NST/CST Part 1A Mathematics Past Exam Questions

This document last updated: 20 December 2024.

These pages provide comments on past exam papers for the Natural Sciences/Computer Sciences Part 1A Mathematics Course. Where there is no comment for a question, it probably means I've not yet had a go at it. An asterisk (*) denotes particularly good questions to try.

NB: the question numbering for Section B of the 2008 papers differed between the paper actually sat in the examination hall and the version now online. The paper provided in the examination hall had questions starting at B1, whereas the version now online had questions numbered as below.

2006 Papers 1 and 2, 2008 Paper 1, 2010 Paper 1, 2016 Paper 1 and 2023 Paper 1 were hard overall. Don't start with any of these when revising! 2012 Paper 2 was relatively easy.

Comments on papers prior to 2001 are here

Year	P	Qu	Topic	Comments
2001	I	1	Vectors: geometric	OK
2001	I	2	Fourier	OK
2001	I	3	Matrices: eigenvalues/vectors	OK
2001	I	4	Misc: integration	(c) may mislead you as to which end to start from
2001	I	5	Misc: integration, stationary values	OK
2001	I	6	Vector surface integrals	OK
2001	I	7	Matrices, simultaneous eqns	OK
2001	I	8	Vector surface integrals	OK
2001	I	9	Taylor series	OK
2001	I	10	Matrices	OK
2001	I	11	Complex numbers	OK
2001	I	12	Probability/statistics	OK
2001	II	1	ODEs: 1st order	Very hard, and (c) is vindictive
2001	II	2	Leibnitz	OK but hard and rather dull
2001	II	3	Misc	Seems to me to need 2nd year material
2001	II	4	ODEs: 2nd order	OK
2001	II	5	Line integrals, conservative fields	OK
2001	II	6	Lagrange	OK
2001	II	7	Matrices: determinants, simultaneous eqns	OK
2001	II	8	Multiple integrals	OK
2001	II	9	Differentials: transformations	Looks like (a) still holds for (b), which is bad style, but otherwise OK
2001	II	10	Differentials: thermodynamics	OK
2001	II	11	Probability/statistics	OK (rather easy)
2001	II	12	Series, limits	OK (pretty easy)
2002	I	1	Vectors: geometric	OK
2002	I	2	Fourier	OK
2002	I	3	Misc: stationary values, eqns of lines	OK
2002	I	4	Lagrange	OK though not easy to solve the simultaneous eqns
2002	I	5	Multiple integrals	OK
2002	I	6	Matrices	OK (rather easy)
2002	I	7	ODEs: 1st order	OK though a bit long and not easy
2002	I	8	Matrices	OK
2002	I	9	Line integrals, conservative fields	OK
2002	I	10	PDEs: diffusion	OK though last part unclear
2002	I	11	Complex numbers	OK
2002	I	12	PDEs	OK but not well-designed
2002	II	1	Vectors: geometric	Curve in (b) looks to be a confusing mess
2002	II	2	Differentiation of integrals	OK
2002	II	3	Multiple integrals	OK
2002	II	4	Probability/statistics	OK (potentially quite tricky)
2002	II	5	Matrices, simultaneous eqns	OK
2002	II	6	Vector surface integrals	OK (not easy)
2002	II	7	ODEs: 2nd order	OK
2002	II	8	Matrices: orthogonal, eigenvalues/vectors	OK
2002	II	9	Taylor series	OK
2002	II	10	Series, limits	OK (not easy)
2002	II	11	Differentials: transformations	OK*
2002	II	12	Stationary values	OK*
2003	I	1	Vectors: eqns	OK*
2003	I	2	Limits	OK
2003	I	3	Stationary values/Curve sketching/Integration	OK
2003	I	4	Integration	OK
2003	I	5	Matrices	OK
2003	I	6	PDEs: heat conduction	OK* (not long)
2003	I	7	Line integrals, conservative fields	OK
2003	I	8	Taylor series	OK*
2003	I	9	Hyperbolic functions	OK (fairly easy)
2003	I	10	Misc: series, integration	OK though (b) is slightly unnerving
2003	I	11	ODEs: 1st order	OK (pretty quick)
2003	I	12	Multiple integrals	Not easy
2003	II	1	Vectors: geometric	OK (fairly easy)
2003	II	2	Fourier	OK
2003	II	3	Matrices: eigenvalues/vectors	OK
2003	II	4	Vector surface integrals	OK* except for the ambiguity regarding the word "evaluate"
2003	II	5	Probabilitiy/Probability distributions	OK
2003	II	6	Matrices, simultaneous equations	OK (quite quick)
2003	II	7	Vector surface integrals	Unusual - intellectually interesting but a bit odd
