Mathematics 1

The compulsory core-maths module every ESAT candidate sits: number, algebra, graphs, geometry, trigonometry, statistics and probability.

Number

9 min read

Fractions, indices, standard form, surds, rounding and estimation: the fluency the whole test is built on.

6 min read

SI prefixes, compound units like speed, density and pressure, and converting confidently between them.

8 min read

Sharing in a ratio, direct and inverse proportion, percentage change and compound growth and decay.

10 min read

Expanding, factorising, the laws of indices in algebra, rearranging formulae and generating sequences.

9 min read

Linear and simultaneous equations, the three ways to solve a quadratic, and solving linear inequalities.

10 min read

Straight lines, the standard curve shapes, gradients and areas under graphs, and reading kinematics graphs.

11 min read

Angles, polygons, congruence and similarity, Pythagoras, the circle theorems, mensuration and vectors.

7 min read

SOH-CAH-TOA in right-angled triangles, the exact values you must know, and the sine and cosine graphs.

7 min read

Averages and spread, grouped data and frequency density, and reading scatter graphs and correlation.

7 min read

Single and combined events, the AND/OR rules, tree diagrams and expected outcomes.