Cambridge International · AS & A Level9709 AS & A Level Mathematics
6 components38 topics38 with lessons
Candidates take different combinations of papers for AS and A Level. Select the papers you sit when your school confirms your route.
Source: Cambridge International 9709 specification · Confirm the syllabus year with your school.
Exam infoExam structure, syllabus and formula booklet3 official documents
Syllabus for exams in 2026–2027 (the 2028–2030 syllabus has no significant changes)
| Paper | Time | Marks | Weighting |
|---|
| Paper 1 Pure Mathematics 1 | 1 h 50 min | 75 | 60% AS · 30% A Level |
| Paper 2 Pure Mathematics 2 | 1 h 15 min | 50 | 40% AS (AS only) |
| Paper 3 Pure Mathematics 3 | 1 h 50 min | 75 | 30% A Level |
| Paper 4 Mechanics | 1 h 15 min | 50 | 40% AS · 20% A Level |
| Paper 5 Probability & Statistics 1 | 1 h 15 min | 50 | 40% AS · 20% A Level |
| Paper 6 Probability & Statistics 2 | 1 h 15 min | 50 | 20% A Level |
- AS Level routes: Papers 1 + 2, 1 + 4, or 1 + 5. The 1 + 2 route is pure-only and cannot be carried forward to the full A Level.
- A Level routes: Papers 1, 3, 4 and 5, or Papers 1, 3, 5 and 6. Papers 4 and 6 cannot be combined, and Papers 2 and 3 cannot be taken in the same series.
- Exams are in June and November (and March in India).
- A scientific calculator is expected. Graphic calculators and calculators that do symbolic algebra, differentiation or integration are not allowed.
- Give non-exact answers to 3 significant figures (angles in degrees to 1 decimal place) unless the question says otherwise. Answers with no working get no marks.
- The formula list MF19 is provided in every paper.
Summarised from the official specification, checked 16 Oct 2026. The board's document is the final word.
PDFExams 2026–2027Version 4
AS & A Level Mathematics 9709 syllabus — exams in 2026 and 2027
The current syllabus. It sets out every topic for Papers 1–6, the allowed paper combinations (for example, Paper 2 and Paper 3 cannot be taken in the same series, and Papers 4 and 6 cannot be combined for A Level), calculator rules and the assessment objectives.
PDFFrom 2028Version 1 (September 2025)
AS & A Level Mathematics 9709 syllabus — exams in 2028, 2029 and 2030
The next syllabus, for students sitting exams from 2028. Cambridge states there are no significant changes that affect teaching: the wording has been made clearer, and textbooks endorsed for the 2020 syllabus remain suitable.
PDFMF19, for use from 2020
List of formulae and statistical tables (MF19)
The formula booklet given to you in every 9709 and 9231 exam: mensuration, algebra, trigonometry, calculus and vector results, mechanics and statistics formulae, and the normal, t, χ² and Wilcoxon tables. Learn where things are in it before the exam.