2003	II	8	Matrices, suffix notation	OK*
2003	II	9	Differentials: thermodynamics	OK (easier than many of this type)
2003	II	10	Partial differentiation: transformations	OK
2003	II	11	ODEs: 2nd order	OK
2003	II	12	Lagrange/transformation of axes	Quite hard for the unfamilar
2004	I	1	Vectors: eqns, geometric	OK
2004	I	2	Series	OK
2004	I	3	Vector surface integrals	OK
2004	I	4	Integration	OK (fairly easy)
2004	I	5	Probability distributions	OK (slightly unusual)
2004	I	6	Matrices	OK
2004	I	7	Matrices, determinants	OK if you know about epsilon(ijk)
2004	I	8	Line integrals, conservative fields	OK (easy)
2004	I	9	Complex numbers, hyperbolic functions	OK (fairly easy after (a))
2004	I	10	Complex numbers, hyperbolic functions	OK (though a strange combination of parts)
2004	I	11	ODEs: 1st order	OK
2004	I	12	Multiple integrals	OK
2004	II	1	Vectors: geometric	OK (though not clear which way they intend for (b) to be done)
2004	II	2	Fourier	OK
2004	II	3	Matrices	OK* (not easy)
2004	II	4	Misc: integration, stationary values	Not easy and not fun
2004	II	5	Probabilitiy/Probability distributions	OK
2004	II	6	PDEs	OK* (not easy but interesting)
2004	II	7	Vector surface integrals	OK
2004	II	8	Taylor Series	OK ((a) is dull and a bit tedious)
2004	II	9	Partial differentiation, Taylor Series	OK but a bit dull
2004	II	10	Integration, Series	Doable but tedious
2004	II	11	ODEs: 2nd order	OK
2004	II	12	Lagrange	OK
2005	I	1	Taylor Series	Harder and less well-designed than usual
2005	I	2	Matrices	Hard if you really have to use suffix notation througout
2005	I	3	Probability	OK
2005	I	4	Probability distributions	OK but wording vague in (b(i))
2005	I	5	Vectors: geometric	OK
2005	I	6	Vector surface integrals	OK (hard but illustrative)
2005	I	7	Misc: integration, approximations	(c) is interesting; rest is tedious
2005	I	8	Multiple integrals	OK ((c) is interesting and not easy)
2005	I	9	ODEs: 1st order	OK*
2005	I	10	ODEs: 2nd order	OK but tedious
2005	I	11	Misc: integration, stationary values	OK*
2005	I	12	Fourier	OK (fairly quick)
2005	II	1	Line integrals, conservative fields, Vectors: geometric	OK
2005	II	2	Vector surface and volume integrals	OK once you understand it's just a thick spherical shell
2005	II	3	Matrices	OK
2005	II	4	Lagrange	OK
2005	II	5	Complex numbers	OK*
2005	II	6	Vectors: geometric	OK
2005	II	7	Differentials: thermodynamics	OK
2005	II	8	Differentials: exact	OK (not easy but doable)
2005	II	9	Matrices: eigenvalues/vectors	OK
2005	II	10	Integration, Series	OK (not easy but doable)
2005	II	11	Integration	OK*
2005	II	12	PDEs: diffusion equation	OK (seems very quick)
2006	I	1	Matrices	Part (b) is very hard in that the obvious approach doesn't work
2006	I	2	Matrices: eigenvalues/vectors	OK though a bit long
2006	I	3	Complex numbers	(a) and (b) are OK but rather tedious; (c) is hard until you spot the method
2006	I	4	Stoke's Theorem	OK
2006	I	5	Vectors: geometric	OK
2006	I	6	Vectors: algebraic, geometric	OK but dull
2006	I	7	Probability	OK (fairly quick)
2006	I	8	Lagrange	OK (very quick if you understand (b))
2006	I	9	Taylor Series	Tedious
2006	I	10	ODEs: 2nd order	Not without merit, but rather lost in the tedium
2006	I	11	Fourier	OK*
2006	I	12	PDEs: Laplace	OK (mischievous but interesting)
2006	II	1	Misc: Differentiation, Taylor, Integration	OK (not easy)
2006	II	2	Matrices: suffix notation	Pretty hard, as well as scary
2006	II	3	Line integrals, conservative fields	OK*
2006	II	4	Vector surface integrals	Strange and a bit confusing
2006	II	5	Volume integrals	Strange: easy but confusing - best avoided
2006	II	6	Misc: integration, approximations	OK
2006	II	7	Differentials: exact	OK* (Quick if you can spot the shortcuts)
2006	II	8	Probability	OK (quick)
2006	II	9	ODEs	(b) is very hard until you see it and (d) is a plausible solution for (b), so not terribly satisfactory overall
