Unfortunately I am not supervising this paper any more, and the information below relates to the course prior to the major revisions in 2015-16 and has not been updated since then. Therefore the style and content of the questions may well not reflect what is set this year. However, I will leave the old material here as some students have asked for it.

Where there is no comment for a question, it probably means I've not yet had a go at it yet. A star (*) meant the question was good in some way - interesting or particularly useful for practice, though the changes to the course in 2015-16 mean that may no longer be true.

Year | Sec | Qu | Topic | Comments |

1999 | A | 1 | Linear Algebra (diagonalisation) | OK but quick |

1999 | A | 2 | Linear Algebra (securities, vector spaces) | OK |

1999 | A | 3 | Linear Algebra (difference eqns) | OK but relatively long |

1999 | A | 4 | Statistics (distribution functions) | OK, except you can't have a "density" in a discrete situation |

1999 | A | 5 | Statistics (estimators) | OK, though done as an examples sheet question |

1999 | A | 6 | Statistics (Bayes) | OK but quick |

1999 | A | 7 | Calculus (optimisation) | OK |

1999 | A | 8 | Calculus (equilibrium points & stability) | OK |

1999 | A | 9 | Calculus (Taylor Series) | OK but rather dull |

1999 | B | 1 | Linear Algebra (linear programming) | No longer on syllabus |

1999 | B | 2 | Linear Algebra (vector spaces) | OK, though unclear how much detail is needed in (a) |

1999 | B | 3 | Statistics (estimators) | OK but rather long and not easy |

1999 | B | 4 | Statistics (MGFs) | OK |

1999 | B | 5 | Calculus (optimisation) | OK |

1999 | B | 6 | Calculus (difference eqns) | OK |

2000 | A | 1 | Linear Algebra (vector spaces) | OK |

2000 | A | 2 | Linear Algebra (vector spaces) | OK except I think "orthogonal components" no longer in syllabus |

2000 | A | 3 | Linear Algebra (linear programming) | No longer on syllabus |

2000 | A | 4 | Statistics (MGFs) | OK (useful) |

2000 | A | 5 | Statistics (estimators) | OK |

2000 | A | 6 | Statistics (hypothesis testing) | (a) and (b) OK; (c) no longer in syllabus |

2000 | A | 7 | Calculus (differential eqns) | OK but quick |

2000 | A | 8 | Calculus (homogeneous functions) | OK but easy and dull |

2000 | A | 9 | Calculus (optimisation) | OK |

2000 | B | 1 | Linear Algebra (definiteness) | OK |

2000 | B | 2 | Linear Algebra (input/output models) | OK (not easy but interesting) |

2000 | B | 3 | Statistics (estimators) | (a) and (b) OK; (c) is confusing |

2000 | B | 4 | Statistics (hypothesis testing) | OK, except (a) and (d) no longer in syllabus |

2000 | B | 5 | Calculus (equilibrium points & stability) | OK though (d) is unclear |

2000 | B | 6 | Calculus (optimisation) | Long and unclear |

2001 | A | 1 | Linear Algebra (vector spaces) | OK |

2001 | A | 2 | Linear Algebra (eigenvalues/vectors) | (a) and (b) OK; (c) is unclear |

2001 | A | 3 | Linear Algebra (definiteness) | OK if you ignore their statement that one of the eigenvalues is 2 |

2001 | A | 4 | Calculus (stationary values) | OK |

2001 | A | 5 | Calculus (difference eqns) | OK |

2001 | A | 6 | Calculus (equilibrium points & stability) | OK |

2001 | A | 7 | Statistics (MGFs) | OK* |

2001 | A | 8 | Statistics (estimators) | OK |

2001 | A | 9 | Statistics (estimators) | OK (bit odd in (a)) |

2001 | B | 1 | Linear Algebra (input/output models, vector spaces) | Unclear |

2001 | B | 2 | Linear Algebra (difference eqns) | OK |

2001 | B | 3 | Calculus (homogeneous functions) | OK but hard |

2001 | B | 4 | Calculus (homogeneous functions) | Algebra tiresome on (a)(iii) and (b) is unclear |

