This document last updated: 26 December 2022.

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 sat 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 and 2016 Paper 1 were hard overall. Don't start there 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 |

Ian Rudy ()