All Cambridge documents: exam rules, key dates and grade thresholds →
Paper 1Pure Mathematics 18 topics
- Quadratics
Completing the square and the vertex · Solving quadratic equations · The discriminant and the nature of roots · Linear and quadratic inequalities · Simultaneous equations and lines meeting curves5 lessons - Functions
Functions, domain and range · Composite functions · One-one and inverse functions · Graphs of a function and its inverse · Transformations of graphs5 lessons - Coordinate geometry
Gradient, length, midpoint and equations of lines · Parallel and perpendicular lines · The equation of a circle · Tangents, chords and intersections4 lessons - Circular measure
Radians · Arc length and sector area · Segments, chords and composite shapes3 lessons - Trigonometry
Exact values and the unit circle · Graphs and transformations · Inverse trigonometric functions · Trigonometric identities · Solving trigonometric equations5 lessons - Series
Binomial expansion · Arithmetic progressions · Geometric progressions · Sum to infinity4 lessons - Differentiation
Gradients and the power rule · The chain rule · Tangents and normals · Stationary points and increasing functions · Optimisation and rates of change5 lessons - Integration
Indefinite integration · Integrating (ax + b)ⁿ · Definite integrals · Areas under and between curves · Volumes of revolution5 lessons
Paper 2Pure Mathematics 26 topics
- Algebra
Modulus graphs and equations · Modulus inequalities · Polynomials: division, factor and remainder theorems3 lessons - Logarithmic and exponential functions
Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms5 lessons - Trigonometry
Reciprocal functions and their identities · Compound-angle formulae · Double-angle formulae · The R-form (harmonic form)4 lessons - Differentiation
Derivatives of eˣ, ln x and trigonometric functions · The product and quotient rules · Implicit differentiation · Parametric differentiation · Stationary points and tangents5 lessons - Integration
Integrating eˣ, 1/x and trigonometric functions · Integration using trigonometric identities · Exact definite integrals and logarithms · The trapezium rule4 lessons - Numerical solution of equations
Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs3 lessons
Paper 3Pure Mathematics 39 topics
- Algebra
Modulus graphs and equations · Modulus inequalities · Polynomials: division, factor and remainder theorems · Partial fractions · Binomial expansion for any rational n5 lessons - Logarithmic and exponential functions
Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms5 lessons - Trigonometry
Reciprocal functions and their identities · Compound-angle formulae · Double-angle formulae · The R-form (harmonic form)4 lessons - Differentiation
Derivatives of eˣ, ln x and trigonometric functions · The product and quotient rules · Implicit differentiation · Parametric differentiation · Stationary points and tangents5 lessons - Integration
Integrating eˣ, 1/x and trigonometric functions · Integration using trigonometric identities · Exact definite integrals and logarithms · Integration by substitution · Integration by parts5 lessons - Numerical solution of equations
Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs3 lessons - Vectors
Position vectors, magnitude and unit vectors · The scalar product and angles · The vector equation of a line · Intersecting, parallel and skew lines · Foot of the perpendicular and shortest distances5 lessons - Differential equations
Forming differential equations · Separating the variables · Particular solutions with harder integrals · Modelling with differential equations4 lessons - Complex numbers
Arithmetic and conjugates · The Argand diagram, modulus and argument · Polar and exponential forms · Polynomial equations and square roots · Loci and regions in the Argand diagram5 lessons
Paper 4Mechanics5 topics
- Forces and equilibrium
Forces, components and resultants · Equilibrium of a particle · Friction · Inclined planes4 lessons - Kinematics of motion in a straight line
Constant acceleration (suvat) · Vertical motion under gravity · Motion graphs · Variable acceleration4 lessons - Momentum
Momentum and its conservation · Coalescing and loss of kinetic energy · Directions, rebounds and several collisions3 lessons - Newton's laws of motion
Newton’s laws and F = ma · Motion on inclined planes · Connected particles and pulleys · Lifts and vertical motion4 lessons - Energy, work and power
Work done · Kinetic and potential energy · The work–energy principle · Power4 lessons
Paper 5Probability & Statistics 15 topics
- Representation of data
Stem-and-leaf diagrams and box plots · Histograms and cumulative frequency · Mean and standard deviation · Coded and combined data4 lessons - Permutations and combinations
Arrangements and factorials · Arrangements with restrictions · Selections (combinations)3 lessons - Probability
Combined events and Venn diagrams · Tree diagrams and conditional probability · Independent and mutually exclusive events3 lessons - Discrete random variables
Probability distributions · Expectation and variance · The binomial distribution · The geometric distribution4 lessons - The normal distribution
Standardising and normal probabilities · Inverse normal and finding μ and σ · Normal approximation to the binomial3 lessons
Paper 6Probability & Statistics 25 topics
- The Poisson distribution
Poisson probabilities · Scaling rates and sums · Poisson and normal approximations3 lessons - Linear combinations of random variables
E and Var of aX + b and aX + bY · Sums of observations and multiples · Combining normal and Poisson variables3 lessons - Continuous random variables
Probability density functions · Mean and variance · Median and percentiles3 lessons - Sampling and estimation
Sampling and unbiased estimates · The sample mean and the Central Limit Theorem · Confidence intervals3 lessons - Hypothesis tests
Binomial and Poisson tests · Tests for a population mean · Type I and Type II errors3 lessons