2006	II	10	Series	Quite hard
2006	II	11	PDEs: transformations	A standard method, but very tedious here
2006	II	12	Stationary values	Very tedious
2007	I	B1	Vectors: algebraic	OK
2007	I	B2	Complex numbers	OK*
2007	I	B3	Taylor Series	(a) OK* (b) Tedious
2007	I	B4	Probability	OK*
2007	I	B5	Exact differentials, ODEs: 1st order	OK
2007	I	B6	Stationary values	OK*
2007	I	B7	Multiple integrals	OK*
2007	I	B8	Matrices	OK (indicative marks for (a) subparts unindicative!)
2007	I	B9	Series and integration	OK (last parts of (a) are quite hard)
2007	I	B10	Differentiation of integrals	Horrid
2007	II	B1	Misc: Cartesian and polar coordinates	OK (unnervingly unusual)
2007	II	B2	Inegration	OK* - though quick
2007	II	B3	Probability	OK if you know enough stats
2007	II	B4	ODEs: 2nd order	(a) too simple (b) sketch seems hard for just 4 marks
2007	II	B5	Differentials: thermodynamics	OK - straightforward
2007	II	B6	Vector surface and line integrals	(b) needs one to assume the coordinates are spherical polars and is rather tedious
2007	II	B7	Matrices	OK
2007	II	B8	Fourier	OK* though time consuming
2007	II	B9	Lagrange	OK - rather quick though diagram is fiddly
2007	II	B10	PDEs	OK - straightforward
2008	I	B11	Vectors: geometric	OK but confusing
2008	I	B12	Complex numbers	Quite hard; only 2 marks for (b)iii!
2008	I	B13	Taylor Series	OK but (c) is tedious
2008	I	B14	Multiple integrals	To do with multiple integrals (as the question implies) is very hard unless you get the right order of integration variables, and still not easy even then. There is a very quick geometrical argument...
2008	I	B15	Probability	I gave up on (b)
2008	I	B16	ODEs: 1st order	Long and difficult
2008	I	B17	Stationary values; grad	OK
2008	I	B18	Matrices	Straightforward if dull
2008	I	B19	Limits and series	OK
2008	I	B20	Leibnitz; Schwartz	Bookwork or hard
2008	II	B10	Vectors: geometric, algebraic	OK but long and not easy
2008	II	B11	Probability	OK but be very careful how you interpret part (a)
2008	II	B12	Integration	I can now do this, but it is very difficult
2008	II	B13	ODEs: 2nd order	OK but dull
2008	II	B14	PDEs	OK
2008	II	B15	Line integrals, conservative fields	OK - bit fiddly
2008	II	B16	Matrices	OK but long and a bit tedious
2008	II	B17	Fourier	OK
2008	II	B18	Vector surface integrals	OK (looks scary but doable)
2008	II	B19	PDEs	(a) long but OK (b) OK if you realise they are using Sigma to denote a function of x, with Sigma0 being a constant
2009	I	B11	Misc: differentiation, mainly	Seems tedious and error-prone
2009	I	B12	Probability	Fairly easy
2009	I	B13	Matrices: eigenvalues/vectors	Tedious and you need to know about diagonalisation
2009	I	B14	Complex numbers	Fairly quick
2009	I	B15	Vectors: geometric, algebraic	(a)(i) unclear, rest OK
2009	I	B16	Integration	OK*
2009	I	B17	ODEs: 1st order	(a)(ii) very hard unless you know how; rest OK
2009	I	B18	Partial differentiation	Very tedious - I gave up on (c)
2009	I	B19	PDEs	OK
2009	I	B20	Series; limits	OK* ((b)(iii) is hard)
2009	II	B11	Misc: geometry	OK
2009	II	B12	ODEs: 2nd order	Tedious and error-prone
2009	II	B13	Stationary values	(a) is very tedious and error-prone; (b) is interesting but needs (a)