2001 | B | 5 | Statistics (moments) | Useful though quite quick and easy for Section B |

2001 | B | 6 | Statistics (hypothesis testing) | OK, except (a) no longer in syllabus |

2002 | A | 1 | Linear Algebra (definiteness) | OK* |

2002 | A | 2 | Linear Algebra (Misc) | OK |

2002 | A | 3 | Linear Algebra (Misc) | Some find this non-obvious |

2002 | A | 4 | Statistics (probabilities) | OK if one assumes one has to prove (iii) from the others! |

2002 | A | 5 | Statistics (Chebyshev) | OK though the last bit is tiresome in the detail, and I think the question should have saved you from even considering what happens if k<-1 |

2002 | A | 6 | Statistics (probabilities) | OK |

2002 | A | 7 | Calculus (differential/difference eqns) | OK |

2002 | A | 8 | Calculus (stationary values) | OK |

2002 | A | 9 | Calculus (equilibrium points & stability) | OK |

2002 | B | 1 | Linear Algebra (input/output models) | OK |

2002 | B | 2 | Linear Algebra (input/output models/difference eqns) | OK |

2002 | B | 3 | Statistics (estimators) | OK |

2002 | B | 4 | Statistics (estimators) | OK |

2002 | B | 5 | Calculus (Misc) | OK |

2002 | B | 6 | Calculus (optimisation) | Mostly OK but confusing as to what they want in places |

2003 | A | 1 | Linear Algebra (simultaneous eqns and vector spaces) | OK |

2003 | A | 2 | Linear Algebra (Misc) | OK |

2003 | A | 3 | Linear Algebra (Misc) | OK |

2003 | A | 4 | Calculus (stationary values) | Dull and (a) is not entirely clear |

2003 | A | 5 | Calculus (differential eqns) | OK |

2003 | A | 6 | Calculus (homogeneous functions/Lagrange) | OK |

2003 | A | 7 | Statistics (discrete probability distributions) | OK |

2003 | A | 8 | Statistics (estimators/hypothesis testing) | OK but I don't see the point |

2003 | A | 9 | Statistics (estimators) | Unclear |

2003 | B | 1 | Linear Algebra (difference eqns) | OK |

2003 | B | 2 | Linear Algebra (Misc) | OK (not easy) |

2003 | B | 3 | Calculus (equilibrium points & stability) | OK (nowhere near as bad as it looks at first) |

2003 | B | 4 | Calculus (Euler/stationary values) | (a) and (b) OK; (c) seems to me to have an error |

2003 | B | 5 | Statistics (estimation) | OK |

2003 | B | 6 | Statistics (joint distributions) | OK |

2004 | A | 1 | Linear Algebra (ISLM and Cramer's Rule) | OK |

2004 | A | 2 | Linear Algebra (determinants and inverses) | OK (easy) |

2004 | A | 3 | Linear Algebra (Vector spaces) | OK* |

2004 | A | 4 | Calculus (limits) | OK (easy & quick) |

2004 | A | 5 | Calculus (partial differentiation, Taylor Series) | OK though wording is confusing |

2004 | A | 6 | Calculus (coupled differential equations) | OK (though long via the matrix method) |

2004 | A | 7 | Statistics (probabilities) | OK (not easy) |

2004 | A | 8 | Statistics (probability distributions, Chebyshev) | OK |

2004 | A | 9 | Statistics (Bayes with distributions) | OK (though may not be your cup of tea) |

