UKMT Senior Challenge Full Mock — Paper 13
UKMT Senior Mathematical Challenge practice paper 13: 30 questions in 90 minutes, marked +4 / -1, matching the real SMC penalty for guessing, with a worked so
About this test
UKMT Senior Challenge Full Mock — Paper 13 is a full 30-question paper you attempt online in 90 minutes. It follows the American Mathematics Competition 10 pattern, so the timing, the question style and the marking match the real exam. Each correct answer scores 4 and each wrong answer loses 1. Guessing carries a real cost, exactly as it does on the day.
You get your score the moment you submit, question by question, with a step-by-step solution to every problem. 25 questions in 75 minutes. A high score qualifies for the AIME.
What it covers
Sections
- Logarithms — 2 questions
- Trigonometry — 2 questions
- Roots of a quadratic — 2 questions
- Geometric series — 2 questions
- Modular arithmetic — 2 questions
- Arithmetic series — 2 questions
- Binomial coefficients — 2 questions
- Law of cosines — 2 questions
- Algebraic manipulation — 2 questions
- Divisors — 2 questions
- Floor sums — 2 questions
- Diophantine equations — 2 questions
- Complex numbers — 2 questions
- Binomial identities — 2 questions
- Functional equations — 2 questions
Difficulty spread
- 4 medium questions
- 14 hard questions
A look at the questions
Questions people ask
How is this paper marked?
Marked +4 / -1, matching the real SMC penalty for guessing. A blank always scores zero.
How long should it take?
90 minutes, matching the real challenge. The questions get harder towards the end, so do not expect to finish — deciding which to attempt is part of the skill.
Are solutions included?
Yes, every question has a worked solution that names the method, so a wrong answer tells you what to revise.