This document last updated: 20 June 2011.
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.
Comments on papers from 2001 onwards are here
| Year | P | Qu | Topic | Comments |
| 1990 | I | 1 | Vectors: eqns | OK* |
| 1990 | I | 2 | Vectors: geometric | OKish |
| 1990 | I | 3 | Misc: series, complex numbers, limits | OKish |
| 1990 | I | 4 | Misc: eqns | Not finished |
| 1990 | I | 5 | PDEs: transformations | OK* |
| 1990 | I | 6 | Stationary values | OK |
| 1990 | I | 7 | Line integrals, conservative fields | OK* |
| 1990 | I | 8 | ODEs: 1st order | OK* |
| 1990 | I | 9 | Fourier | OK* |
| 1990 | I | 10 | PDEs: heat conduction, Fourier | OK* |
| 1990 | I | 11 | Simultaneous eqns | ? |
| 1990 | I | 12 | Matrices: eigenvalues/vectors | Not yet done - hard |
| 1990 | II | 1 | Taylor series, limits | OK* |
| 1990 | II | 2 | Integration | OK* |
| 1990 | II | 3 | Integration: series approximation | OK, not easy |
| 1990 | II | 4 | Oscillations | OK |
| 1990 | II | 5 | Differentials: exact | OK* (fairly easy) |
| 1990 | II | 6 | Lagrange (Boltzmann) | Hard unless you know how |
| 1990 | II | 7 | ODEs: 2nd order | OK, bit long |
| 1990 | II | 8 | Misc | OKish, not sure about soln |
| 1990 | II | 9 | Fourier | OK* - good |
| 1990 | II | 10 | PDEs: wave eqn | OKish |
| 1990 | II | 11 | Matrices: eigenvalues/vectors-like | OK, bit odd |
| 1990 | II | 12 | Matrices: eigenvalues/vectors | OK* - unusual but illustrative |
| 1991 | I | 1 | Vectors: eqns, geometric | Quite hard but illustrative |
| 1991 | I | 2 | Misc: eqns | OK, not easy |
| 1991 | I | 3 | Complex numbers | OKish |
| 1991 | I | 4 | Integration: series approximation | Oddish |
| 1991 | I | 5 | Differentials: exact | OK |
| 1991 | I | 6 | Lagrange | OK - fairly easy |
| 1991 | I | 7 | ODEs: 1st order | OK* - good |
| 1991 | I | 8 | ODEs: 2nd order | OKish |
| 1991 | I | 9 | Fourier | OK - easyish |
| 1991 | I | 10 | Misc: continuity, differentiability | V odd |
| 1991 | I | 11 | Matrices | OK but rather long |
| 1991 | I | 12 | Matrices, simulataneous eqns | OK |
| 1991 | II | 1 | Spherical polars | OK* - good |
| 1991 | II | 2 | Taylor series, series | OK* - good |
| 1991 | II | 3 | Fourier | OK |
| 1991 | II | 4 | Misc: Schwarz | OK, quite hard |
| 1991 | II | 5 | Stationary values | Long & boring |
| 1991 | II | 6 | PDEs: transformations | OK* - quite good |
| 1991 | II | 7 | Line integrals, conservative fields | OK* - good but bit long |
| 1991 | II | 8 | Div/Grad/Curl | OK |
| 1991 | II | 9 | PDEs | OK |
| 1991 | II | 10 | PDEs: heat conduction, pseudo-Fourier | OK |
| 1991 | II | 11 | Matrices | OKish |
| 1991 | II | 12 | Matrices: eigenvalues/vectors | OK |
| 1992 | I | 1 | Taylor series | Unclear |
| 1992 | I | 2 | Complex numbers | OK* - good |
| 1992 | I | 3 | Misc: continuity, differentiability, Differentitation of integrals | OK |
| 1992 | I | 4 | Differentials: exact | OK* - good |
| 1992 | I | 5 | Lagrange | OK - easy |
| 1992 | I | 6 | Integration: reduction formulae | OK - fairly easy |
| 1992 | I | 7 | Vector surface integrals | OK |
| 1992 | I | 8 | ODEs: 1st order | OK - (b) not easy |
| 1992 | I | 9 | ODEs: 2nd order | OK - fairly easy |
| 1992 | I | 10 | Fourier | OK |
| 1992 | I | 11 | Matrices | (a) unclear (b), (c) OK |
| 1992 | I | 12 | Matrices: eigenvalues/vectors (degenerate) | OK |
| 1992 | II | 1 | Vectors: eqns | Not yet done |
