QCE Mathematical Methods past exams 2020–2025, by year and topic

The rest of the syllabus

Question-level mapping for these areas is still being verified. Every official paper covering them is in the year table above.

• Further calculus (Unit 3, Topics 1–4) — Differentiation of exponential and logarithmic functions · Differentiation of trigonometric functions and further differentiation rules (product, quotient, chain) · Further applications of differentiation (curve sketching, optimisation, rates of change) · Introduction to integration (antidifferentiation, integrating as the reverse of differentiation, displacement from velocity/acceleration)
• Introduction to statistics (Unit 3, Topic 5) — Discrete random variables and probability distributions · Bernoulli distributions · Binomial distributions and their use in modelling repeated independent trials
• Further integration (Unit 4, Topic 1) — Fundamental theorem of calculus and definite integrals · Using sums (e.g. rectangles) to estimate the area under curves · Applications of integration to area and other contexts
• Trigonometry (Unit 4, Topic 2) — Sine rule including the ambiguous case · Cosine rule · Area of a triangle formula · Modelling problems in two and three dimensions (bearings, directions, angles of elevation/depression)
• Continuous random variables and the normal distribution (Unit 4, Topic 3) — General continuous random variables and probability density functions · Identifying contexts suitable for normal modelling · Normal distribution notation X ~ N(μ, σ²) · Calculating probabilities and quantiles for normal distributions
• Sampling and proportions (Unit 4, Topic 4) — Concept and purpose of random sampling · Distribution of sample proportions · Point estimates for population proportions
• Interval estimates for proportions (Unit 4, Topic 5) — Confidence intervals for a population proportion · Margin of error and its relationship to sample size · Interpreting and calculating approximate confidence intervals in context
• Surds, algebra, functions and probability (Units 1–2 foundations, examinable groundwork) — Surds and index laws · Relationships between variables, functions and their graphs · Binomial theorem and expansion of powers of a binomial · Quadratic, cubic and reciprocal functions · Trigonometric functions and equations · Probability fundamentals, conditional probability and independence