Economics Tripos Part IIA Paper 6 Past Exam Questions: 2015 and before

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
1999A1Linear Algebra (diagonalisation)OK but quick
1999A2Linear Algebra (securities, vector spaces)OK
1999A3Linear Algebra (difference eqns)OK but relatively long
1999A4Statistics (distribution functions)OK, except you can't have a "density" in a discrete situation
1999A5Statistics (estimators)OK, though done as an examples sheet question
1999A6Statistics (Bayes)OK but quick
1999A7Calculus (optimisation)OK
1999A8Calculus (equilibrium points & stability)OK
1999A9Calculus (Taylor Series)OK but rather dull
1999B1Linear Algebra (linear programming)No longer on syllabus
1999B2Linear Algebra (vector spaces)OK, though unclear how much detail is needed in (a)
1999B3Statistics (estimators)OK but rather long and not easy
1999B4Statistics (MGFs)OK
1999B5Calculus (optimisation)OK
1999B6Calculus (difference eqns)OK
2000A1Linear Algebra (vector spaces)OK
2000A2Linear Algebra (vector spaces)OK except I think "orthogonal components" no longer in syllabus
2000A3Linear Algebra (linear programming)No longer on syllabus
2000A4Statistics (MGFs)OK (useful)
2000A5Statistics (estimators)OK
2000A6Statistics (hypothesis testing)(a) and (b) OK; (c) no longer in syllabus
2000A7Calculus (differential eqns)OK but quick
2000A8Calculus (homogeneous functions)OK but easy and dull
2000A9Calculus (optimisation)OK
2000B1Linear Algebra (definiteness)OK
2000B2Linear Algebra (input/output models)OK (not easy but interesting)
2000B3Statistics (estimators)(a) and (b) OK; (c) is confusing
2000B4Statistics (hypothesis testing)OK, except (a) and (d) no longer in syllabus
2000B5Calculus (equilibrium points & stability)OK though (d) is unclear
2000B6Calculus (optimisation)Long and unclear
2001A1Linear Algebra (vector spaces)OK
2001A2Linear Algebra (eigenvalues/vectors)(a) and (b) OK; (c) is unclear
2001A3Linear Algebra (definiteness)OK if you ignore their statement that one of the eigenvalues is 2
2001A4Calculus (stationary values)OK
2001A5Calculus (difference eqns)OK
2001A6Calculus (equilibrium points & stability)OK
2001A7Statistics (MGFs)OK*
2001A8Statistics (estimators)OK
2001A9Statistics (estimators)OK (bit odd in (a))
2001B1Linear Algebra (input/output models, vector spaces)Unclear
2001B2Linear Algebra (difference eqns)OK
2001B3Calculus (homogeneous functions)OK but hard
2001B4Calculus (homogeneous functions)Algebra tiresome on (a)(iii) and (b) is unclear
2001B5Statistics (moments)Useful though quite quick and easy for Section B
2001B6Statistics (hypothesis testing)OK, except (a) no longer in syllabus
2002A1Linear Algebra (definiteness)OK*
2002A2Linear Algebra (Misc)OK
2002A3Linear Algebra (Misc)Some find this non-obvious
2002A4Statistics (probabilities)OK if one assumes one has to prove (iii) from the others!
