Cambridge O Level

Mathematics (Syllabus D) 4024

Core mathematics for O Level, from number and algebra to geometry, vectors and statistics, assessed across two written papers.

Exam year

Syllabus version: 2025–2027 syllabusChecked against the Cambridge syllabusExam year 2027 is covered by the 2025–2027 syllabus.

Subject review complete (21 Oct 2026). All 40 Mathematics (Syllabus D) questions were re-solved and checked against the syllabus and Cambridge mark-scheme conventions, and their auto-marking was tested with correct and incorrect answers: 26 approved as written, 14 corrected.

Paper 1 Non-calculator50%
Paper 2 Calculator50%

Original questions40

Topics covered9/9

Papers2

Mock papers2

What is assessed

2 components. Question formats: short answer, structured.

Paper 1 Non-calculator

2 h100 marksWeighting 50%

Structured and unstructured questions on any of the subject content except 1.14 Using a calculator; all questions answered on the paper with working shown.

What the paper looks like

About 25 questions worth 100 marks in 2 hours, with no calculator. Early questions are short (1–3 marks: rounding, simplifying, factorising, reading a chart); later ones are longer multi-part questions of up to about 8 marks on algebra, geometry, vectors, functions and statistics. Answers are written on the paper, often requiring exact forms (fractions, surds, terms of π). Diagrams are marked “not to scale” where appropriate, and some questions need a ruler, protractor or compasses (constructions, bearings, histograms). Common command words: Work out, Find, Simplify, Factorise, Solve, Write down, Show that, Give a reason. Method marks are available, so working must be shown.

Short answerStructuredGeometrical instruments (pair of compasses, protractor, ruler); List of formulas printed on page 2; tracing paper on request; no calculator

Checked against the Cambridge syllabus

Paper 2 Calculator

2 h100 marksWeighting 50%

Structured and unstructured questions on any of the subject content; non-exact answers to 3 significant figures, or 1 decimal place for angles in degrees, unless stated.

What the paper looks like

100 marks in 2 hours with a scientific calculator required. Papers have varied from about a dozen long, multi-part questions to over 20 shorter ones; questions range from short calculations to structured contexts with parts (a), (b), (c)(i) etc. on percentages and finance, mensuration, trigonometry (including bearings, sine and cosine rules and 3D), graphs and statistics. Tables of values, graphs to draw or read, timetables and data tables are common. Non-exact answers go to 3 significant figures (angles to 1 decimal place) unless stated; use the π key or 3.142. Command words include Calculate, Work out, Find, Draw, Plot, Sketch, Show that and Explain.

Short answerStructuredScientific calculator required (algebraic or graphical calculators not permitted); geometrical instruments; List of formulas printed on page 2; tracing paper on request

Checked against the Cambridge syllabus

Assessment overview

From the 2025–2027 syllabus. Checked against the Cambridge syllabus

All candidates

Paper 1Paper 2

Untiered: all candidates take both papers and are eligible for grades A* to E.

Assessment objective	O Level weighting
AO1 Knowledge and understanding of mathematical techniques	40–50%
AO2 Analyse, interpret and communicate mathematically	50–60%

Changes in this syllabus version

Revised syllabus for first examination in 2025: Paper 1 is non-calculator and Paper 2 is calculator; each is 2 hours, 100 marks and 50% of the qualification (Paper 1 rose to 100 marks and Paper 2 was shortened to 2 hours).
Both papers now mix structured and unstructured questions and print a List of formulas on page 2; mark schemes give more credit for method.
New topics: 1.17 Exponential growth and decay and 1.18 Surds. Loci and Matrices were removed.
Content added within topics includes reciprocals, recurring decimals, expanding three brackets, factorising ax³ + bx² + cx, inequality conventions, gradients of curves, more graph types (n = ±½, ab^x + c), sketching curves with asymptotes, domain and range, composite functions, the alternate segment theorem and the angle between a line and a plane.
Content removed includes proper subsets, increasing or decreasing by a ratio, reading dials, mapping notation f : x ↦ y, constructing perpendicular and angle bisectors and proving congruence.
Version 2 (February 2024): the term prism clarified in 5.4, expectations for drawing reciprocal and exponential graphs clarified in 2.11, and the term random added to guidance in 8.2.2.

