Every topic on the ESAT, in one checklist.
Saved locally50 topic headings and 270 numbered points, taken from the official ESAT content specification published by UAT-UK for assessment in October 2026 and January 2027.
Which modules do you sit?
Everyone answers Mathematics 1. Most courses ask for two more, but check what your course lists before you rule anything out.
Mathematics 1
0 of 7 held
Biology
0 of 11 held
Chemistry
0 of 17 held
Physics
0 of 7 held
Mathematics 2
0 of 8 held
Mathematics 1 or Mathematics 2? Where the line falls
Mathematics 2 assumes everything in Mathematics 1 and adds the topics labelled MM. Six topics sit on both sides of the line; here is what each module covers, with the specification’s own clause numbers.
| Topic | Mathematics 1 | Mathematics 2 adds |
|---|---|---|
| Calculus | M4.14 Calculate or estimate gradients of graphs and areas under graphs, for example on distance-time and speed-time graphs. No differentiation or integration. | MM6, MM7 Differentiation of x^n (tangents, normals, stationary points) and integration (definite and indefinite, trapezium rule, dy/dx = f(x)). |
| Trigonometry | M5.18, M4.12 sin, cos and tan in right-angled triangles, exact values at 0°, 30°, 45°, 60° and 90°, and their graphs in degrees. The specification says candidates are not expected to recall or use the sine or cosine rules. | MM4 Sine and cosine rules, ½ab sin C, radians with arc length and sector area, identities and solving trigonometric equations in an interval. |
| Exponentials and logarithms | M4.12e Recognise and sketch y = k^x for positive k. | MM5 Laws of logarithms and solving a^x = b. |
| Sequences and series | M4.18, M4.19 Term-to-term and position-to-term rules; nth term of linear and quadratic sequences. | MM2 Arithmetic and finite geometric series sums, and binomial expansion with n! and nCr. |
| Circles | M5.8, M5.9 Circle vocabulary and the standard circle theorems. | MM3.2 The equation of a circle, in (x - a)² + (y - b)² = r² and expanded form. |
| Quadratics | M4.11, M4.16 Roots, turning points by completing the square, factorising and the quadratic formula. | MM1.3 Adds the discriminant and the wider theory of quadratic functions and graphs. |
Is calculus in ESAT Mathematics 1?
No. Differentiation and integration are Mathematics 2 topics (MM6 and MM7). Mathematics 1 only asks you to calculate or estimate gradients of graphs and areas under graphs, for example on a speed-time graph (M4.14).
Do I need the sine and cosine rules for ESAT Mathematics 1?
No. The specification says Mathematics 1 candidates are not expected to recall or use the sine or cosine rules (M5.18). They are Mathematics 2 content (MM4.1). Right-angled trigonometry and exact values are in Mathematics 1.
Is a calculator allowed in the ESAT?
No. Calculators may not be used in any ESAT module. You get an erasable booklet for working.
Does Mathematics 1 content appear in the science modules?
Yes. Biology, Chemistry, Physics and Mathematics 2 all assume knowledge of the Mathematics 1 topics.
Source: UAT-UK ESAT Content Specification, October 2026 and January 2027 (PDF), read 26 September 2026. Related: which modules your courses need, ESAT booking checklist, Imperial Design Engineering (Mathematics 1 and 2 only).
Topic names and identifiers follow the ESAT content specification (PDF), UAT-UK, for assessment in October 2026 and January 2027. Read it in full before you rely on any summary, including this one.