QCE Essential Mathematics past exams 2023–2025, 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.

• Unit 3 — Calculations — Estimation, decimal rounding, percentages, ratios and consistent units support every topic. Check whether a context requires rounding up, down or to a given precision. Show a formula or a clear calculation pathway, carry unrounded intermediate values, then interpret the answer in context.
• Unit 3 — Measurement — Describe prisms, pyramids and their nets. Work with metric length, area, volume, capacity and mass; calculate perimeter, arcs, surface area and volume. Identify exposed surfaces in compound objects and state when a base or join is excluded. Convert squared and cubed units using the correct powers of the conversion factor.
• Unit 3 — Scales, plans and models — Read scale drawings and find actual dimensions before calculating perimeter, area, quantity or cost. Use Pythagoras and right-triangle trigonometry for lengths and angles, including elevation and depression. Label a diagram, identify the relevant angle and distinguish slant length from perpendicular height.
• Unit 3 — Probability and relative frequencies — List possible outcomes systematically with arrays and tree diagrams. Use probabilities in everyday settings, compare observed relative frequency with a theoretical model, and conduct or interpret simulations. Describe replacement, independence and equal-likelihood assumptions; increasing the number of trials does not guarantee exact agreement with a theoretical probability.
• Unit 4 — Bivariate graphs and linear models — Use Cartesian coordinates and linear functions. Describe scatterplot direction, form and strength, use a line of best fit and correlation coefficient, and distinguish prediction within the data from extrapolation. Explain why association alone cannot establish causation and interpret each variable in its context.
• Unit 4 — Summarising and comparing data — Calculate and interpret mean, median, mode, range, interquartile range and standard deviation. Read quartiles, deciles and percentiles from displays, construct or interpret box plots, histograms and back-to-back stem plots, and compare groups with context, centre, spread and unusual values.
• Unit 4 — Loans and compound interest — Compare simple and compound interest with consistent rate and time units. Use the annual compound-interest relationship and technology to investigate payment periods. Build and interpret reducing-balance loan tables or spreadsheets, separating interest charged, repayment and remaining principal. Treat every supplied rate or fee as a hypothetical task input.