2002A5Statistics (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
2002A6Statistics (probabilities)OK
2002A7Calculus (differential/difference eqns)OK
2002A8Calculus (stationary values)OK
2002A9Calculus (equilibrium points & stability)OK
2002B1Linear Algebra (input/output models)OK
2002B2Linear Algebra (input/output models/difference eqns)OK
2002B3Statistics (estimators)OK
2002B4Statistics (estimators)OK
2002B5Calculus (Misc)OK
2002B6Calculus (optimisation)Mostly OK but confusing as to what they want in places
2003A1Linear Algebra (simultaneous eqns and vector spaces)OK
2003A2Linear Algebra (Misc)OK
2003A3Linear Algebra (Misc)OK
2003A4Calculus (stationary values)Dull and (a) is not entirely clear
2003A5Calculus (differential eqns)OK
2003A6Calculus (homogeneous functions/Lagrange)OK
2003A7Statistics (discrete probability distributions)OK
2003A8Statistics (estimators/hypothesis testing)OK but I don't see the point
2003A9Statistics (estimators)Unclear
2003B1Linear Algebra (difference eqns)OK
2003B2Linear Algebra (Misc)OK (not easy)
2003B3Calculus (equilibrium points & stability)OK (nowhere near as bad as it looks at first)
2003B4Calculus (Euler/stationary values)(a) and (b) OK; (c) seems to me to have an error
2003B5Statistics (estimation)OK
2003B6Statistics (joint distributions)OK
2004A1Linear Algebra (ISLM and Cramer's Rule)OK
2004A2Linear Algebra (determinants and inverses)OK (easy)
2004A3Linear Algebra (Vector spaces)OK*
2004A4Calculus (limits)OK (easy & quick)
2004A5Calculus (partial differentiation, Taylor Series)OK though wording is confusing
2004A6Calculus (coupled differential equations)OK (though long via the matrix method)
2004A7Statistics (probabilities)OK (not easy)
2004A8Statistics (probability distributions, Chebyshev)OK
2004A9Statistics (Bayes with distributions)OK (though may not be your cup of tea)
2004B1Linear Algebra (vector spaces)OK but not easy
2004B2Linear Algebra (Markov)OK (relatively easy)
2004B3Calculus (stationary values)OK
2004B4Calculus (concavity, homogeneity)Unreasonably hard
2004B5Statistics (estimators)OK*
2004B6Statistics (estimators)OK though (d) should say Bernoulli, and is not easy; quite long overall
2005A1Linear Algebra (Vector spaces)OK
2005A2Linear Algebra (Vector spaces)OK other than lack of definition for x2
2005A3Linear Algebra (Misc)OK (not easy)
2005A4Calculus (homogeneous functions)Design of question confusing
2005A5Calculus (hessians, optimisation)OK*
2005A6Calculus (differential equations)(c) is absurdly tedious
2005A7Statistics (expectations)Question confusing
2005A8Statistics (expectations, independence)OK
2005A9Statistics (probabilities, Bayes)OK (relatively easy)
2005B1Linear Algebra (misc, eigenvalues/vectors)(a) is bookwork but hard if do not know, rest is easy
2005B2Linear Algebra (vector spaces)(a) is hard, (b) is interesting, (c) is bookwork
2005B3Calculus (distributions, l'Hopital)OK* ((c) is hard)
2005B4Calculus (optimisation, Envelope Theorem)OK, though (b) is bookwork
2005B5Statistics (estimators)Seems easy but not clear what they want
2005B6Statistics (moment generating functions, hypothesis testing)Seems easy but not clear what they want
2006A1Statistics (estimators)OK
2006A2Statistics (estimators)OK
2006A3Statistics (estimators)(a) Requires a principle not taught (b) is badly-worded and identical to a question in the previous year
2006A4Calculus (misc)OK*
2006A5Calculus (Mean Value Theorem)Great idea for a question, messed up by MVT
2006A6Calculus (coupled differential equations)OK
2006A7Linear Algebra (Markov)OK
2006A8Linear Algebra (misc)OK (bit simple)
2006A9Linear Algebra (portfolios)OK
2006B10Statistics (estimators)For b read beta; OK but identical to an examples sheet question
2006B11Statistics (Bayes)OK except that (a) is ambiguous and (c) is ambiguous in whether you need to prove result for mean of Beta distribution
2006B12Calculus (stationary values)OK* though ignore (a) initially
2006B13Calculus (homogeneous functions/Lagrange)Identical to 2003 A6 :-(
2006B14Linear Algebra (input/output models)OK if you can be bothered
2006B15Linear Algebra (vector spaces)OK except (d) is not clear
2007A1Linear Algebra (IS-LM)OK except we don't have enough info on coefficients for (b)
2007A2Linear Algebra (simultaneous eqns)OK (quite interesting but a bit messy)
