This course prepares students for the ESAT Mathematics 1 and Mathematics 2 modules required by many UK STEM degree programmes. It combines full curriculum teaching with ESAT-specific problem solving, timed multiple-choice technique, and a diagnostic-led study plan.
Students begin by learning how the ESAT mathematics modules are used, how to choose modules sensibly for different applications, and how timing, scoring, and question handling work in practice. An initial diagnostic across both modules is then used to identify strengths, gaps, and timing issues, leading to a personal revision plan and structured error log.
Mathematics 1 coverage focuses on the core skills needed for fast, accurate non-calculator work:
- Algebra foundations: arithmetic fluency, surds, factorisation, indices, quadratics, simultaneous equations, inequalities, algebraic fractions, powers, and roots
- Functions and graphs: notation, domains, ranges, graph families, transformations, composite and inverse functions, and graphical equation solving
- Equations and sequences: linear and quadratic methods, discriminants, arithmetic and geometric sequences, recurrence relations, and short algebraic proof
- Geometry and coordinate methods: angles, polygons, area, volume, similarity, Pythagoras, distance, gradients, line equations, circles, and loci
- Trigonometry: right-angled methods, exact values, sine and cosine rules, trig graphs, equations, and modelling
- Probability, statistics, and data interpretation: sample spaces, tree diagrams, Venn diagrams, averages, charts, scatter graphs, and expected value
- Problem solving: translating words into maths, decomposing multi-step questions, estimation, bounds, unit handling, efficient method choice, and common ESAT traps
Mathematics 2 extends this into higher-level material commonly needed by competitive applicants:
- Advanced algebra: polynomial structure, factor and remainder reasoning, partial fractions, logarithms, exponentials, parameter problems, identities, and proof
- Advanced functions: rational, exponential, logarithmic, modulus, piecewise, inverse, and transformed functions, including qualitative graph analysis
- Higher trigonometry: radians, identities, transformed trig graphs, advanced trig equations, approximation awareness, and modelling
- Calculus foundations: derivatives, tangents, normals, stationary points, optimisation, integration, and simple area interpretation
- Vectors: notation, operations, position vectors, vector lines, ratios, magnitudes, and diagram-based vector problem solving
- Deeper multi-topic problem solving: parameter reasoning, case analysis, and linking algebra, graphs, and calculus
Each lesson is designed to teach the underlying mathematics rather than relying on shortcuts alone. Students work through:
- clear concept explanations
- worked examples and guided practice
- independent practice and short quizzes
- common mistake analysis
- original ESAT-style multiple-choice questions with full solutions
- cumulative review and timed drills
- mistake-log activities to target repeated weaknesses
By the end of the course, students should be able to:
- choose and prioritise the correct ESAT mathematics modules for their degree applications
- handle core and advanced mathematics topics tested in Mathematics 1 and Mathematics 2 with greater confidence
- solve multiple-choice questions more efficiently without sacrificing accuracy
- use estimation, elimination, graph interpretation, and algebraic checking under time pressure
- identify personal weak areas from diagnostics, mocks, and error-log review, then revise them systematically
This course is suitable for students applying to engineering, natural sciences, and related STEM courses who need strong preparation in both ESAT Mathematics 1 and Mathematics 2.