| 1992 | II | 2 | Limits | OK* - quite good |
| 1992 | II | 3 | Oscillations | OK - quite hard |
| 1992 | II | 4 | Misc: series, limits | (a), (c) OK (b) ? |
| 1992 | II | 5 | PDEs: transformations | V odd (hints make it too easy) |
| 1992 | II | 6 | Stationary values | OK |
| 1992 | II | 7 | Misc: conservative fields | Hard |
| 1992 | II | 8 | ODEs: 2nd order parameterised | OK |
| 1992 | II | 9 | PDEs: wave eqn | OK |
| 1992 | II | 10 | PDEs: diffusion, Fourier | OK |
| 1992 | II | 11 | Simultaneous eqns | Unclear |
| 1992 | II | 12 | Matrices | OK |
| 1993 | I | 1 | Vectors: geometric | Quite hard |
| 1993 | I | 2 | Taylor series | OK but boring |
| 1993 | I | 3 | Complex numbers | OK - rather easy |
| 1993 | I | 4 | PDEs: transformations | OK - straightforward but dull |
| 1993 | I | 5 | ODEs: 1st order, Exact differentials | OK - fairly easy |
| 1993 | I | 6 | ODEs: 2nd order | OK - pretty easy |
| 1993 | I | 7 | Integration: reduction formulae | OK |
| 1993 | I | 8 | Multiple integrals | OK |
| 1993 | I | 9 | PDEs | OK |
| 1993 | I | 10 | Fourier | |
| 1993 | I | 11 | Matrices | OK |
| 1993 | I | 12 | Matrices | OK |
| 1993 | II | 1 | Spherical geometry | Not tried |
| 1993 | II | 2 | Series | OK |
| 1993 | II | 3 | Complex numbers | OK* - quite good |
| 1993 | II | 4 | ODEs: 1st order | OK but short |
| 1993 | II | 5 | ODEs: 2nd order | OK - fairly easy |
| 1993 | II | 6 | Stationary values, Lagrange | OK* - good |
| 1993 | II | 7 | Line integrals, conservative fields | OK* - good |
| 1993 | II | 8 | Stoke's Theorem | OK - quite straightforward |
| 1993 | II | 9 | Fourier | Very tedious |
| 1993 | II | 10 | PDEs: Fourier | OK but a bit tedious |
| 1993 | II | 11 | Matrices | Very easy with summation convention |
| 1993 | II | 12 | Matrices, simultaneous eqns | OK* - good |
| 1994 | I | 1 | Spherical geometry | Not tried |
| 1994 | I | 2 | Taylor series | Easy |
| 1994 | I | 3 | Complex numbers | OK* - good |
| 1994 | I | 4 | Differentials: exact | OK |
| 1994 | I | 5 | ODEs: 1st order | Easy |
| 1994 | I | 6 | ODEs: 2nd order | Easy |
| 1994 | I | 7 | Stationary values, Lagrange | OK |
| 1994 | I | 8 | Vector surface integrals, grad, div | OK |
| 1994 | I | 9 | PDEs | Not done yet |
| 1994 | I | 10 | Fourier | OK |
| 1994 | I | 11 | Matrices | Easy |
| 1994 | I | 12 | Matrices | Fairly hard |
| 1994 | II | 1 | Vectors: eqns, geometric | Silly - unclear & tedious |
| 1994 | II | 2 | Series | OK |
| 1994 | II | 3 | Partial Differentiation: transformations | Tedious & silly |
| 1994 | II | 4 | PDEs | Pointless |
| 1994 | II | 5 | Misc: eqns, ODEs | Pointless |
| 1994 | II | 6 | Integration | OK - quite tough |
| 1994 | II | 7 | Multiple integrals | OK* - good |
| 1994 | II | 8 | Vector surface integrals | OK* - quite good |
| 1994 | II | 9 | PDEs, Vector surface integrals | OK |
| 1994 | II | 10 | Fourier | Easy |
| 1994 | II | 11 | Simultaneous eqns | Hard |
| 1994 | II | 12 | Matrices: eigenvalues/vectors | Hard & a bit long |
| 1995 | I | 1 | Integration | Easy |
| 1995 | I | 2 | Fourier | OK - short |
| 1995 | I | 3 | Vectors: eqns, geometric | OK* |
| 1995 | I | 4 | Probability/statistics | Yuk |
| 1995 | I | 5 | Integration: trapezium approx | OK - rather tedious |
| 1995 | I | 6 | Line integrals | OK* - good |
| 1995 | I | 7 | ODEs: 1st order | OK - fairly easy |
