Syllabus
What A-Level covers
Pure Mathematics
- Proof, including proof by contradiction
- Algebra and functions: surds, quadratics, inequalities, partial fractions
- Coordinate geometry: straight lines and circles
- Sequences and series, including the binomial expansion
- Trigonometry: radians, identities, the sine and cosine rules
- Exponentials, logarithms and growth/decay models
- Differentiation and integration, including implicit differentiation and numerical methods
- Vectors in 2D and 3D
Statistics
- Statistical sampling techniques
- Data presentation and interpretation
- Probability: Venn and tree diagrams
- Statistical distributions: binomial and normal
- Hypothesis testing, correlation and regression, using Pearson's pre-released Large Data Set
Mechanics
- Quantities and units
- Kinematics: SUVAT equations and calculus-based motion
- Forces and Newton's laws, including friction and connected particles
- Moments
Exam Pattern
How A-Level is assessed
Paper 1 — Pure Mathematics 1
Draws from any Pure Mathematics topic; calculator permitted (non-CAS).
Paper 2 — Pure Mathematics 2
Further Pure Mathematics content; calculator permitted (non-CAS).
Paper 3 — Statistics & Mechanics
Section A is Statistics, Section B is Mechanics; students answer every question, no choice.
Required Materials
What you'll need
Scientific or graphical calculator
A non-CAS calculator such as the Casio fx-991EX/fx-991CW ClassWiz is commonly recommended; graphical calculators like the fx-CG50 are permitted but not required.
Official formulae book
Pure, Mechanics and Statistics formulae plus statistical tables, provided in the exam room — know what is and isn't included.
Pearson Edexcel Large Data Set
Pre-released Met Office weather data that Paper 3 statistics questions are set around; familiarity with its structure is expected.
Try It Yourself
Sample questions, solved step by step
Scroll into view to watch each solution build itself, one step at a time, exactly how our tutors walk students through it.
Sample question
Prove by contradiction that √2 is irrational.
Animated solution
Assume the opposite
Suppose √2 is rational: √2 = a/b for integers a, b sharing no common factor
Square both sides
2 = a²/b² → a² = 2b², so a² is even, which means a itself must be even: a = 2k
Substitute back
(2k)² = 2b² → 4k² = 2b² → b² = 2k², so b² is even, meaning b is also even
Reach a contradiction
a and b were assumed to share no common factor, yet both are even — contradiction
Answer: √2 is irrational (proof by contradiction)
Sample question
A ball is thrown vertically upward with initial speed 19.6 m/s. Using g = 9.8 m/s², find (a) the time to reach maximum height and (b) the maximum height reached.
Animated solution
Use v = u − gt at maximum height (v = 0)
0 = 19.6 − 9.8t
Solve for t
t = 19.6 / 9.8 = 2 seconds
Use v² = u² − 2gs with v = 0
0 = 19.6² − 2(9.8)s → s = 19.6² / (2 × 9.8)
Compute
19.6² = 384.16, 2 × 9.8 = 19.6, so s = 384.16 / 19.6 = 19.6 m
Answer: t = 2 s, maximum height = 19.6 m