2004 | B | 1 | Linear Algebra (vector spaces) | OK but not easy |

2004 | B | 2 | Linear Algebra (Markov) | OK (relatively easy) |

2004 | B | 3 | Calculus (stationary values) | OK |

2004 | B | 4 | Calculus (concavity, homogeneity) | Unreasonably hard |

2004 | B | 5 | Statistics (estimators) | OK* |

2004 | B | 6 | Statistics (estimators) | OK though (d) should say Bernoulli, and is not easy; quite long overall |

2005 | A | 1 | Linear Algebra (Vector spaces) | OK |

2005 | A | 2 | Linear Algebra (Vector spaces) | OK other than lack of definition for x2 |

2005 | A | 3 | Linear Algebra (Misc) | OK (not easy) |

2005 | A | 4 | Calculus (homogeneous functions) | Design of question confusing |

2005 | A | 5 | Calculus (hessians, optimisation) | OK* |

2005 | A | 6 | Calculus (differential equations) | (c) is absurdly tedious |

2005 | A | 7 | Statistics (expectations) | Question confusing |

2005 | A | 8 | Statistics (expectations, independence) | OK |

2005 | A | 9 | Statistics (probabilities, Bayes) | OK (relatively easy) |

2005 | B | 1 | Linear Algebra (misc, eigenvalues/vectors) | (a) is bookwork but hard if do not know, rest is easy |

2005 | B | 2 | Linear Algebra (vector spaces) | (a) is hard, (b) is interesting, (c) is bookwork |

2005 | B | 3 | Calculus (distributions, l'Hopital) | OK* ((c) is hard) |

2005 | B | 4 | Calculus (optimisation, Envelope Theorem) | OK, though (b) is bookwork |

2005 | B | 5 | Statistics (estimators) | Seems easy but not clear what they want |

2005 | B | 6 | Statistics (moment generating functions, hypothesis testing) | Seems easy but not clear what they want |

2006 | A | 1 | Statistics (estimators) | OK |

2006 | A | 2 | Statistics (estimators) | OK |

2006 | A | 3 | Statistics (estimators) | (a) Requires a principle not taught (b) is badly-worded and identical to a question in the previous year |

2006 | A | 4 | Calculus (misc) | OK* |

2006 | A | 5 | Calculus (Mean Value Theorem) | Great idea for a question, messed up by MVT |

2006 | A | 6 | Calculus (coupled differential equations) | OK |

2006 | A | 7 | Linear Algebra (Markov) | OK |

2006 | A | 8 | Linear Algebra (misc) | OK (bit simple) |

2006 | A | 9 | Linear Algebra (portfolios) | OK |

2006 | B | 10 | Statistics (estimators) | For b read beta; OK but identical to an examples sheet question |

2006 | B | 11 | Statistics (Bayes) | OK except that (a) is ambiguous and (c) is ambiguous in whether you need to prove result for mean of Beta distribution |

2006 | B | 12 | Calculus (stationary values) | OK* though ignore (a) initially |

2006 | B | 13 | Calculus (homogeneous functions/Lagrange) | Identical to 2003 A6 :-( |

2006 | B | 14 | Linear Algebra (input/output models) | OK if you can be bothered |

2006 | B | 15 | Linear Algebra (vector spaces) | OK except (d) is not clear |

2007 | A | 1 | Linear Algebra (IS-LM) | OK except we don't have enough info on coefficients for (b) |

2007 | A | 2 | Linear Algebra (simultaneous eqns) | OK (quite interesting but a bit messy) |

2007 | A | 3 | Linear Algebra (eigenvalues and Markov) | (a) depends on your definition of eigenvalues/vectors (b) OK |

2007 | A | 4 | Calculus (misc) | Doable but tiresomely theoretical |

2007 | A | 5 | Calculus (misc) | OK but not easy |

2007 | A | 6 | Calculus (coupled and uncoupled differential equations) | OK* |

2007 | A | 7 | Statistics (probability density functions) | OK* |

2007 | A | 8 | Statistics (moment generating functions) | OK |

2007 | A | 9 | Statistics (estimators) | OK |

2007 | B | 10 | Linear Algebra (matrices) | OK |

2007 | B | 11 | Linear Algebra (vector spaces) | (a) regurgitate your lecture handout (b) OK* |

