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Cambridge International A Level

Mathematics 9709

Pure mathematics, probability & statistics and mechanics, with flexible combinations of AS and A Level papers.

Syllabus version: 2026–2027 syllabusChecked against the Cambridge syllabusExam year 2027 is covered by the 2026–2027 syllabus.
Subject review complete (19 Oct 2026). All 36 Mathematics 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: 11 approved as written, 25 corrected.

Weighting by paper. Some papers are alternatives (for example Core or Extended, or practical or alternative to practical), so the figures add up to more than 100%.

  • Paper 1 Pure Mathematics 130%
  • Paper 3 Pure Mathematics 330%
  • Paper 4 Mechanics20%
  • Paper 5 Probability & Statistics 120%
  • Paper 6 Probability & Statistics 220%
Original questions36
Topics covered6/6
Papers5
Mock papers5

What is assessed

5 components. Question formats: structured.

Paper 1 Pure Mathematics 1AS & A Level
1 h 50 min75 marks30% of A Level

10 to 12 structured questions on the Pure Mathematics 1 content; compulsory for both AS Level and A Level and the foundation for every other paper.

What the paper looks like

About 10–12 compulsory questions, 75 marks in 1 h 50 min. Early questions are short (3–5 marks); later ones are multi-part (8–11 marks) blending topics, e.g. functions with transformations or calculus with coordinate geometry. Command words: find, show that, solve, sketch, determine. Exact answers often requested; otherwise 3 s.f. or 1 d.p. for degrees. Calculator allowed but full working required.

StructuredList of formulae and statistical tables (MF19) provided
Checked against the Cambridge syllabus
Paper 3 Pure Mathematics 3A Level only
1 h 50 min75 marks30% of A Level

9 to 11 structured questions on the Pure Mathematics 3 content; compulsory for A Level only.

What the paper looks like

9–11 compulsory questions, 75 marks in 1 h 50 min, with a higher AO2 share (55%). Questions often run 6–10 marks across parts: partial fractions then expansion or integration, differential equations in context, vector lines in 3D, complex numbers with Argand loci. Expect “show that”, “hence” and “find the exact value” wording.

StructuredList of formulae and statistical tables (MF19) provided
Checked against the Cambridge syllabus
Paper 4 MechanicsAS & A Level
1 h 15 min50 marks20% of A Level

6 to 8 structured questions on the Mechanics content; may be taken as part of AS Level or A Level.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min, mostly numerical with g = 10. Questions use diagrams of particles on planes, strings over pulleys or vehicles with power; parts of 2–6 marks ask to find forces, accelerations, speeds or distances. Answers to 3 s.f. (angles 1 d.p.); a clear force diagram is expected.

StructuredList of formulae and statistical tables (MF19) provided; take g = 10 m s⁻²
Checked against the Cambridge syllabus
Paper 5 Probability & Statistics 1AS & A Level
1 h 15 min50 marks20% of A Level

6 to 8 structured questions on the Probability & Statistics 1 content; compulsory for A Level and an AS option.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min. Data questions with stem-and-leaf, box plots, histograms or summary totals; counting problems with cases; tree-diagram conditional probability; binomial and geometric models; normal distribution with unknown parameters and normal approximation. Parts are usually 1–5 marks; exact fractions are acceptable.

StructuredList of formulae and statistical tables (MF19) provided
Checked against the Cambridge syllabus
Paper 6 Probability & Statistics 2A Level only
1 h 15 min50 marks20% of A Level

6 to 8 structured questions on the Probability & Statistics 2 content; offered only as part of A Level and builds on Paper 5.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min. Poisson modelling and approximations, linear combinations of normal variables, pdfs with an unknown constant, unbiased estimates and confidence intervals, and hypothesis tests (binomial, Poisson, normal mean) with Type I/II errors. Conclusions must be in context; parts typically 2–6 marks.

StructuredList of formulae and statistical tables (MF19) provided
Checked against the Cambridge syllabus