2009	II	B14	Matrices: equations, determinants	OK*
2009	II	B15	Fourier	Rather tedious unless there's a trick for (b)
2009	II	B16	Div/Grad/Curl	Rather tedious unless there are shortcuts
2009	II	B17	Probability/statistics	OK
2009	II	B18	Multiple integrals	OK
2009	II	B19	Vector surface integrals	OK
2009	II	B20	Misc: Leibnitz, Binomial expansion	OK but badly structured ((a) presumably still holds for (b), and (b) for (c))
2010	I	B11	Taylor Series	OK; relatively quick
2010	I	B12	Probability	Hard unless you spot the right approaches for (e) and (f)
2010	I	B13	Matrices: eigenvalues/vectors	Utterly tedious
2010	I	B14	Complex numbers	OK but repetitious
2010	I	B15	Vectors: algebraic, geometric	Hard
2010	I	B16	Integration	OK though (d) needs a Jacobian and (c) is quite hard
2010	I	B17	ODEs: 1st, 2nd order	OK; bit fiddly
2010	I	B18	Partial differentiation	OK; not easy
2010	I	B19	Misc: partial differentiation, PDEs	OK though quite quick; (c) is interesting
2010	I	B20	Limits and series	OK; interesting though quick if you know how
2010	II	B11	Misc: geometry	OK
2010	II	B12	Misc: vectors, ODEs	OK
2010	II	B13	Stationary values	OK except the sketch is unpleasant
2010	II	B14	Matrices	OK; interesting though quick if you know how
2010	II	B15	Fourier	OK
2010	II	B16	Line integrals, conservative fields	OK
2010	II	B17	Probability	OK; quite quick; (c) is interesting
2010	II	B18	Multiple integrals	OK
2010	II	B19	Lagrange	OK
2010	II	B20	Misc: Leibnitz	OK
2011	I	B11	Taylor Series	OK; very quick
2011	I	B12	Probability	Too long
2011	I	B13	Matrices: eigenvalues/vectors	OK but fiddly
2011	I	B14	Fourier, ODEs	OK, though wording in (e) could be clearer
2011	I	B15	Vectors: algebraic, geometric	OK; fairly quick
2011	I	B16	ODEs: 1st, 2nd order	OK
2011	I	B17	Complex numbers	OK; very quick
2011	I	B18	Differentials: exact	OK
2011	I	B19	Vector surface integrals	OK*
2011	I	B20	Functions, continuity, differentiability	(a) is quite hard, and horrendous to sketch f1 and f2 without a computer; (b) is interesting
2011	II	B11	Line integrals, vector surface integrals	Technically doable but crazy
2011	II	B12	Spherical trigonometry	(b) is fiddly and tiresome; (c) the l^2+m^2+n^2=1 bit is best ignored, I think; (d) very quick
2011	II	B13	Misc: hyperbolic functions, grad, stationary values	OK; quite quick
2011	II	B14	Matrices	OK, except (b) is equivalent to 2010 II 14(b)
2011	II	B15	ODEs: second order	Tedious algebra though physically interesting
2011	II	B16	Integration	OK*
2011	II	B17	Probability	OK; quick
2011	II	B18	Multiple integrals	OK; quick
2011	II	B19	PDEs	Hard but interesting
2011	II	B20	Misc: Leibnitz, ODEs, orthogonality	Hard
2012	I	B11	Simultaneous equations, vectors	OK; quite useful
2012	I	B12	Complex numbers	OK*; quite quick
2012	I	B13	ODEs: 1st order	OK until (c) gets tedious
2012	I	B14	Vectors: algebraic, geometric	Not easy; you need to understand r x p=q
2012	I	B15	Misc: coordinate transformations, integration	(a) hard if you've not seen before (c) has nasty twist
2012	I	B16	Stationary values	Too easy
2012	I	B17	Fourier	OK
2012	I	B18	Probability, distributions	OK; fairly easy
2012	I	B19	Functions, continuity, differentiability	OK