| 1995 | I | 8 | ODEs: 2nd order | OK |
| 1995 | I | 9 | Matrices: determinants | Absurdly easy |
| 1995 | I | 10 | Matrices, simulataneous eqns | Absurdly easy |
| 1995 | I | 11 | Differentials: exact | OK - fairly easy |
| 1995 | I | 12 | Complex numbers | OK* - quite good |
| 1995 | II | 1 | Stationary values, Lagrange | OK but tedious |
| 1995 | II | 2 | Div/Grad/Curl | Unclear |
| 1995 | II | 3 | Misc | OK - bit unusual |
| 1995 | II | 4 | Probability/statistics | Boring & easy |
| 1995 | II | 5 | Integration: reduction formulae | OK |
| 1995 | II | 6 | Vector surface integrals, Multiple integrals | OK* - good |
| 1995 | II | 7 | ODEs: misc | OK -fairly easy |
| 1995 | II | 8 | PDEs: Laplace | Not done yet |
| 1995 | II | 9 | Matrices: determinants, eigenvalues/vectors | OK* - good |
| 1995 | II | 10 | Series | OK - bit odd |
| 1995 | II | 11 | Taylor series | Easy |
| 1995 | II | 12 | Misc: differentiation, PDEs | OK - bit odd |
| 1996 | I | 1 | Stationary values | OK but dull |
| 1996 | I | 2 | Fourier Series | OK - short |
| 1996 | I | 3 | Vectors: geometric | OK |
| 1996 | I | 4 | Probability/statistics | OK |
| 1996 | I | 5 | Multiple integrals | OK |
| 1996 | I | 6 | Line integrals, conservative fields | OK - easy |
| 1996 | I | 7 | ODEs: 2nd order | OK |
| 1996 | I | 8 | ODEs: 1st order | OK |
| 1996 | I | 9 | Matrices, but impossible without diagram! | N/A |
| 1996 | I | 10 | Complex numbers | OK |
| 1996 | I | 11 | Taylor series | OK |
| 1996 | I | 12 | Partial Differentiation: transformations | OK but dull |
| 1996 | II | 1 | Misc: limits | Dull & odd |
| 1996 | II | 2 | Stationary values, Lagrange | Dull & easy |
| 1996 | II | 3 | Probability/statistics | OK but easy |
| 1996 | II | 4 | Vectors: geometric | OK |
| 1996 | II | 5 | Stoke's Theorem | OK |
| 1996 | II | 6 | Vector surface integrals | OK* - quite hard but good |
| 1996 | II | 7 | PDEs: Laplace | Long & a bit tedious |
| 1996 | II | 8 | PDEs: transformations | OK* |
| 1996 | II | 9 | Matrices, determinants | OK |
| 1996 | II | 10 | Matrices: eigenvalues/vectors | OK |
| 1996 | II | 11 | Misc: integration | Error in part (iii)? |
| 1996 | II | 12 | Differentials: exact | OK* - good |
| 1997 | I | 1 | Fourier | OK (not easy but not long) |
| 1997 | I | 2 | Differentials: thermodynamics | OK |
| 1997 | I | 3 | Misc: curve sketching, stationary values, integration | OK though not pretty |
| 1997 | I | 4 | Div/Grad/Curl | OK though used in an examples sheet |
| 1997 | I | 5 | ODEs: 1st order | OK though not pretty |
| 1997 | I | 6 | Multiple integrals | Forgot to do it! |
| 1997 | I | 7 | ODEs: 2nd order | OK |
| 1997 | I | 8 | Complex numbers | OK if you ignore the phrase "factorise f(z)" |
| 1997 | I | 9 | Matrices | OK |
| 1997 | I | 10 | Vectors: geometric | OK but dull |
| 1997 | I | 11 | Taylor series | OK but rather easy & dull |
| 1997 | I | 12 | Probability/statistics | OK but a bit tedious |
| 1997 | II | 1 | Partial Differentiation: transformations | Long and a bit tedious |
| 1997 | II | 2 | Lagrange | Very original but quite hard & fiddly |
| 1997 | II | 3 | Vector surface integrals, Grad/Div/Curl | OKish |
| 1997 | II | 4 | Vector surface integrals, Grad/Div/Curl | Strange and unclear |
| 1997 | II | 5 | Integration, series | OK though not very illustrative |
| 1997 | II | 6 | PDEs: Laplace, Fourier | OK but hugely dull |
