The links below provide examples of solutions and mark schemes for some questions on the 2011 Part IA examination. There are example solutions to one short and two long questions per subject.

Please read this comment on the purpose of these solutions, and how best to prepare for your exams.

- Analysis I
- Vectors and Matrices
- Differential Equations
- Probability
- Groups
- Vector Calculus
- Dynamics and Relativity
- Numbers and Sets

### Comment on the Use of these Examples

These solutions were written by graduate students who have been through the Tripos themselves. The mark schemes were those used by the actual Examiners in 2011.

Coming up to your first proper exams in Cambridge, it is possible to worry needlessly about "what is an alpha?" (to which the only sensible answer is a mark of 15+/20) or "how much should I write?" (to which the only sensible answer is that it depends on what the question is asking you to do).

These examples of mark schemes and solutions are provided in an attempt to dispel any hints of mystique and to reduce your worries about how much is expected. We hope that after glancing through them once you might conclude that the mark schemes are much as you might expect and the solutions are the sort of thing your supervisors have been encouraging you to write all year! If you have any remaining general concerns, you should discuss them with your Director of Studies or supervisors.

But you certainly need not spend time studying the details of these particular questions, memorising bits of the answers, copying their layout or worrying about whether the statement of a particular theorem is worth 2 or 3 marks. That would be missing the point! Such things are not what you should be thinking about when preparing for your exams - and are not what we are trying to test, which is a combination of knowledge and understanding of the theory presented in lectures and the ability to apply that knowledge to solve mainly *unseen* problems.

Questions vary (in content, length and difficulty) from one year to the next (as do the examiners). Hence, in terms of exam preparation, there is no substitute for doing many past questions yourself (perhaps self-timed), and having your solutions checked over and commented on by your supervisors. This will give you experience of the range of things you might be asked about and of different styles of question. When combined with all of the knowledge, skills and mathematical maturity that you have acquired throughout the year, this will put you in the best possible position to approach your exams with confidence.