2012	I	B20	Lagrange	OK
2012	II	B11	Matrices: eigenvalues/vectors	OK*; fairly easy
2012	II	B12	Misc: integration, recurrence relations	OK* except ignore their hint
2012	II	B13	ODEs: second order	OK; quick
2012	II	B14	Vectors, vector areas	OK*
2012	II	B15	Vector fields, diferential equations	OK; quick if you know how
2012	II	B16	Exact differentials, ODEs: 1st order	(a) is tedious; rest is very easy
2012	II	B17	Taylor Series	OK; quite useful
2012	II	B18	Probability	OK; fairly easy but fiddly
2012	II	B19	Differentiation of integrals	OK; (b) is interesting
2012	II	B20	PDEs	OK
2013	I	B11	Simultaneous equations	(a) tedious (b) OK (not easy)
2013	I	B12	Complex numbers	(a),(b),(c) good, (d) could be horrendous
2013	I	B13	ODEs: 1st order	OK*
2013	I	B14	Vectors	(b) could be horrid unless you know how
2013	I	B15	Multiple integrals	(b) too hard for 4 marks (c) OK (not easy)
2013	I	B16	Stationary values	(a) tiresome (b) OK but mark distribution unfair
2013	I	B17	Fourier	Dull but OK
2013	I	B18	Probability	Very easy and quick
2013	I	B19	Limits and series	(b) interesting, rest is dull bookwork
2013	I	B20	Lagrange	(a) easy (b) too long and somewhat ambiguous
2013	II	B11	Distributions	OK*; fairly easy
2013	II	B12	Matrices and suffix notation	(a) useful (b)(vi) hard, rest OK
2013	II	B13	Integration	OK* (not easy)
2013	II	B14	ODEs: 2nd order	(a) tedious (b)(ii) hard
2013	II	B15	Equations of curves	(a),(b),(c) OK but not easy, (d) horrendous unless you get lucky
2013	II	B16	Vector fields	OK, albeit unusual in (a)(iv)
2013	II	B17	Exact differentials	Standard Maxwell stuff
2013	II	B18	Misc: partial differentiation, curve sketching	OK
2013	II	B19	Vector surface integrals	OK
2013	II	B20	Integration	OK
2014	I	B11	Matrices: eigenvalues/vectors	OK except (d) unclear
2014	I	B12	Complex numbers	OK
2014	I	B13	ODEs: 1st, 2nd order	OK
2014	I	B14	Vectors: geometric	(a) is not easy unless you know; (b) is ambiguous
2014	I	B15	Multiple integrals	OK though (a)(iii) and (b) hard if you don't see the tricks
2014	I	B16	Stationary values	OK
2014	I	B17	Fourier	OK (fairly quick)
2014	I	B18	Probability/statistics	Rather easy
2014	I	B19	Taylor series, series	(d) is hard
2014	I	B20	Lagrange	Time-consuming and not easy
2014	II	B11	Probability/statistics	OK
2014	II	B12	Matrices, simulataneous eqns	Irritating question
2014	II	B13	Integration	(a)(ii) tedious (d) interesting
2014	II	B14	Differentials: exact	OK
2014	II	B15	Taylor series	OK (c) is tedious but adds variety
2014	II	B16	Vector surface integrals, line integrals, conservative fields	Bit tedious but otherwise fine
2014	II	B17	Grad	Far too quick
2014	II	B18	Misc: chain rule	(e) is tedious and error-prone
2014	II	B19	PDEs: wave eqn	Hard
2014	II	B20	Integration, Schwarz	(a) bookwork (b) ugly (c) interesting and not easy
2015	I	B11	Complex numbers	Hard overall
2015	I	B12	Differentials: exact, stationary values	Easy and quick apart from the plot
2015	I	B13	PDEs	Algebra tedious
2015	I	B14	Misc: some integration	Not easy but interesting*
2015	I	B15	Taylor series	Tedious but doable
2015	I	B16	Probability/statistics	Interesting but too easy
