Applying for Maths at Cambridge | Taylor Tuition

What Makes Cambridge Maths Unique

Cambridge's Mathematics course offers exceptional depth and breadth, taught by world-leading researchers who've shaped modern mathematical thought. Unlike many universities that separate pure and applied mathematics, Cambridge integrates both from the outset, allowing you to explore everything from abstract algebra to theoretical physics within a single degree programme.

The tripos system grants remarkable flexibility. After Part IA (first year), you can continue with pure Mathematics, switch to Mathematics with Physics, or pursue the highly theoretical Mathematical Tripos Schedule B. This adaptability means your interests in second year needn't match those at application—the course evolves with your developing mathematical identity.

Cambridge's supervision system transforms how you learn. Typically, you'll attend two to three supervisions weekly in pairs or small groups, working through problem sheets with world-class mathematicians. This intensive, personalised teaching accelerates understanding far beyond lecture-based learning alone.

Competition Statistics

Mathematics remains one of Cambridge's most competitive subjects. Recent application cycles saw approximately 1,800 applicants competing for around 250 places—a success rate of roughly 14%. However, this varies significantly between colleges, with some receiving far more applications than others for the same number of places.

Successful applicants typically achieve A*A*A* at A-Level or 42-43 points in the IB. The median STEP performance for offer-holders sits at grade 1 in STEP 2 and STEP 3, though variations exist depending on overall application strength.

What Admissions Tutors Seek

Cambridge tutors prioritise mathematical potential over current knowledge. They're searching for students who:

Demonstrate exceptional problem-solving ability rather than simply memorising techniques
Show genuine curiosity about mathematics beyond the curriculum
Can think creatively when approaching unfamiliar problems
Communicate mathematical reasoning clearly and precisely
Persist with challenging concepts rather than becoming discouraged

Your grades matter, but tutors care more about how you think mathematically than what you've already covered.

Entry Requirements

A-Level Requirements

Cambridge requires A*A*A at A-Level, with both the A* grades in Mathematics and Further Mathematics. Some colleges accept A*A*A with the A*s in Mathematics and one other subject if Further Mathematics isn't available at your school, but this significantly reduces your chances. Physics A-Level, whilst not required, strengthens applications for those interested in applied mathematics.

IB Requirements

IB candidates need 40-42 points overall, with 776 at Higher Level. Mathematics: Analysis and Approaches HL is essential; Mathematics: Applications and Interpretation HL is insufficient. Physics HL complements applications well but isn't mandatory.

Additional Qualifications

Beyond school qualifications, Cambridge assesses applicants using STEP (Sixth Term Examination Paper). Typical offers require grade 1 in both STEP 2 and STEP 3, though some colleges may request 1,1 or occasionally accept 1,2 combinations for particularly strong candidates.

Participation in mathematical competitions—British Mathematical Olympiad, UKMT Senior Challenge, or international equivalents—demonstrates genuine engagement beyond the classroom. Whilst not required, strong performances indicate the problem-solving aptitude Cambridge values.

Application Timeline

UCAS Deadline: 15 October

Your UCAS application, including personal statement and teacher reference, must reach Cambridge by 6pm UK time on 15 October. Unlike most university applications, this deadline is absolute—late applications are rejected regardless of circumstances.

Admissions Test: Late October

Until 2024, Cambridge used the TMUA (Test of Mathematics for University Admission). From the 2025 entry cycle onwards, you'll sit college-specific written assessments during interview week in December rather than a pre-interview test. This represents a significant change to the application process.

Interview Period: Early to Mid-December

Mathematics interviews typically occur in the first two weeks of December. Most applicants attend their chosen college, though some colleges pool strong candidates who weren't initially selected by their first-choice college. Expect two to three interviews, each lasting 20-30 minutes, focussed entirely on mathematical problem-solving.

Decisions: Mid-January

Cambridge releases decisions in mid-January. Successful applicants receive conditional offers, almost always requiring specific STEP grades. You'll then have until June to prepare for these challenging examinations.

