Mathematics 9709 (Cambridge International AS & A Level)
Original practice questions with long-form, step-by-step worked solutions, organised by the 9709 syllabus strands. Everything here is free to read.
- Subject code
- 9709
- Tier
- AS & A2
- Topics
- 15
- Worked questions
- 150
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Official Cambridge references: 9709 syllabus ↗ · past papers ↗
Pure Mathematics 1
Quadratics
Complete the square and use the discriminant to analyse ax² + bx + c; solve quadratic equations and inequalities by factorising, completing the square or the…
Coordinate Geometry
Find the equation of a line from given information and use its forms to solve distance, gradient, midpoint and intersection problems, including…
Functions
Understand domain, range, one-one functions, inverse functions and composition; find inverses and compositions in simple cases; sketch a function alongside…
Series, Progressions and the Binomial Expansion
Expand (a + b)ⁿ for positive integer n using binomial coefficients; recognise arithmetic and geometric progressions and use their nth-term and sum formulae…
Trigonometry
Sketch and use the sine, cosine and tangent graphs for angles of any size in degrees or radians; recall exact values at 30°, 45°, 60° and related angles; use…
Differentiation
Interpret the derivative as the limiting gradient of a chord; differentiate xⁿ for rational n and combinations of functions via the chain rule; apply…
Integration
Recognise integration as the reverse of differentiation and integrate (ax + b)ⁿ (n ≠ −1) and linear combinations of such terms; evaluate definite integrals…
Pure Mathematics 3
Mechanics
Forces and Equilibrium
Represent the forces acting on a particle with a force diagram and resolve them into components; apply the condition that forces on a particle in equilibrium…
Kinematics of Motion in a Straight Line
Distinguish the scalar quantities distance and speed from the vector quantities displacement, velocity and acceleration; interpret displacement–time and…
Momentum
Define linear momentum as a vector quantity for motion in one dimension and apply conservation of linear momentum to direct-impact collisions, including cases…
Probability & Statistics 1
Permutations and Combinations
Distinguish permutations from combinations and count arrangements and selections; handle arrangements in a line with repeated items or with restrictions such…
Probability
Evaluate probabilities by counting equiprobable outcomes or using permutations/combinations; combine probabilities with addition and multiplication rules…
Discrete Random Variables
Construct a probability distribution table for a discrete random variable and compute E(X) and Var(X); apply the binomial and geometric distribution formulae…
The Normal Distribution
Use the normal distribution N(μ, σ²) to model a continuous random variable and read normal distribution tables; standardise to find, or work backward from…