2007A3Linear Algebra (eigenvalues and Markov)(a) depends on your definition of eigenvalues/vectors (b) OK
2007A4Calculus (misc)Doable but tiresomely theoretical
2007A5Calculus (misc)OK but not easy
2007A6Calculus (coupled and uncoupled differential equations)OK*
2007A7Statistics (probability density functions)OK*
2007A8Statistics (moment generating functions)OK
2007A9Statistics (estimators)OK
2007B10Linear Algebra (matrices)OK
2007B11Linear Algebra (vector spaces)(a) regurgitate your lecture handout (b) OK*
2007B12Calculus (Lagrange)Pointlessly messy - I gave up
2007B13Calculus (misc)(b) is gory and tiresome
2007B14Statistics (estimators)Doable though a bit odd; I assume (b) means possible *unbiased* estimator
2007B15Statistics (maximum likelihood estimators)Doable but a bit odd; I assume alpha0 is still zero in (d)
2008A1Linear Algebra (determinants)OK (quick)
2008A2Linear Algebra (linear dependency)OK ((b) not easy)
2008A3Linear Algebra (in/definite matrices)OK
2008A4Calculus (continuity/differentiability)(c) is interesting; rest OK but dull
2008A5Calculus (misc)Avoid (unusual, ambiguous and confusing)
2008A6Calculus (misc)Avoid (unusual, confusing in the sheer detail, and seems incomplete)
2008A7Statistics (probability set theory)OK (quick)
2008A8Statistics (probability distribution functions)OK if you've seen it before, otherwise hard
2008A9Statistics (hypothesis testing)Similar to a supervision question, and not very clear
2008B10Linear Algebra (vector spaces: securities and portfolios)Challenging conceptually and horrendous in the detail
2008B11Linear Algebra (coupled difference equations)Infamous in that r1=2, not 0.2, quite long and error prone
2008B12Calculus (misc)Avoid (unusual, long, confusing, unclear)
2008B13Calculus (optimisation)OK-ish
2008B14Statistics (prior/posterior probability distributions)OK but very simple
2008B15Statistics (maximum likelihood estimators)OK, though I think their hint in (b) is invalid
2009A1Linear Algebra (determinants)OK (quick)
2009A2Linear Algebra (simultaneous eqns)OK (quick but useful)
2009A3Linear Algebra (vector spaces)OK (quick and easy)
2009A4Statistics (expectations)Seems to need strict convexity rather than just convexity?
2009A5Statistics (moment generating functions)OK (good)
2009A6Statistics (Bayes)Repeat of 2006 B11
2009A7Statistics (regression)Hard!
2009A8Calculus (functions)OK
2009A9Calculus (difference equations)OK
2009A10Calculus (differentiation)Near-identical to a supervision question
2009B11Linear Algebra (ISLM)(a) is 1st year material, (b) is tiresome
2009B12Linear Algebra (eigenvalues and eigenvectors)Long and tedious but not difficult
2009B13StatisticsAvoid (partly interesting but needs concepts not taught)
2009B14Statistics (regression, maximum likelihood estimators)Needs matrix notation and unclear in places what they want
2009B15Calculus (optimisation)Fairly easy
2009B16Calculus (optimisation)Confusing in places but OK if you can follow it
2010A1Linear Algebra (vector spaces/linear dependency)Interesting but (b) is quite time-consuming, and not easy overall
2010A2Linear Algebra (simultaneous eqns)OK*
2010A3Linear Algebra (singular matrices)OK, except (a) can be done in more than one way, hence potentially mucking up (b)
2010A4Calculus (limits)(a) useful (b) not easy if you've not seen it before
2010A5Calculus (implicit function theorem)OK (easy)
2010A6Calculus (optimisation)OK (easy if you understand the question)
2010A7Statistics (regression)Horrendous
2010A8Statistics (probabilities)Trivial
2010A9Statistics (Chebyshev)OK (quite quick)
2010B10Linear Algebra (misc)(a) OK though fiddly (b) quite hard (c) hard
2010B11Linear Algebra (vector spaces/simultaneous eqns)(a) confusing and quite hard (b) tedious
2010B12Calculus (difference equations)OK except (c) is a bit vague as to what they want
2010B13Calculus (optimisation)OK*
2010B14Statistics (Bayes)OK, in places a bit confusing or vague
2010B15Statistics (maximum likelihood estimators)Unfair to expect you to judge how to handle censored data, in my view
2011A1Linear Algebra (traces and suffix notation)OK (quick)
2011A2Linear Algebra (vector spaces/linear dependency)OK
2011A3Linear Algebra (quadratic forms and definiteness)OK (quick)
2011A4Calculus (functions)OK
2011A5Calculus (limits)OK*
2011A6Calculus (differential equations)OK (quick)