STEP Examinations: June

STEP 2 and STEP 3 occur in June, after A-Levels. Results arrive in mid-August. Meeting your STEP conditions confirms your place; missing them by a small margin might trigger a college phone call, but significant underperformance results in rejection.

Personal Statement

What to Include

Your personal statement should demonstrate why you're passionate about mathematics and ready for Cambridge's intensive course. Focus on:

Mathematical topics you've explored beyond the curriculum
Books, papers, or online resources that've influenced your thinking
Problems you've wrestled with and what the process taught you
How your mathematical understanding has developed over time

Cambridge tutors read hundreds of statements. Specificity matters enormously—mentioning you've read "several popular mathematics books" says nothing, whilst discussing how a particular theorem in Hardy's "A Mathematician's Apology" changed your perspective on mathematical beauty demonstrates genuine engagement.

Subject-Specific Focus

Mathematics applications should be 90-95% subject-focussed. Tutors care little about your Duke of Edinburgh award or football captaincy unless you can link them meaningfully to mathematical thinking. Every sentence should reinforce that you're intellectually equipped and passionate about mathematics.

Avoid superficial name-dropping. Don't claim to have "studied Galois theory" if you've merely watched a YouTube video. Tutors often ask interview questions based on personal statements, and false claims become immediately apparent.

Demonstrating Passion and Potential

Rather than stating you're passionate about mathematics, show it through your actions. Discuss the problem that kept you thinking for weeks, the concept that initially confused you but eventually clicked, or the theorem whose proof you found unexpectedly elegant.

Tutors value intellectual humility. Acknowledging what you don't yet understand whilst showing determination to learn demonstrates more potential than pretending comprehensive knowledge.

Common Mistakes

Avoid these typical errors:

Generic statements applicable to any mathematics course at any university
Lengthy descriptions of what you've studied in lessons (tutors already know the syllabus)
Exaggerated claims about mathematical knowledge or abilities
Excessive detail about extra-curricular activities unrelated to mathematics
Poor writing—spelling errors, unclear structure, or convoluted sentences suggest careless thinking

Admissions Tests

Current Requirements

From 2025 entry onwards, Cambridge no longer requires pre-interview admissions tests for Mathematics. Instead, you'll complete written assessments during your December interview period. These college-specific papers test problem-solving ability using material from the standard A-Level or IB curriculum, though questions demand deeper understanding than typical examinations.

Assessment Format

Expect two to three written papers during interview week, each lasting 60-90 minutes. Questions focus on:

Pure mathematics (algebra, calculus, proof techniques)
Applied mathematics (mechanics, statistics)
Problem-solving using unfamiliar contexts
Mathematical reasoning and communication

Unlike A-Levels, these papers contain far fewer questions, each requiring extended solutions. You're assessed on your approach, reasoning quality, and ability to tackle problems you haven't seen before.

Preparation Strategy

Begin preparing in summer before Year 13. Focus on:

Strengthening your grasp of A-Level Further Mathematics topics
Practising STEP papers (excellent preparation despite no longer being a pre-interview requirement)
Working through Cambridge's published specimen papers
Developing problem-solving stamina—work on difficult problems for extended periods without hints
Learning to show your working clearly, even when uncertain about the final answer

Preparation requires consistent effort over months, not cramming in weeks. Allocate 5-10 hours weekly from September onwards.

Detailed Test Guidance

For comprehensive preparation strategies, worked examples, and practice resources, see our detailed STEP Preparation Guide, which remains highly relevant for Cambridge's written assessments.

Interview Preparation

Interview Format

Mathematics interviews are working sessions rather than interrogations. You'll typically have two to three interviews across different colleges, each lasting 20-30 minutes. One or two mathematicians will present problems and observe how you approach them.

Expect to work at a whiteboard or on paper whilst thinking aloud. Interviewers want to understand your thought process, so verbalising your reasoning—even when uncertain—proves crucial.