2015	I	B17	Integration	OK, bit tedious; (a) is unusual
2015	I	B18	Matrices: eigenvalues/vectors	Not without merit, but rather lost in the tedium
2015	I	B19	Series	Way too hard, long and confusing
2015	I	B20	Vector surface integrals, div, curl	OK: quite interesting but not easy
2015	II	B11	Vectors: geometric, algebraic	OK
2015	II	B12	Multiple integrals	Not easy
2015	II	B13	Line integrals, conservative fields	Easy and dull
2015	II	B14	Probability/statistics	Dull and a bit confusing at the end
2015	II	B15	ODEs: 2nd order	OK*
2015	II	B16	ODEs: 1st order, Exact differentials	Way too long and hard
2015	II	B17	Matrices: eigenvalues/vectors	Bit long, and confusing as to which matrix they mean in (c)
2015	II	B18	Fourier	Too long and tedious; I didn't bother to do (b) in full
2015	II	B19	Lagrange	Quick
2015	II	B20	PDEs	OK
2016	I	B11	Complex numbers	OK; (d) not easy
2016	I	B12	Partial differentiation; stationary values	OK except (b)(ii) too hard except by computer
2016	I	B13	Line integrals, conservative fields	Too long and tedious
2016	I	B14	Matrices: eigenvalues/vectors	Too hard, long, unclear
2016	I	B15	Taylor series	Too long, boring and unpredictable
2016	I	B16	Probability/statistics	Too long and confusing
2016	I	B17	ODEs	OK
2016	I	B18	Integration	Bit too long and not easy
2016	I	B19	Partial Differentiation: transformations	OK
2016	I	B20	Line integrals; surface integrals	OK
2016	II	B11	Vectors: geometric, algebraic	Not easy but interesting*
2016	II	B12	Multiple integrals	Interesting but too long and (e) is unpredictable
2016	II	B13	Curve sketching; misc	Horrendous
2016	II	B14	ODEs: 1st order	Way too long
2016	II	B15	Matrices, simultaneous eqns	OK except I don't think (a) is within the syllabus
2016	II	B16	Probability/statistics	OK (fairly easy)
2016	II	B17	PDEs	OK
2016	II	B18	Fourier	OK but dull
2016	II	B19	Lagrange; limits	OK*
2016	II	B20	PDEs	OK (fairly easy)
2017	I	B11	Complex numbers	OK*
2017	I	B12	Partial differentiation; Exact differentials	A bit long and hard unless you did the supervision question
2017	I	B13	ODEs: 1st order	Hard
2017	I	B14	Stationary values	Somewhat long; last part strange
2017	I	B15	Taylor Series	OK
2017	I	B16	Probability/statistics	OK, but note the hint
2017	I	B17	Integration	Too easy after first integral
2017	I	B18	Matrices: eigenvalues/vectors	OK but too time-consuming; last part unclear
2017	I	B19	Newton-Raphson; Series	(d) seems ridiculous, the rest is potentially interesting but too long
2017	I	B20	ODEs: 1st order; Misc	OK*
2017	II	B11	Vectors: algebraic, geometric	OK (not easy)
2017	II	B12	Multiple integrals	OK, though (b) has a hard step
2017	II	B13	Line integrals, conservative fields	OK but dull
2017	II	B14	Probability/statistics	OK (fairly easy)
2017	II	B15	ODEs: 1st order	(a) too long; (b) OK
2017	II	B16	Surface integral, multiple integrals	OK
2017	II	B17	ODEs with eigenvalues/vectors	Standard method but not in syllabus??
2017	II	B18	Fourier	OK
2017	II	B19	Lagrange	OK
2017	II	B20	ODEs: 1st order, PDEs	OK
2018	I	B11	Complex numbers	OK
2018	I	B12	Multiple integrals	Both parts of (b) need a trick; otherwise OK
2018	I	B13	ODEs: 1st order	(c) is easy if you spot the trick and horrid otherwise