2011A7Statistics (expectations, variances, Taylor Series)OK once you know
2011A8Statistics (Bayes)OK
2011A9Statistics (estimators)OK
2011B10Linear Algebra (simultaneous equations / linear mappings)OK, though (a) is 2003A1, (b) looks scary but isn't so bad
2011B11Linear Algebra (ISLM / convex functions / misc)(b) is increasingly tough, rest OK
2011B12Calculus (optimisation)OK but too easy for Section B
2011B13Calculus (Gini Index - unusual)Hard if you've never encountered Gini Indexes
2011B14Statistics (Chebyshev)Bit confusing but OK
2011B15Statistics (maximum likelihood estimators)OK but too easy for Section B
2012A1Linear Algebra (vector spaces)OK
2012A2Linear Algebra (eigenvalues and vectors)Very quick but useful*
2012A3Linear Algebra (orthogonal matrices, quadratic forms and definiteness)Very easy
2012A4Statistics (Bayes)OK (quick)
2012A5Statistics (Neyman-Pearson, UMP tests)OK* though too long for Section A
2012A6Statistics (maximum likelihood estimators)OK*
2012A7Calculus (functions, convexity)OK*
2012A8Calculus (functions, optimisation)OK though hard if you aren't used to (b)
2012A9Calculus (optimisation)Hard going
2012B10Linear Algebra (ISLM and Cramer's Rule)OK but too easy for Section B
2012B11Linear Algebra (matrices, determinants, induction)OK* though too short for Section B
2012B12Statistics (Chebyshev)OK though too short for Section B
2012B13Statistics (maximum likelihood estimators)Long, confusing as to what they want in places
2012B14Calculus (functions, Fundamental Theorem of Calculus)OK though too short for Section B
2012B15Calculus (Bidding functions, utility)Odd but doable and quite short
2013A1Linear Algebra (eigenvalues and vectors)OK*
2013A2Linear Algebra block matrices)Pretty hard unless you spot it
2013A3Linear Algebra (linear dependency)OK (quick)
2013A4Statistics (estimators)OK*
2013A5Statistics (matrix formulation of OLS)Boring bookwork
2013A6Statistics (moment generating functions, estimators)Not ideal in that it needs Jensen's Inequality but unclear that one is allowed to assume it
2013A7Calculus (functions, convexity, Taylor)OK (very easy)
2013A8Calculus (integration)OK (very easy)
2013A9Calculus (optimisation)OK*
2013B10Linear Algebra (input/output models)OK, though a bit ambiguous
2013B11Linear Algebra (determinant proofs)Boring proof
2013B12Statistics (maximum likelihood estimators)Ridiculously long
2013B13Statistics (Bayes)OK
2013B14Calculus (functions, differentiability)OK* though (e) ambiguous
2013B15Calculus (difference equations)OK except needs complex numbers
2014A1Linear Algebra (properties of matrices and determinants)OK
2014A2Linear Algebra (vector spaces)OK (very easy)
2014A3Linear Algebra (orthogonal matrices)OK
2014A4Statistics (moment generating functions)OK
2014A5Statistics (Bayes)Not entirely clear what is wanted
2014A6Statistics (Chebyshev)OK
2014A7Calculus (functions)OK (not easy unless you spot the method)
2014A8Calculus (quasiconcavity)OK
2014A9Calculus (optimisation)Crazy: probably a mistake in question
2014B10Linear Algebra (vector space bases)OK except (c) is ambiguous as to "smallest"
2014B11Linear Algebra (Markov)OK unless you do (b) in fractions like I did
2014B12Statistics (estimators)Too long; (c) unclear on definition of Xi
2014B13Statistics (maximum likelihood estimators)Too long; (c) somewhat scary but OK
2014B14Calculus (integration)A bit odd, especially (c), where it is best to ignore the formula given
2014B15Calculus (differential equations)OK except for the phase plot
2015A1Linear Algebra (vector spaces)OK*
2015A2Linear Algebra (vector spaces)(c) is weird; rest largely OK
2015A3Linear Algebra (eigenvalues and vectors)Not obvious what the best method is.
2015A4Statistics (Chebyshev)OK
2015A5Statistics (Bayes)Repeat of 2009 A6
2015A6Statistics (estimators)OK*
2015A7Calculus (functions)OK
2015A8Calculus (Misc)OK
2015A9Calculus (optimisation)Not sure what this is getting at
2015B10Linear Algebra (vector space bases)Fairly straightforward
2015B11Linear Algebra (Markov-ish)Question initially unclear
2015B12StatisticsRepeat of 2009 B13
2015B13Statistics (estimators)Too long; (d) unclear re large/small sample
2015B14Calculus (Misc)Very quick
2015B15Calculus (differential/difference eqns)OK if you understand the notation

Ian Rudy (graphic containing email address for iar1)