| 1997 | II | 7 | ODEs: 1st order simulataneous | Not terribly illustrative or clear |
| 1997 | II | 8 | Matrices | OK |
| 1997 | II | 9 | Matrices, simultaneous eqns | OK |
| 1997 | II | 10 | Multiple integrals | OK but not easy |
| 1997 | II | 11 | Misc: continuity, differentiability | Haven't tried it |
| 1997 | II | 12 | Probability/statistics | Part (d) is very hard |
| 1998 | I | 1 | Stationary values, Lagrange | OK except it turns out not to be a Lagrange question |
| 1998 | I | 2 | Integration: reduction formulae | OK but tedious |
| 1998 | I | 3 | Taylor series | Messy and not very interesting |
| 1998 | I | 4 | Matrices | OK though not particularly challenging or interesting |
| 1998 | I | 5 | Fourier | OK |
| 1998 | I | 6 | Differentiation of integrals | OK though dull |
| 1998 | I | 7 | Probability/statistics | Strangely easy |
| 1998 | I | 8 | ODEs: 1st order, Exact differentials | OK |
| 1998 | I | 9 | Vectors: algebraic | Proofs: shouldn't have been set in my view |
| 1998 | I | 10 | Line integrals, conservative fields | Strange question: too easy |
| 1998 | I | 11 | ODEs: 2nd order | OK* |
| 1998 | I | 12 | Matrices: orthogonal, eigenvalues/vectors | Quite easy and quick |
| 1998 | II | 1 | Stationary values | Haven't tried it yet |
| 1998 | II | 2 | Differentials: thermodynamics | OK, though last bit is dull |
| 1998 | II | 3 | PDEs: Laplace, complex numbers | First part useful, last part hard |
| 1998 | II | 4 | Complex numbers | Quite hard |
| 1998 | II | 5 | Multiple integrals | Not difficult but not pointful |
| 1998 | II | 6 | Series | Difficult and unclear |
| 1998 | II | 7 | Probability/statistics | Used in an examples sheet |
| 1998 | II | 8 | Limits | Seems pointlessly easy |
| 1998 | II | 9 | Vectors: geometric | OK if you know the trick |
| 1998 | II | 10 | Vector surface integrals | Unpleasant |
| 1998 | II | 11 | ODEs: 2nd order | Not difficult |
| 1998 | II | 12 | Matrices, determinants | OK |
| 1999 | I | 1 | Multiple integrals | OK* |
| 1999 | I | 2 | Differentials: thermodynamics | OK* |
| 1999 | I | 3 | Taylor series | OK - fairly easy |
| 1999 | I | 4 | Matrices | OK* |
| 1999 | I | 5 | Integration, curve sketching | OK* |
| 1999 | I | 6 | Matrices | OK |
| 1999 | I | 7 | Complex numbers | OK |
| 1999 | I | 8 | Matrices: determinants | OK (fairly simple) |
| 1999 | I | 9 | ODEs: 2nd order | OK (fairly quick) |
| 1999 | I | 10 | Vector surface integrals | First part confusing |
| 1999 | I | 11 | Fourier | OK except first part is odd |
| 1999 | I | 12 | Misc: continuity, differentiability | Strange question |
| 1999 | II | 1 | Vector surface integrals | OK (fairly short) |
| 1999 | II | 2 | Series, limits | OK* |
| 1999 | II | 3 | Lagrange | Very tedious |
| 1999 | II | 4 | Misc: cylindrical and spherical polars | OK though first part not clear |
| 1999 | II | 5 | ODEs: 1st order | Interesting but long |
| 1999 | II | 6 | Line integrals, Div/Grad/Curl | Quite hard and long |
| 1999 | II | 7 | PDEs | Quick except that (c) is potentially hard |
| 1999 | II | 8 | Probability/statistics | OK |
| 1999 | II | 9 | Vectors: geometric, algebraic | OK |
| 1999 | II | 10 | Matrices: orthogonal, eigenvalues/vectors | OK |
| 1999 | II | 11 | ODEs: 2nd order | Bit messy but quite easy |
| 1999 | II | 12 | Differentiation of integrals | OK* |
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