Command words used in Mathematics (Syllabus D) papers (13)

Calculate: Work out an answer from the facts, figures or information given.
Construct: Produce an accurate drawing, for example with ruler and compasses.
Determine: Find a result with certainty.
Describe: Give the main points or characteristics of something.
Explain: Give reasons or purposes, make relationships clear and support them with evidence.
Give: Produce an answer from a source or from memory.
Plot: Mark one or more points on a graph.
Show (that): Give structured working that leads to the stated result.
Sketch: Draw freehand, showing the key features (from 2028: with care over proportions).
State: Express clearly in words.
Work out: Calculate from the information given, with or without a calculator.
Write: Give an answer in a particular form.
Write down: Give an answer without significant working.

Examiner guidance from recent reports (14)

Number. On Paper 1 you have no calculator, so practise long multiplication, division by decimals and fraction work until it is secure; examiners regularly see marks lost to simple arithmetic slips rather than misunderstanding.

Number. Reverse percentage questions are among the most frequently missed: divide by the multiplier (for example 0.9 after a 10% reduction) instead of adding the percentage back on to the new value.

Number. For bounds of a difference or quotient, think about which combination makes the result biggest or smallest (upper − lower, lower ÷ upper and so on); using both upper bounds is a common error. A value that is exact, such as a count, has no bounds.

Number. When asked to estimate, round every value to 1 significant figure first and show those rounded values; an exact calculation does not earn the method mark, and 0.30 is not 1 significant figure.

Algebra and graphs. Most lost marks in algebra come from sign errors, especially multiplying a bracket by a negative number. Write every step, and check solutions by substituting back.

Algebra and graphs. For composite functions, fg(x) means do g first. Do not confuse f(2x) with 2f(x), and for f⁻¹ swap x and y before rearranging.

Algebra and graphs. Draw tangents with a ruler, touching the curve at the required point only, and use a large triangle to find the gradient. Plot points with small crosses and join non-linear graphs with a smooth curve, not straight segments.

Coordinate geometry. Read questions on lines carefully: a perpendicular bisector must pass through the midpoint and use the negative reciprocal gradient. Give equations fully simplified in the form requested.

Geometry. When reasons are asked for, quote the property in full, for example “angle at the centre is twice the angle at the circumference”; vague answers such as “circle theorem” or “alternate” on its own do not earn credit.

Mensuration. Check units before calculating: convert to one unit first, remember 1 m³ = 1000 litres, and use the square or cube of the length factor for area and volume conversions.

Trigonometry. On Paper 2 keep full calculator values in intermediate steps and round only at the end (3 significant figures, angles to 1 decimal place). Premature rounding is a frequent reason for losing accuracy marks.

Transformations and vectors. Describe a single transformation fully (type, centre or line, angle and direction, scale factor or vector). Giving two transformations scores nothing. In vector questions, follow a clear route and simplify the final expression.

Probability. Read whether items are replaced. Without replacement, both numerator and denominator change on the second branch; give probabilities as fractions, decimals or percentages, never as ratios or “1 in 4”.

Statistics. Histograms need frequency density, not frequency, and cumulative frequency points go at the upper class boundary. When comparing distributions, compare an average and a measure of spread and say which group is which, in context.

Topic map

Practice types

Free sample questions

FAQs

Are these official 4024 past-paper questions?

No. They are original questions written to match the Mathematics (Syllabus D) syllabus topics. Official past papers are available to schools through Cambridge.

Why choose an exam year?

Cambridge updates syllabuses periodically. Your exam year selects the matching configuration so topics and components follow the right version.

Is a calculator allowed?

It depends on the paper. Each component card shows the calculator rule from this configuration.