down the source page) AU081 Q3(ii-c) 2 Text data, search and container comparison Convert the dictionary into pandas Series D D A D A B A

English passage 24 (53% down the source page) AU082 Q3(ii-d) 2 Text data, search and container comparison test Series Successful and unsuccessful searches D D A D A B A

English passage 25 (55% down the source page) AU083 Q3(ii-e) 6 Text data, search and container comparison Compare and explain the running times of four search structures D D A D A B A

English passage 26 (64% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 27 (66% down the source page) AU084 Q1(a) 2 Visualisation of two-dimensional scalar and vector fields Construct two high-resolution one-dimensional coordinate arrays A D D D D D A

English passage 28 (68% down the source page) AU085 Q1(b) 2 Visualisation of two-dimensional scalar and vector fields Construct a two-dimensional grid A D D D D D A

English passage 29 (70% down the source page) AU086 Q1(c) 3 Visualisation of two-dimensional scalar and vector fields Display the scalar-field colour map correctly A D D D D D A

English passage 30 (72% down the source page) AU087 Q1(d) 2 Visualisation of two-dimensional scalar and vector fields Plot contours of the scalar field A D D D D D A

English passage 31 (74% down the source page) AU088 Q1(e) 2 Visualisation of two-dimensional scalar and vector fields Construct a low-resolution coordinate array A D D D D D A

English passage 32 (76% down the source page) AU089 Q1(f) 2 Visualisation of two-dimensional scalar and vector fields Construct a low-resolution two-dimensional grid A D D D D D A

English passage 33 (78% down the source page) AU090 Q1(g) 2 Visualisation of two-dimensional scalar and vector fields Plot the rotated-gradient vector field A D D D D D A

English passage 34 (81% down the source page) AU091 Q1(h) 2 Visualisation of two-dimensional scalar and vector fields Red contours overlaid on a blue vector field A D D D D D A

English passage 35 (83% down the source page) AU092 Q1(i) 3 Visualisation of two-dimensional scalar and vector fields Plot a three-dimensional wireframe surface A D D D D D A

English passage 36 (85% down the source page) AU093 Q2(a) 1 Pritchard sieve Describe experimentally tile A D D D D D A

English passage 37 (87% down the source page) AU094 Q2(b) 1 Pritchard sieve Describe experimentally flatnonzero A D D D D D A

English passage 38 (89% down the source page) AU095 Q2(c) 2 Pritchard sieve initialisation Pritchard Sieve state A D D D D D A

Source page 4

Mathematical typesetting and diagrams are retained below. Chinese prose is replaced by the English passages that follow, in source reading order.

$Mathematical content of source page 4 with translated prose supplied below$

English passage 1 (93% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials ) number 4 page

English passage 2 (7% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 3 (10% down the source page) AU096 Q2(d) 1 Pritchard sieve Create a Boolean array of discard flags A D D D D D A

English passage 4 (12% down the source page) AU097 Q2(e) 1 Pritchard sieve Initialise the algorithm's scalar state A D D D D D A

English passage 5 (14% down the source page) AU098 Q2(f) 5 Pritchard sieve Execute step by step Pritchard sieve A D D D D D A

English passage 6 (16% down the source page) AU099 Q2(g) 2 Pritchard sieve Extract primes from the two state arrays A D D D D D A

English passage 7 (18% down the source page) AU100 Q2(h) 5 Pritchard sieve Wrap a general implementation Pritchard Sieve function A D D D D D A

English passage 8 (20% down the source page) AU101 Q2(i) 2 Pritchard sieve Test typical, boundary and five-digit inputs A D D D D D A

English passage 9 (22% down the source page) AU102 Q3(a) 2 Adjacent-entry operations and Stern-Brocot Implement the adjacent-sum list function A D D D D D A

English passage 10 (24% down the source page) AU103 Q3(b) 1 Adjacent-entry operations and Stern-Brocot Check the adjacent-sum example A D D D D D A

English passage 11 (26% down the source page) AU104 Q3(c) 2 Adjacent-entry operations and Stern-Brocot Interleave the original list with adjacent sums A D D D D D A

English passage 12 (28% down the source page) AU105 Q3(d) 1 Adjacent-entry operations and Stern-Brocot check riffled output A D D D D D A

English passage 13 (30% down the source page) AU106 Q3(e) 3 Adjacent-entry operations and Stern-Brocot Generate iteratively Stern-Brocot number n generation and convert Rational A D D D D D A

English passage 14 (32% down the source page) AU107 Q3(f) 1 Adjacent-entry operations and Stern-Brocot Check the 3 generation rational-number list A D D D D D A

English passage 15 (41% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 16 (44% down the source page) AU108 Q1(i-a) 1 Elementary row operations and row-echelon form Test the given row_add In-place row replacement D A D D D D A

English passage 17 (46% down the source page) AU109 Q1(i-b) 2 Elementary row operations and row-echelon form Implement in-place scaling of a row D A D D D D A