2007 | B | 12 | Calculus (Lagrange) | Pointlessly messy - I gave up |

2007 | B | 13 | Calculus (misc) | (b) is gory and tiresome |

2007 | B | 14 | Statistics (estimators) | Doable though a bit odd; I assume (b) means possible *unbiased* estimator |

2007 | B | 15 | Statistics (maximum likelihood estimators) | Doable but a bit odd; I assume alpha0 is still zero in (d) |

2008 | A | 1 | Linear Algebra (determinants) | OK (quick) |

2008 | A | 2 | Linear Algebra (linear dependency) | OK ((b) not easy) |

2008 | A | 3 | Linear Algebra (in/definite matrices) | OK |

2008 | A | 4 | Calculus (continuity/differentiability) | (c) is interesting; rest OK but dull |

2008 | A | 5 | Calculus (misc) | Avoid (unusual, ambiguous and confusing) |

2008 | A | 6 | Calculus (misc) | Avoid (unusual, confusing in the sheer detail, and seems incomplete) |

2008 | A | 7 | Statistics (probability set theory) | OK (quick) |

2008 | A | 8 | Statistics (probability distribution functions) | OK if you've seen it before, otherwise hard |

2008 | A | 9 | Statistics (hypothesis testing) | Similar to a supervision question, and not very clear |

2008 | B | 10 | Linear Algebra (vector spaces: securities and portfolios) | Challenging conceptually and horrendous in the detail |

2008 | B | 11 | Linear Algebra (coupled difference equations) | Infamous in that r1=2, not 0.2, quite long and error prone |

2008 | B | 12 | Calculus (misc) | Avoid (unusual, long, confusing, unclear) |

2008 | B | 13 | Calculus (optimisation) | OK-ish |

2008 | B | 14 | Statistics (prior/posterior probability distributions) | OK but very simple |

2008 | B | 15 | Statistics (maximum likelihood estimators) | OK, though I think their hint in (b) is invalid |

2009 | A | 1 | Linear Algebra (determinants) | OK (quick) |

2009 | A | 2 | Linear Algebra (simultaneous eqns) | OK (quick but useful) |

2009 | A | 3 | Linear Algebra (vector spaces) | OK (quick and easy) |

2009 | A | 4 | Statistics (expectations) | Seems to need strict convexity rather than just convexity? |

2009 | A | 5 | Statistics (moment generating functions) | OK (good) |

2009 | A | 6 | Statistics (Bayes) | Repeat of 2006 B11 |

2009 | A | 7 | Statistics (regression) | Hard! |

2009 | A | 8 | Calculus (functions) | OK |

2009 | A | 9 | Calculus (difference equations) | OK |

2009 | A | 10 | Calculus (differentiation) | Near-identical to a supervision question |

2009 | B | 11 | Linear Algebra (ISLM) | (a) is 1st year material, (b) is tiresome |

2009 | B | 12 | Linear Algebra (eigenvalues and eigenvectors) | Long and tedious but not difficult |

2009 | B | 13 | Statistics | Avoid (partly interesting but needs concepts not taught) |

2009 | B | 14 | Statistics (regression, maximum likelihood estimators) | Needs matrix notation and unclear in places what they want |

2009 | B | 15 | Calculus (optimisation) | Fairly easy |

2009 | B | 16 | Calculus (optimisation) | Confusing in places but OK if you can follow it |

2010 | A | 1 | Linear Algebra (vector spaces/linear dependency) | Interesting but (b) is quite time-consuming, and not easy overall |

2010 | A | 2 | Linear Algebra (simultaneous eqns) | OK* |

2010 | A | 3 | Linear Algebra (singular matrices) | OK, except (a) can be done in more than one way, hence potentially mucking up (b) |

