Readable syllabus overview and practice questions
Cambridge International AS & A Level Mathematics 9709
Examinations 2026–2027. Readable text and equivalent practice questions. Practice scores are not Cambridge grades.
1 · Mathematics 9709
Cambridge International AS & A Level
Mathematics 9709
Explore the topics you will study and the skills you will develop.
Examinations 2026–2027 · Syllabus Overview
2 · How the course is organised
AS routes: Papers 1+2, 1+4 or 1+5. The Pure Mathematics only route (1+2) cannot be carried forward to A Level. Full A Level routes: 1+3+4+5 or 1+3+5+6. Papers 4 and 6 cannot be combined. Study the sections for your approved combination, not all six sections.
Use the syllabus for examinations 2026–2027. Confirm your examination year and any options with your centre.
3 · 1 Pure Mathematics 1 · Paper 1 · 1
Required in every AS and A Level combination.
1.1 Quadratics
Solve quadratic equations and analyse quadratic functions.
1.2 Functions
Work with functions, their inverses and compositions.
4 · 1 Pure Mathematics 1 · Paper 1 · 2
Required in every AS and A Level combination.
1.3 Coordinate geometry
Use algebra to describe geometric relationships.
5 · 1 Pure Mathematics 1 · Paper 1 · 1
Required in every AS and A Level combination.
1.4 Circular measure
Use radians to study arcs and sectors.
1.5 Trigonometry
Work with trigonometric functions, identities and equations.
6 · 1 Pure Mathematics 1 · Paper 1 · 2
Required in every AS and A Level combination.
1.6 Series
Explore progressions and series.
7 · 1 Pure Mathematics 1 · Paper 1
Required in every AS and A Level combination.
1.7 Differentiation
Use derivatives to describe gradients and rates of change.
1.8 Integration
Find integrals and apply them to areas.
8 · 2 Pure Mathematics 2 · Paper 2 · 1
AS Pure Mathematics only route; not part of a full A Level combination.
2.1 Algebra
Extend algebraic methods for expressions and equations.
2.2 Logarithmic and exponential functions
Use logarithms and exponentials to solve problems.
9 · 2 Pure Mathematics 2 · Paper 2 · 2
AS Pure Mathematics only route; not part of a full A Level combination.
2.3 Trigonometry
Extend trigonometric identities and equations.
10 · 2 Pure Mathematics 2 · Paper 2 · 1
AS Pure Mathematics only route; not part of a full A Level combination.
2.4 Differentiation
Develop differentiation techniques and applications.
2.5 Integration
Develop integration techniques and applications.
11 · 2 Pure Mathematics 2 · Paper 2 · 2
AS Pure Mathematics only route; not part of a full A Level combination.
2.6 Numerical solution of equations
Approximate roots using numerical methods.
12 · 3 Pure Mathematics 3 · Paper 3 · 1
Required for the full A Level, alongside Paper 1.
3.1 Algebra
Extend algebraic techniques for more complex expressions.
3.2 Logarithmic and exponential functions
Apply logarithmic and exponential relationships.
13 · 3 Pure Mathematics 3 · Paper 3 · 2
Required for the full A Level, alongside Paper 1.
3.3 Trigonometry
Use further trigonometric identities and equations.
14 · 3 Pure Mathematics 3 · Paper 3 · 1
Required for the full A Level, alongside Paper 1.
3.4 Differentiation
Apply advanced differentiation techniques.
3.5 Integration
Apply further integration methods.
15 · 3 Pure Mathematics 3 · Paper 3 · 2
Required for the full A Level, alongside Paper 1.
3.6 Numerical solution of equations
Use numerical approaches to approximate solutions.
16 · 3 Pure Mathematics 3 · Paper 3 · 1
Required for the full A Level, alongside Paper 1.
3.7 Vectors
Represent and solve geometric problems using vectors.
3.8 Differential equations
Model change and solve differential equations.
17 · 3 Pure Mathematics 3 · Paper 3 · 2
Required for the full A Level, alongside Paper 1.
3.9 Complex numbers
Represent and manipulate complex numbers.
18 · 4 Mechanics · Paper 4 · 1
Available in AS 1+4 and A Level 1+3+4+5.
4.1 Forces and equilibrium
Model forces acting on bodies in equilibrium.
4.2 Kinematics of motion in a straight line
Describe straight-line motion mathematically.
19 · 4 Mechanics · Paper 4 · 2
Available in AS 1+4 and A Level 1+3+4+5.
4.3 Momentum
Apply momentum ideas to interactions.
20 · 4 Mechanics · Paper 4
Available in AS 1+4 and A Level 1+3+4+5.
4.4 Newton’s laws of motion
Link forces and acceleration using mechanical models.
4.5 Energy, work and power
Use energy methods to analyse motion.
21 · 5 Probability & Statistics 1 · Paper 5 · 1
Available in AS 1+5; required in both full A Level routes.
5.1 Representation of data
Summarise and display data appropriately.
5.2 Permutations and combinations
Count arrangements and selections.