2018	I	B14	Stationary values	Danger of death by boredom
2018	I	B15	Taylor Series	OK
2018	I	B16	Probability/statistics	OK, though not easy
2018	I	B17	Integration	OK if you see substitution for (a); nasty otherwise
2018	I	B18	Matrices: eigenvalues/vectors	OK
2018	I	B19	Continuity/differentiability; Series	OK
2018	I	B20	Misc: differentiation of integrals	OK*
2018	II	B11	Vectors: algebraic, geometric	Too long, quite hard and unsatisfactory; (c) is too long
2018	II	B12	Partial differentiation	Too long and algebra is tedious
2018	II	B13	Line integrals, conservative fields	OK
2018	II	B14	Probability/statistics	Strange question
2018	II	B15	ODEs: 2nd order	OK
2018	II	B16	Vector fields	Not easy
2018	II	B17	Matrices, simulataneous eqns	OK though a bit unclear as to what proofs are required
2018	II	B18	Fourier	Hard, especially as to what form to use for y_f_0 in (c)
2018	II	B19	Lagrange	(b) is way too long and hard
2018	II	B20	PDEs	(a)(ii) doesn't follow on from (a)(i), annoyingly
2019	I	B11	Complex numbers	OK, (a) and (b) a bit tedious
2019	I	B12	Multiple integrals	Unnerving throughout, (c) is hard
2019	I	B13	ODEs: 1st order, PDEs	OK
2019	I	B14	Differentials, PDEs	A bit tedious and error-prone
2019	I	B15	Taylor series	OK
2019	I	B16	Probabilitiy	Tedious and a bit odd
2019	I	B17	Integration	Not easy
2019	I	B18	Matrices	(a) Tedious unless you see the trick (b) Tedious
2019	I	B19	Series, Newton-Raphson	(a) OK (b) Ignore the ambiguous reference to Taylor Series, then it's doable but tedious
2019	I	B20	Integration	OK, but many ways to go wrong on (c)
2019	II	B11	Vectors: geometric	OK*
2019	II	B12	Stationary values	(a) and (b) OK (c) Hard and boring without computer
2019	II	B13	Line integrals, conservative fields	OK
2019	II	B14	Probabilitiy density functions	OK
2019	II	B15	ODEs: 2nd order	OK
2019	II	B16	Surface integrals	OK*
2019	II	B17	Matrices	OK
2019	II	B18	Fourier	OK
2019	II	B19	Lagrange	OK (distribution of marks strange though)
2019	II	B20	PDEs	OK
2018	II	B11	Vectors: algebraic, geometric	Too long, quite hard and unsatisfactory; (c) is too long
2018	II	B12	Partial differentiation	Too long and algebra is tedious
2018	II	B13	Line integrals, conservative fields	OK
2018	II	B14	Probability/statistics	Strange question
2018	II	B15	ODEs: 2nd order	OK
2018	II	B16	Vector fields	Not easy
2018	II	B17	Matrices, simulataneous eqns	OK though a bit unclear as to what proofs are required
2018	II	B18	Fourier	Hard, especially as to what form to use for y_f_0 in (c)
2018	II	B19	Lagrange	(b) is way too long and hard
2018	II	B20	PDEs	(a)(ii) doesn't follow on from (a)(i), annoyingly
2019	I	B11	Complex numbers	OK, (a) and (b) a bit tedious
2019	I	B12	Multiple integrals	Unnerving throughout, (c) is hard
2019	I	B13	ODEs: 1st order, PDEs	OK
2019	I	B14	Differentials, PDEs	A bit tedious and error-prone
2019	I	B15	Taylor series	OK
2019	I	B16	Probabilitiy	Tedious and a bit odd
2019	I	B17	Integration	Not easy
2019	I	B18	Matrices	(a) Tedious unless you see the trick (b) Tedious
2019	I	B19	Series, Newton-Raphson	(a) OK (b) Ignore the ambiguous reference to Taylor Series, then it's doable but tedious