2010 | A | 4 | Calculus (limits) | (a) useful (b) not easy if you've not seen it before |

2010 | A | 5 | Calculus (implicit function theorem) | OK (easy) |

2010 | A | 6 | Calculus (optimisation) | OK (easy if you understand the question) |

2010 | A | 7 | Statistics (regression) | Horrendous |

2010 | A | 8 | Statistics (probabilities) | Trivial |

2010 | A | 9 | Statistics (Chebyshev) | OK (quite quick) |

2010 | B | 10 | Linear Algebra (misc) | (a) OK though fiddly (b) quite hard (c) hard |

2010 | B | 11 | Linear Algebra (vector spaces/simultaneous eqns) | (a) confusing and quite hard (b) tedious |

2010 | B | 12 | Calculus (difference equations) | OK except (c) is a bit vague as to what they want |

2010 | B | 13 | Calculus (optimisation) | OK* |

2010 | B | 14 | Statistics (Bayes) | OK, in places a bit confusing or vague |

2010 | B | 15 | Statistics (maximum likelihood estimators) | Unfair to expect you to judge how to handle censored data, in my view |

2011 | A | 1 | Linear Algebra (traces and suffix notation) | OK (quick) |

2011 | A | 2 | Linear Algebra (vector spaces/linear dependency) | OK |

2011 | A | 3 | Linear Algebra (quadratic forms and definiteness) | OK (quick) |

2011 | A | 4 | Calculus (functions) | OK |

2011 | A | 5 | Calculus (limits) | OK* |

2011 | A | 6 | Calculus (differential equations) | OK (quick) |

2011 | A | 7 | Statistics (expectations, variances, Taylor Series) | OK once you know |

2011 | A | 8 | Statistics (Bayes) | OK |

2011 | A | 9 | Statistics (estimators) | OK |

2011 | B | 10 | Linear Algebra (simultaneous equations / linear mappings) | OK, though (a) is 2003A1, (b) looks scary but isn't so bad |

2011 | B | 11 | Linear Algebra (ISLM / convex functions / misc) | (b) is increasingly tough, rest OK |

2011 | B | 12 | Calculus (optimisation) | OK but too easy for Section B |

2011 | B | 13 | Calculus (Gini Index - unusual) | Hard if you've never encountered Gini Indexes |

2011 | B | 14 | Statistics (Chebyshev) | Bit confusing but OK |

2011 | B | 15 | Statistics (maximum likelihood estimators) | OK but too easy for Section B |

2012 | A | 1 | Linear Algebra (vector spaces) | OK |

2012 | A | 2 | Linear Algebra (eigenvalues and vectors) | Very quick but useful* |

2012 | A | 3 | Linear Algebra (orthogonal matrices, quadratic forms and definiteness) | Very easy |

2012 | A | 4 | Statistics (Bayes) | OK (quick) |

2012 | A | 5 | Statistics (Neyman-Pearson, UMP tests) | OK* though too long for Section A |

2012 | A | 6 | Statistics (maximum likelihood estimators) | OK* |

2012 | A | 7 | Calculus (functions, convexity) | OK* |

2012 | A | 8 | Calculus (functions, optimisation) | OK though hard if you aren't used to (b) |

2012 | A | 9 | Calculus (optimisation) | Hard going |

2012 | B | 10 | Linear Algebra (ISLM and Cramer's Rule) | OK but too easy for Section B |

2012 | B | 11 | Linear Algebra (matrices, determinants, induction) | OK* though too short for Section B |

2012 | B | 12 | Statistics (Chebyshev) | OK though too short for Section B |

2012 | B | 13 | Statistics (maximum likelihood estimators) | Long, confusing as to what they want in places |

2012 | B | 14 | Calculus (functions, Fundamental Theorem of Calculus) | OK though too short for Section B |

2012 | B | 15 | Calculus (Bidding functions, utility) | Odd but doable and quite short |