22 · 5 Probability & Statistics 1 · Paper 5 · 2
Available in AS 1+5; required in both full A Level routes.
5.3 Probability
Calculate and interpret probabilities.
23 · 5 Probability & Statistics 1 · Paper 5
Available in AS 1+5; required in both full A Level routes.
5.4 Discrete random variables
Model discrete outcomes with probability distributions.
5.5 The normal distribution
Use the normal distribution to model continuous data.
24 · 6 Probability & Statistics 2 · Paper 6 · 1
Available in A Level 1+3+5+6; depends on Paper 5 content.
6.1 The Poisson distribution
Model counts using the Poisson distribution.
6.2 Linear combinations of random variables
Analyse combined random variables.
25 · 6 Probability & Statistics 2 · Paper 6 · 2
Available in A Level 1+3+5+6; depends on Paper 5 content.
6.3 Continuous random variables
Use probability density functions.
26 · 6 Probability & Statistics 2 · Paper 6
Available in A Level 1+3+5+6; depends on Paper 5 content.
6.4 Sampling and estimation
Use samples to estimate population properties.
6.5 Hypothesis tests
Test claims using statistical evidence.
27 · Skills you will develop
Use mathematical reasoning, communicate logical steps and interpret solutions in context. The section number identifies content and paper; confirm your component combination before planning study.
28 · Keep the syllabus beside you
– Use the official syllabus for 2026–2027.
– Find each numbered topic or labelled option in the subject-content section.
– Use its detailed requirements to plan study and review progress.
[Open the official Cambridge syllabus](https://www.cambridgeinternational.org/Images/697427-2026-2027-syllabus.pdf)
The next five questions check your understanding of this topic map. They are optional practice with feedback and retries, not Cambridge grades.
Topic check 1 · Find the right area
Which topic concerns testing claims using statistical evidence?
– 1.4 Circular measure
– 6.5 Hypothesis tests
– 4.3 Momentum
Show answer and feedback
Correct: 6.5 Hypothesis tests
Correct feedback: 6.5 Hypothesis tests: Test claims using statistical evidence. Review slide 26.
If 1.4 Circular measure is selected: 1.4 Circular measure: Use radians to study arcs and sectors. Review slide 05 and 06. The best match to this question is 6.5 Hypothesis tests.
If 4.3 Momentum is selected: 4.3 Momentum: Apply momentum ideas to interactions. Review slide 18 and 19. The best match to this question is 6.5 Hypothesis tests.
Topic check 2 · Understand the course structure
True or false: The AS Papers 1+2 result can be carried forward to complete A Level.
Show answer and feedback
Correct: False
Correct feedback: Correct. The Pure Mathematics only AS route cannot be carried forward to A Level.
Incorrect feedback: Revisit slide 02. The Pure Mathematics only AS route cannot be carried forward to A Level.
Topic check 3 · Complete the topic title
Represent and solve geometric problems using vectors.
Complete the missing word in this topic title: 3.7 ____
Show answer and feedback
Accepted answer: Vectors. Ignore case and surrounding whitespace; do not require the topic number.
Correct feedback: 3.7 Vectors: Represent and solve geometric problems using vectors. Review slide 16 and 17.
Incorrect feedback: Use the description to identify the topic. The missing word is “Vectors”; the complete title is 3.7 Vectors. Review slide 16 and 17.
Topic check 4 · Match topics to their focus
Match each description with its topic label. Use each label once.
Draggable labels: 1.4 Circular measure; 3.9 Complex numbers; 5.2 Permutations and combinations
– Use radians to study arcs and sectors. → [drop zone]
– Represent and manipulate complex numbers. → [drop zone]
– Count arrangements and selections. → [drop zone]
Show answer and feedback
– Row 1: 1.4 Circular measure. Review slide 05 and 06.
– Row 2: 3.9 Complex numbers. Review slide 16 and 17.
– Row 3: 5.2 Permutations and combinations. Review slide 21 and 22.
Correct feedback: Each label now matches its study focus.
Incorrect/partial feedback: Keep correct matches and revisit the topic descriptions above; use the solution to compare each pair.
Topic check 5 · Identify the study areas
Select the two topic labels that match these descriptions:
– Link forces and acceleration using mechanical models.
– Use samples to estimate population properties.
Selectable text:
4.4 Newton’s laws of motion / 1.1 Quadratics / 6.4 Sampling and estimation / 1.2 Functions
Show answer and feedback
Correct labels: 4.4 Newton’s laws of motion; 6.4 Sampling and estimation.
Incorrect labels: 1.1 Quadratics; 1.2 Functions.
Correct feedback: 4.4 Newton’s laws of motion: Link forces and acceleration using mechanical models. Review slide 20. 6.4 Sampling and estimation: Use samples to estimate population properties. Review slide 26.
Incorrect/partial feedback: Match the meaning of each description, not just a familiar word. 1.1 Quadratics: Solve quadratic equations and analyse quadratic functions. Review slide 03 and 04. 1.2 Functions: Work with functions, their inverses and compositions. Review slide 03 and 04.