2019	I	B20	Integration	OK, but many ways to go wrong on (c)
2019	II	B11	Vectors: geometric	OK*
2019	II	B12	Stationary values	(a) and (b) OK (c) Hard and boring without computer
2019	II	B13	Line integrals, conservative fields	OK
2019	II	B14	Probabilitiy density functions	OK
2019	II	B15	ODEs: 2nd order	OK
2019	II	B16	Surface integrals	OK*
2019	II	B17	Matrices	OK
2019	II	B18	Fourier	OK
2019	II	B19	Lagrange	OK (distribution of marks strange though)
2019	II	B20	PDEs	OK
2020		B11	Complex numbers	OK, though (b) is not easy
2020		B12	Multiple integrals	OK
2020		B13	ODEs: 1st, 2nd order	OK though a bit tedious
2020		B14	Stationary values	Horrible
2020		B15	Taylor series	OK
2020		B16	Probabilitiy	OK
2020		B17	Integration	OK
2020		B18	Matrices	Not easy
2020		B19	Vector surface integrals	OK
2020		B20	Line integrals	OK except (b) is tedious and (e) is unpredictable
2021	I	B11	Complex numbers	OK though fiddly
2021	I	B12	Multiple integrals	OK
2021	I	B13	ODEs: 1st, 2nd order	Quick
2021	I	B14	Differentials, PDEs	Fairly easy
2021	I	B15	Taylor series	OK other than the convergence issue in (d)
2021	I	B16	Probabilitiy	OK
2021	I	B17	Integration	OK
2021	I	B18	Matrices	OK
2021	I	B19	Misc: continuity, differentiability, limits	OK
2021	I	B20	Integration	OK
2021	II	B11	Vectors: eqns, geometric	OK
2021	II	B12	Stationary values	OK
2021	II	B13	Line integrals, conservative fields	OK
2021	II	B14	Probabilitiy density functions	(a) OK (b) hard if you don't know
2021	II	B15	ODEs: 1st, 2nd order	OK
2021	II	B16	Vector fields	(a) OK (b) very error-prone
2021	II	B17	Matrices	OK though a bit fiddly
2021	II	B18	Fourier	Long
2021	II	B19	Stationary values, Lagrange	OK
2021	II	B20	PDEs	OK: interesting but fiddly
2022	I	B11	Complex numbers	OK though not easy in places
2022	I	B12	Multiple integrals	OK
2022	I	B13	ODEs: 1st order	OK
2022	I	B14	Exact differentials, partial differentiation	One interesting challenge but lots of tedium
2022	I	B15	Taylor series	Conceptually interesting but the algebra is tedious
2022	I	B16	Probabilitiy/statistics	OK
2022	I	B17	Integration	OK
2022	I	B18	Matrices	OK
2022	I	B19	Series	OK other than whether a proof is needed for (b).
2022	I	B20	Integration	OK but fiddly
2022	II	B11	Vectors: eqns, geometric	Quick
2022	II	B12	Stationary values	Tedious, difficult without a computer
2022	II	B13	Line integrals, conservative fields	OK but hard
2022	II	B14	Probability	OK but algebra is tedious
2022	II	B15	ODEs: 1st, 2nd order	OK (part (a) is unusual)
2022	II	B16	Vector fields	Not easy
2022	II	B17	Matrices, suffix notation	OK (part (a) is a useful test)
2022	II	B18	Fourier	OK, quite quick
2022	II	B19	Stationary values, Lagrange	OK, quite quick
2022	II	B20	PDEs	OK
2023	I	B11	Complex numbers	Algebra fiddly in places
2023	I	B12	Multiple integrals	Weird and algebra is tedious
2023	I	B13	ODEs: 1st order	OK
2023	I	B14	Differentials, PDEs: transformations	OK
2023	I	B15	Taylor series	OK. Algebra on (c) a bit tedious
2023	I	B16	Probabilitiy/statistics	OK. Unusual
2023	I	B17	Fourier	OK, but first part of (e) is hard
2023	I	B18	Matrices	OK, though (e) is fairly hard
2023	I	B19	Limits and series	(b)(i) unclear on what one can assume; (d)(iii) hard
2023	I	B20	Lagrange	Quite hard
2023	II	B11	Vectors: geometric, algebraic	Far too easy
2023	II	B12	Stationary values	Question seems wrong and plots are hard without computer
2023	II	B13	Line integrals, conservative fields	OK
2023	II	B14	Probability	OK
2023	II	B15	ODEs: 1st, 2nd order	OK*
2023	II	B16	Vector fields	OK but not easy
2023	II	B17	Matrices	OK
2023	II	B18	Fourier	Time-consuming and (a) is +not+ obvious.
2023	II	B19	Schwarz Inequality	(a) done in lectures; (b) OK but not easy
2023	II	B20	PDEs	OK
2024	I	B11	Complex numbers	Long and difficult for the marks available
2024	I	B12	Multiple integrals	Doable but long and not easy
2024	I	B13	ODEs: 1st order, Exact differentials	OK
2024	I	B14	Differentials, partial differentiation	OK except (c) hard if you don't know
2024	I	B15	Taylor series	OK but fiddly
2024	I	B16	Probability	Long unless you can find tricks
2024	I	B17	Integration	OK but not easy, especially (d)
2024	I	B18	Matrices	OK
2024	I	B19	Analysis, limits and series	(a) and (c) are OK, (b) is irritating at best
2024	I	B20	Differentation of integrals	OK
2024	II	B11	Vectors: geometric, algebraic	OK if you know; hard if you don't
2024	II	B12	Stationary values	OK
2024	II	B13	Line integrals, conservative fields	OK
2024	II	B14	Probabilitiy/statistics	OK except (b)(i) is too hard
2024	II	B15	ODEs: 2nd order	OK (quick)
2024	II	B16	Surface integrals	OK
2024	II	B17	Matrices, simultaneous equations	Unpleasant
2024	II	B18	Fourier	OK
2024	II	B19	Lagrange	OK*
2024	II	B20	PDEs	OK but somewhat unnerving

Ian Rudy (

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