2013 | A | 1 | Linear Algebra (eigenvalues and vectors) | OK* |

2013 | A | 2 | Linear Algebra block matrices) | Pretty hard unless you spot it |

2013 | A | 3 | Linear Algebra (linear dependency) | OK (quick) |

2013 | A | 4 | Statistics (estimators) | OK* |

2013 | A | 5 | Statistics (matrix formulation of OLS) | Boring bookwork |

2013 | A | 6 | Statistics (moment generating functions, estimators) | Not ideal in that it needs Jensen's Inequality but unclear that one is allowed to assume it |

2013 | A | 7 | Calculus (functions, convexity, Taylor) | OK (very easy) |

2013 | A | 8 | Calculus (integration) | OK (very easy) |

2013 | A | 9 | Calculus (optimisation) | OK* |

2013 | B | 10 | Linear Algebra (input/output models) | OK, though a bit ambiguous |

2013 | B | 11 | Linear Algebra (determinant proofs) | Boring proof |

2013 | B | 12 | Statistics (maximum likelihood estimators) | Ridiculously long |

2013 | B | 13 | Statistics (Bayes) | OK |

2013 | B | 14 | Calculus (functions, differentiability) | OK* though (e) ambiguous |

2013 | B | 15 | Calculus (difference equations) | OK except needs complex numbers |

2014 | A | 1 | Linear Algebra (properties of matrices and determinants) | OK |

2014 | A | 2 | Linear Algebra (vector spaces) | OK (very easy) |

2014 | A | 3 | Linear Algebra (orthogonal matrices) | OK |

2014 | A | 4 | Statistics (moment generating functions) | OK |

2014 | A | 5 | Statistics (Bayes) | Not entirely clear what is wanted |

2014 | A | 6 | Statistics (Chebyshev) | OK |

2014 | A | 7 | Calculus (functions) | OK (not easy unless you spot the method) |

2014 | A | 8 | Calculus (quasiconcavity) | OK |

2014 | A | 9 | Calculus (optimisation) | Crazy: probably a mistake in question |

2014 | B | 10 | Linear Algebra (vector space bases) | OK except (c) is ambiguous as to "smallest" |

2014 | B | 11 | Linear Algebra (Markov) | OK unless you do (b) in fractions like I did |

2014 | B | 12 | Statistics (estimators) | Too long; (c) unclear on definition of Xi |

2014 | B | 13 | Statistics (maximum likelihood estimators) | Too long; (c) somewhat scary but OK |

2014 | B | 14 | Calculus (integration) | A bit odd, especially (c), where it is best to ignore the formula given |

2014 | B | 15 | Calculus (differential equations) | OK except for the phase plot |

2015 | A | 1 | Linear Algebra (vector spaces) | OK* |

2015 | A | 2 | Linear Algebra (vector spaces) | (c) is weird; rest largely OK |

2015 | A | 3 | Linear Algebra (eigenvalues and vectors) | Not obvious what the best method is. |

2015 | A | 4 | Statistics (Chebyshev) | OK |

2015 | A | 5 | Statistics (Bayes) | Repeat of 2009 A6 |

2015 | A | 6 | Statistics (estimators) | OK* |

2015 | A | 7 | Calculus (functions) | OK |

2015 | A | 8 | Calculus (Misc) | OK |

2015 | A | 9 | Calculus (optimisation) | Not sure what this is getting at |

2015 | B | 10 | Linear Algebra (vector space bases) | Fairly straightforward |

2015 | B | 11 | Linear Algebra (Markov-ish) | Question initially unclear |

2015 | B | 12 | Statistics | Repeat of 2009 B13 |

2015 | B | 13 | Statistics (estimators) | Too long; (d) unclear re large/small sample |

2015 | B | 14 | Calculus (Misc) | Very quick |

2015 | B | 15 | Calculus (differential/difference eqns) | OK if you understand the notation |

Ian Rudy ()