Prepared exclusively for Jayne & Keira
Thank you both for our conversation on 21 October. With the TMUA behind Keira since 16 October, here is how I would prepare her for what comes next: a possible interview in December, STEP in June, and top grades in Maths and Further Maths along the way. Two ways we can work together follow.
The interview, STEP and Further Maths all reward the same thing: finding the idea that opens a problem Keira has never seen before, then carrying it through cleanly. In an interview she also has to do it out loud, in front of someone, and use their hints well.
This is what my method is built to train. I have worked the STEP papers from 2006 to 2025 and tagged each question with the method that cracks it. Keira learns to recognise those methods, then to reach for them under pressure, first on paper and then out loud.
Unfamiliar problems, worked through live, with an interviewer giving hints. We train exactly that, with full mock interviews before the day.
The usual Cambridge offer asks for grade 1 in both. We work them by method, then by full timed paper.
The typical offer is A*A*A, usually with A* in Maths and Further Maths. School topics and mocks get a session whenever they need one.
From now to STEP, in five stages. Click on each step below.
Short open problems out loud in every session, first STEP questions without a time limit, and Further Maths kept comfortably ahead of school. Invitations to interview usually arrive in November.
Full mock interviews online in the run-up, with a short written test first if her College sets one. Extra hours whenever they help.
Decisions arrive in late January. If a College calls her to the winter pool, we prepare that interview too. Then STEP becomes the main thread.
STEP 2 and STEP 3 worked method by method, then full past papers, with A-level mocks and revision alongside. The STEP entry deadline falls in early May.
Final timed papers and exam strategy for STEP 2 and STEP 3 in mid to late June, alongside the A-level exams.
Mostly mathematics: problems worked through with the interviewer. The examiners want to see how Keira thinks, not a rehearsed answer.
No calculator. A typical way an interview might open.
Both exponents are multiples of 100.
2300 = 8100 and 3200 = 9100, so 3200 is larger. In an interview, the follow-up would come straight away, and it is harder: 100101 or 101100?
The official material we will draw on. Keira can start with the first two this week.
Cambridge's own interview guide for mathematics, with advice, examples and mock interview videos.
step.maths.org WatchInterviewers guiding a student through problems on large powers, graphs and tilings. The best way to see the pace of a real interview.
step.maths.org Written testsThree specimen written tests, the kind Trinity sets just before its interview. Not a bank of past interview questions.
trin.cam.ac.uk STEPFree modules for STEP 2 and STEP 3 from the Faculty of Mathematics and NRICH, with worked solutions to past questions.
maths.org/step OfficialThe typical offer, the STEP grades Colleges ask for, and the Colleges offering the flexible STEP offer for 2027 entry.
undergraduate.study.cam.ac.ukThere is no official bank of past interview questions comparable to the STEP archive. These resources are the closest thing, and the ones I recommend.
From the official Cambridge and Faculty of Mathematics pages. Each College sets its own exact interview dates.
The same coaching in both. Only the number of weekly sessions changes.
One hour a week
Two hours a week
We start with the Classic, and can move to twice-weekly later. If Keira is invited to interview, she becomes one of my priority students for December, and I keep my diary flexible for them.
For extra hours beyond either plan, just give me a little notice and we'll agree a rate for the additional time.
Because Keira is preparing three things at once, we put each session where it helps most that week.
Until December, the priority: open problems out loud and mock interviews.
From the start in small doses, then the main thread from January.
A hard topic or a set of mocks coming up: we make it the session's focus.
The objective is simple: every session moves the interview, STEP or her A-levels forward, often all three.
Yes. There are no answers to learn by heart, since the problems are new by design. What can be trained is the habit: starting on an unfamiliar problem without freezing, saying what she is trying and why, and turning a hint into progress. After a few mock interviews, that habit becomes natural, and that is what the interviewers see.
Because the same work serves twice. STEP questions are among the best interview preparation there is, and Cambridge's STEP Support Programme recommends them for exactly that. If the offer comes, it will almost certainly include STEP 2 and STEP 3, so every question worked now is a head start on June.
Nothing is lost. The problem-solving and the STEP work carry straight into her Further Maths and her other applications, and several universities, Warwick among them, use STEP in their maths offers. We would simply shift the weight of the sessions towards her A-levels and the offers she holds.
Yes. We start with the Classic and can move up to twice-weekly whenever it helps, most often when the interview invitation arrives. Once the interview is behind her, we keep whichever rhythm suits STEP and her A-levels.