Question Types

Interview questions fall into several categories:

Extensions of A-Level topics: "We know sin²x + cos²x = 1. What about sin³x + cos³x?"
Unfamiliar problems requiring known techniques: "How many ways can you tile a 2×n rectangle with 1×2 dominoes?"
Proofs and reasoning: "Prove there are infinitely many prime numbers"
Questions starting simple but increasing in complexity: Interviewers guide you towards increasingly difficult versions of a problem

Some questions deliberately lack obvious starting points. Tutors want to see how you react when stuck—do you try different approaches, ask clarifying questions, or simply give up?

How to Prepare

Effective interview preparation involves:

Practising thinking aloud whilst solving problems—this feels unnatural initially but becomes essential
Working through Cambridge's published interview questions and specimen papers
Attempting problems from STEP papers and mathematical olympiads
Conducting mock interviews with teachers or tutors experienced in Oxbridge admissions
Learning to respond constructively to hints rather than becoming flustered
Developing comfort with saying "I don't know" followed by "but here's what I'd try"

Mock interviews prove invaluable. Being questioned whilst solving unfamiliar problems creates pressure you cannot replicate through solo practice.

What Interviewers Assess

Tutors evaluate:

Problem-solving approach—do you break complex problems into manageable pieces?
Mathematical intuition—can you spot patterns and make sensible conjectures?
Resilience—how do you respond when stuck or when your first approach fails?
Communication—can you explain your reasoning clearly?
Receptiveness to guidance—do you incorporate hints effectively?
Intellectual curiosity—do you ask insightful questions when uncertain?

Getting stuck is expected and acceptable. What matters is demonstrating the thinking skills that indicate you'll thrive in Cambridge's intensive mathematical environment.

Taylor Tuition's Oxbridge Support

Specialist Oxbridge Tutors

Our Oxbridge admissions tutors graduated from Cambridge or Oxford and understand precisely what admissions tutors seek. They've navigated this process themselves and subsequently guided dozens of students to Oxbridge offers.

Working with tutors who've experienced Cambridge Mathematics from the inside provides insights no generic admissions consultant can match. They know how the course actually operates, what supervisors value, and how interview questions typically develop.

Personal Statement Guidance

We help you craft a personal statement that demonstrates genuine mathematical passion and intellectual depth. Our tutors:

Review multiple drafts with detailed feedback
Suggest mathematical topics and resources aligned with your interests
Ensure your statement avoids common pitfalls
Help you articulate why Cambridge specifically suits your mathematical aspirations

Your statement should be authentically yours whilst presenting your mathematical journey compellingly.

Admissions Test Preparation

Our STEP and Cambridge written assessment preparation combines:

Regular problem-solving sessions developing examination technique
Comprehensive coverage of challenging Further Mathematics topics
Practise with questions mirroring Cambridge's assessment style
Strategies for managing time pressure and partial credit
Building the mathematical maturity Cambridge expects

We begin preparation early—ideally summer before Year 13—allowing gradual skill development rather than last-minute cramming.

Mock Interviews

Our mock interviews replicate Cambridge's format precisely. Conducted by Oxbridge graduates, these sessions:

Use questions similar to those asked at actual Cambridge interviews
Help you develop comfort thinking aloud under pressure
Provide detailed feedback on your problem-solving approach
Identify areas requiring further preparation
Build confidence through repeated practice

Most students find their first mock interview challenging. By the third or fourth, they're engaging naturally with unfamiliar problems—exactly what Cambridge demands.

Our Approach

Taylor Tuition's Oxbridge programme is:

Personalised: We tailor preparation to your current level, learning style, and target colleges
Intensive: Successful applications require substantial preparation—we ensure you're ready
Realistic: We're honest about your chances and what improvement requires
Comprehensive: From initial strategy through to interview week, we support every application stage

Cambridge Mathematics applications demand exceptional preparation. We provide the expertise, resources, and guidance to maximise your chances.

Begin Your Cambridge Journey

Ready to pursue Mathematics at Cambridge? Contact us today to discuss how our Oxbridge specialists can support your application. We'll develop a personalised preparation plan aligned with your timeline, current abilities, and aspirations.

Securing a Cambridge offer requires starting early and preparing thoroughly. Our tutors ensure you approach every application stage—personal statement, admissions tests, interviews—with confidence and competence.