Assessment overview

From the 2026–2027 syllabus. Checked against the Cambridge syllabus

A Level (Route 3a): Pure 1, Pure 3, Mechanics, Probability & Statistics 1
Paper 1Paper 3Paper 4Paper 5
All four components in the same series.
A Level (Route 3b): Pure 1, Pure 3, Probability & Statistics 1 and 2
Paper 1Paper 3Paper 5Paper 6
All four components in the same series.
A Level staged (Route 2a): Year 1 Pure 1 + Mechanics, Year 2 Pure 3 + P&S 1
Paper 1Paper 4Paper 3Paper 5
AS result carried forward subject to Cambridge Handbook rules and time limits.
A Level staged (Route 2b): Year 1 Pure 1 + P&S 1, Year 2 Pure 3 + P&S 2
Paper 1Paper 5Paper 3Paper 6
AS result carried forward subject to Cambridge Handbook rules and time limits.
A Level staged (Route 2c): Year 1 Pure 1 + P&S 1, Year 2 Pure 3 + Mechanics
Paper 1Paper 5Paper 3Paper 4
Paper 2 is not available for A Level; Paper 2 and Paper 3 may not be taken in the same series.
Assessment objectiveA Level weighting
AO1 Knowledge and understanding52%
AO2 Application and communication48%
Changes in this syllabus version
  • No significant changes affecting teaching compared with the 2023–2025 syllabus; content, papers, timings and weightings are unchanged.
  • Version 2 (Nov 2024): headers on the assessment overview page updated.
  • Version 3 (Feb 2025): typographical errors in the subject content corrected.
  • Version 4 (Dec 2025): a weblink updated; specimen materials were not changed.
Command words used in Mathematics papers (11)
Calculate
Work out a result from the facts, figures or information given.
Describe
State the main points or give the key characteristics and features.
Determine
Establish a result with certainty, usually with supporting working.
Evaluate
Judge or calculate the value, amount, quality or importance of something.
Explain
Give reasons or purposes, making relationships clear, with supporting evidence.
Identify
Name, select or recognise.
Justify
Support a case or claim with evidence or argument.
Show (that)
Give a structured chain of working that leads to a given result.
Sketch
Draw a simple freehand diagram showing key features, with care over proportion.
State
Express clearly and briefly, usually without working.
Verify
Confirm that a given statement or result is true.
Examiner guidance from recent reports (14)
Pure Mathematics 1. Calculator-only answers to quadratic or trigonometric equations lose method marks: write the factorisation, the completed square or the formula with values substituted, then the roots.
Pure Mathematics 1. In trigonometric equations, check the required interval and units before writing the final list; missing a second-quadrant solution or answering in degrees when radians were requested is a common way to drop the final accuracy mark.
Pure Mathematics 1. When a composite function is involved, state which function is applied first and check the range of the inner function lies in the domain of the outer one; for an inverse, restate it in terms of x and give its domain.
Pure Mathematics 1. For areas and volumes, sketch the region and find intersection points first; for a volume between two curves use π∫(y₁² − y₂²) dx, not π∫(y₁ − y₂)² dx.
Pure Mathematics 2. With R sin(θ + α) questions, give R exactly (e.g. √13) and α to at least 2 d.p. in working; rounding α early pushes the final angles outside the accepted range.
Pure Mathematics 2. For iterations, show each iterate to at least one more decimal place than required and continue until two successive values agree to the stated accuracy, or show a sign-change check.
Pure Mathematics 3. In implicit differentiation, products such as xy or x² ln y need the product rule; forgetting the dy/dx factor on terms in y is the most common lost mark.
Pure Mathematics 3. Complex numbers and vectors are often left blank late in the paper — practise them so they are reliable marks. Keep arguments in radians and in the range −π < θ ≤ π unless told otherwise.
Pure Mathematics 3. In binomial expansions with rational n, factor out the constant first, e.g. (2 + x)⁻¹ = ½(1 + x/2)⁻¹, and use brackets around terms like (−x/2)² to avoid sign errors.
Mechanics. Draw and label a force diagram before resolving; most errors come from a missing weight component or friction acting the wrong way. Take g = 10 and work to 4 s.f. before giving 3 s.f. answers.
Mechanics. If velocity or acceleration depends on time, use calculus — constant-acceleration formulae are not valid. For total distance, split the integral wherever the velocity changes sign.
Probability & Statistics 1. In counting problems, set out the separate cases in a list or table and add them; communication of which scenario each term represents earns method credit even if a slip occurs.
Probability & Statistics 1. In normal questions, show the standardisation with the values substituted and a sketch; when finding μ or σ, use z-values to 4 d.p. from the critical values table rather than rounded ones.
Probability & Statistics 2. Hypothesis-test conclusions must be in context and non-assertive, e.g. “there is evidence at the 5% level that the mean has decreased”, and must compare like with like (probability vs significance level, or statistic vs critical value).

Topic map

Practice types

Free sample questions

FAQs

Are these official 9709 past-paper questions?

No. They are original questions written to match the Mathematics 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.

How do AS and A Level differ here?

Both pathways share code 9709. AS pages include AS topics and components only; A Level pages add the A Level content and papers.

Is a calculator allowed?

In this configuration a scientific calculator is permitted for the listed papers. Check your syllabus for the exact rule.