University Maths Exam Revision
Go into a university maths exam able to produce the standard proofs and methods under time pressure, from memory.
This is a starting point — make it yours
Use this goal to build your own roadmap — tailored to you and starting fresh.
Week 1: diagnose
Maths revision fails when it becomes reading. Find out what you cannot do, by trying to do it.
Attempt a past paper cold and mark it strictly~4h
Full time, closed book. Mark to the scheme, giving no credit for "I knew that really" — in the exam you won't get it either.
Done when: one paper is marked and you have a percentage you believe.
Sort every topic into can-do, shaky, and cannot-start~2h
Be honest about the middle category — shaky topics are where the most marks are recoverable, because a small amount of work moves them.
Done when: every syllabus topic sits in exactly one of the three lists.
List the standard proofs the exam expects~2h
Most maths courses have a known set of bookwork proofs that recur nearly every year. Find them from past papers and lecture notes — they are the most reliably earnable marks on the paper.
Done when: the list exists and you know how many marks it typically represents.
Weeks 2-3: calculus and analysis
Technique first, then the proofs. Both are examined and they need different practice.
Drill integration techniques to speed~6h
Substitution, by parts, partial fractions, trigonometric substitution. Twenty integrals in a sitting, timed. This is muscle memory — technique you have to think about is technique that will cost you minutes you don't have.
Done when: you can do twenty standard integrals in forty minutes with at most two errors.
Write out the epsilon-delta and convergence proofs from memory~6h
Limit definitions, continuity, convergence of a sequence, the standard series tests. Closed book, then compare against your notes line by line.
Done when: you can produce three standard proofs correctly with the book shut.
Do every calculus question from three past papers~8h
By topic rather than by paper, so you get repetition on the same idea. Mark each one before moving on — an uncorrected mistake practised ten times is worse than no practice.
Done when: all calculus questions from three papers are done and marked.
Weeks 3-4: linear algebra and probability
The two topics where students most often lose marks to carelessness rather than to not knowing.
Practise eigenvalues, diagonalisation and rank by hand~6h
Small matrices, on paper, no calculator. Exams test whether you can do it, not whether numpy can. Check every answer by multiplying back.
Done when: you can diagonalise a 3x3 matrix correctly in under fifteen minutes, twice running.
Rebuild the standard distributions from their definitions~6h
Binomial, Poisson, normal, exponential: pdf, expectation, variance, and when each is the right model. Derive the expectations rather than memorising them — derivations survive exam nerves better than memorised formulae.
Done when: you can state and derive the mean and variance of four distributions from scratch.
Do every linear algebra and probability question from three papers~8h
Same method as calculus: grouped by topic, marked immediately. Note which errors are conceptual and which are arithmetic — they need completely different fixes.
Done when: all such questions are done, marked, and errors are categorised.
Build a one-page formula and method sheet~3h
Written from memory, corrected afterwards. The act of deciding what belongs on one page forces you to distinguish what you actually need from what merely appeared in lectures.
Done when: one page exists and you can reproduce it from memory in ten minutes.
Weeks 5-6: papers and pressure
Nothing new. Full papers, strict marking, and closing the specific gaps they reveal.
Sit three full papers under exam conditions~12h
Timed, closed book, no interruptions. Mark against the scheme the same day while you can still remember your reasoning.
Done when: three papers are done and marked, with scores recorded.
Rewrite every question you dropped marks on~8h
Not read the solution — write the full answer out yourself, correctly, from the start. Reading a worked solution and understanding it is the single most convincing illusion in maths revision.
Done when: every dropped question has been re-answered in full without reference.
Practise the bookwork proofs to a time limit~5h
These are the marks you can guarantee. Aim to write each in well under its allocation so that they buy time for the harder questions.
Done when: every proof on your list can be written correctly inside its time allocation.
Decide your question order and stuck-rule in advance~2h
Which question you start with, how long before you abandon one and come back, and what you write when you cannot finish — partial method marks are real and are routinely left on the table.
Done when: the plan is written and used in a full paper without overrunning.