English passage 18 (48% down the source page) AU110 Q1(i-c) 1 Elementary row operations and row-echelon form test row_multiply D A D D D D A

English passage 19 (50% down the source page) AU111 Q1(i-e) 3 Elementary row operations and row-echelon form Implement safe in-place row swapping D A D D D D A

English passage 20 (52% down the source page) AU112 Q1(i-f) 1 Elementary row operations and row-echelon form test row_swap D A D D D D A

English passage 21 (54% down the source page) AU113 Q1(ii-a) 2 Elementary row operations and row-echelon form for the 0 column: perform elimination and check D A D D D D A

English passage 22 (56% down the source page) AU114 Q1(ii-b) 2 Elementary row operations and row-echelon form Sequence of consecutive pairs 1, 2 Use elimination to obtain upper-triangular form D A D D D D A

English passage 23 (58% down the source page) AU115 Q1(ii-c) 3 Elementary row operations and row-echelon form Obtain the determinant from the product of the upper-triangular diagonal entries D A D D D D A

English passage 24 (60% down the source page) AU116 Q1(ii-d) 2 Elementary row operations and row-echelon form take 3x4 Reduce the matrix to row-echelon form D A D D D D A

English passage 25 (62% down the source page) AU117 Q1(ii-e) 2 Elementary row operations and row-echelon form take 4x3 Reduce the matrix to row-echelon form D A D D D D A

English passage 26 (64% down the source page) AU118 Q1(ii-f) 3 Elementary row operations and row-echelon form Derive m×n required zero_column degree D A D D D D A

English passage 27 (66% down the source page) AU119 Q1(ii-g) 5 Elementary row operations and row-echelon form Wrap a general implementation that does not change its input row_echelon_form D A D D D D A

English passage 28 (68% down the source page) AU120 Q1(ii-h) 3 Elementary row operations and row-echelon form Test matrices of three shapes REF function D A D D D D A

English passage 29 (70% down the source page) AU121 Q2(i-a) 4 Determinants by elimination and pivot selection Compute a square matrix's determinant using row-echelon form D A D D D D A

English passage 30 (72% down the source page) AU122 Q2(i-b1) 2 Determinants by elimination and pivot selection Numerically test the custom implementation determinant and numpy.det D A D D D D A

English passage 31 (74% down the source page) AU123 Q2(i-b2) 4 Determinants by elimination and pivot selection Symbolically compare determinants by elimination and recursive cofactor expansion D D D D D D D

English passage 32 (76% down the source page) AU124 Q2(i-c) 3 Determinants by elimination and pivot selection Derive elimination determinant of Theta(n^3) D A D D D D A

English passage 33 (78% down the source page) AU125 Q2(i-d) 3 Determinants by elimination and pivot selection Derive the factorial complexity of recursive cofactor expansion D C D D D D C

English passage 34 (81% down the source page) AU126 Q2(ii-a) 1 Determinants by elimination and pivot selection Explain argmax Return the position of the maximum D A D D D D A

English passage 35 (83% down the source page) AU127 Q2(ii-b) 4 Determinants by elimination and pivot selection is zero_column Add partial pivoting D A D D D D A

English passage 36 (85% down the source page) AU128 Q2(ii-c) 1 Determinants by elimination and pivot selection Test elimination with row swapping on a matrix whose first pivot is zero D A D D D D A

English passage 37 (87% down the source page) AU129 Q2(ii-d) 3 Determinants by elimination and pivot selection such that zero_column Return whether a row swap occurred D A D D D D A

English passage 38 (89% down the source page) AU130 Q2(ii-e) 1 Determinants by elimination and pivot selection test swap flagged as True D A D D D D A

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 (93% down the source page) MATH40006 Revised effective-coverage matrix (based on verifiable materials ) number 5 page

English passage 2 (7% down the source page) ID question number marks Competency family Question approach M1 M2 M3 M4 M5 M6 Best

English passage 3 (10% down the source page) AU131 Q2(ii-f) 4 Determinants by elimination and pivot selection REF Track the parity sign of row swaps at the same time D A D D D D A

English passage 4 (12% down the source page) AU132 Q2(ii-g) 3 Determinants by elimination and pivot selection in determinant correct the row-swap sign in D A D D D D A

English passage 5 (14% down the source page) AU133 Q2(ii-h) 2 Determinants by elimination and pivot selection For a matrix with a zero first pivot, compare with numpy.det compare D A D D D D A

English passage 6 (16% down the source page) AU134 Q3(a) 4 Timing data structures and file export construct three types of determinant Nested timing dictionary for the implementations D A D D D B A

English passage 7 (18% down the source page) AU135 Q3(b) 2 Timing data structures and file export use pickle.dump Export the timing dictionary D A D D D B A

English passage 8 (20% down the source page) AU136 Q3(c) 2 Timing data structures and file export Convert the nested dictionary into DataFrame D A D D D B A

English passage 9 (22% down the source page) AU137 Q3(d) 2 Timing data structures and file export Take DataFrame export CSV D A D D D B A