This course prepares advanced students for STEP 2 and STEP 3 with a full programme built around the skills that actually determine performance: solving unfamiliar problems, writing rigorous multi-step solutions, choosing questions strategically, and working accurately under time pressure.
It begins with a diagnostic assessment and personal study plan so students can identify topic gaps, recurring errors, pacing issues, and weaknesses in written argument. From there, the course develops the underlying mathematics in depth rather than relying on shortcuts, with regular mistake-log work, timed practice, and cumulative review.
Core pure mathematics topics include algebraic methods, functions and graphs, equations and inequalities, sequences and series, proof techniques, coordinate geometry, trigonometry, differential calculus, integral calculus, differential equations, and complex numbers. Each topic is taught with attention to the kinds of justification STEP requires: clear notation, valid algebraic steps, explicit assumptions, careful handling of restrictions, and well-structured conclusions.
The course also covers the applied content needed for STEP preparation. In mechanics, students work on modelling assumptions, kinematics, Newton's laws, connected particles, forces on slopes, work-energy methods, momentum, and projectile motion. In probability and statistics, they study counting, conditional probability, distributions, expectation, variance, density functions, and interpretation of statistical models.
Alongside topic teaching, students learn how the STEP papers are structured, how STEP 2 and STEP 3 differ, what examiners reward, and how to manage the paper intelligently. This includes question selection, timing frameworks, decision rules for abandoning or revisiting questions, and methods for securing marks through readable and logically complete solutions.
Learning activities are concrete and exam-focused:
- diagnostic tasks to identify strengths, gaps, and priority topics
- worked examples showing full STEP-style reasoning, not just final answers
- guided and independent problem sets covering pure mathematics, mechanics, and statistics
- proof-writing practice for direct proof, contradiction, induction, case splitting, and invariants
- timed drills and paper-navigation practice to improve pacing and question choice
- mistake-log activities to track errors, corrections, and prevention strategies
- mixed-topic challenge problems that combine algebra, geometry, calculus, mechanics, or probability
- mock-paper preparation with review of strategy, presentation, and final improvement priorities
By the end of the course, students should be able to:
- analyse STEP questions efficiently and choose sensible starting points
- write complete long-form mathematical solutions with clear logical structure
- handle advanced pure mathematics topics with better accuracy and justification
- solve mechanics and probability or statistics problems using correct modelling assumptions
- manage time across a paper and adapt when a solution path stalls
- use diagnostic evidence and error analysis to continue improving after each practice set or mock paper
This course is designed for students applying to highly selective mathematics or related degree programmes where STEP performance matters, and it is especially useful for learners who need both stronger mathematics and a more reliable exam method.