A-Level Maths Tutor

Overview of the Qualification

The Edexcel A-Level Maths consists of three externally-examined papers, all taken at the end of the course.

Total: 300 marks, 6 hours of assessment. All papers are equally weighted (33.33% each).

Paper 1 & 2: Pure Mathematics

These two papers cover all the Pure Maths content, worth 66.7% of the total qualification.

Topic 1: Proof

Proof by deduction, exhaustion, contradiction. Disproof by counter-example.

Topic 2: Algebra and Functions

Laws of indices, surds, quadratics, simultaneous equations, inequalities, polynomials, factor theorem, graphs of functions, composite and inverse functions, transformations, partial fractions, modelling.

Topic 3: Coordinate Geometry

Equation of a straight line, circles, parametric equations. Modelling with straight lines.

Topic 4: Sequences and Series

Binomial expansion, arithmetic and geometric sequences and series, sigma notation, convergence, modelling.

Topic 5: Trigonometry

Sine and cosine rules, radian measure, secant/cosecant/cotangent, identities (sin²θ + cos²θ = 1, sec²θ = 1 + tan²θ), double angle formulae, a cos θ + b sin θ form, solving equations, proofs, modelling.

Topic 6: Exponentials and Logarithms

Exponential functions, eˣ and ln x, laws of logarithms, solving equations, logarithmic graphs, growth and decay models.

Topic 7: Differentiation

First principles, product/quotient/chain rules, tangents and normals, stationary points, second derivative, increasing/decreasing functions, parametric and implicit differentiation, differential equations.

Topic 8: Integration

Fundamental Theorem of Calculus, definite/indefinite integrals, area under curves, integration by substitution and by parts, partial fractions, differential equations (separable variables).

Topic 9: Numerical Methods

Location of roots, iterative methods, Newton-Raphson method, trapezium rule.

Topic 10: Vectors

2D and 3D vectors, magnitude, addition, scalar multiplication, position vectors, distance between points, solving problems in pure maths and contexts (forces).

Paper 3: Statistics and Mechanics

This paper covers the Statistics and Mechanics content, worth 33.3% of the total qualification.

Section A: Statistics

• Statistical Sampling: Populations, samples, sampling techniques (random, stratified, systematic, quota, opportunity).
• Data Presentation and Interpretation: Histograms, box plots, scatter diagrams, regression lines, correlation, standard deviation, outliers, coding.
• Probability: Mutually exclusive events, independent events, Venn diagrams, tree diagrams, conditional probability.
• Statistical Distributions: Binomial distribution, Normal distribution, approximation of binomial by Normal (with continuity correction).
• Statistical Hypothesis Testing: Language of hypothesis testing, tests for proportions (binomial) and means (Normal), correlation coefficients.

Section B: Mechanics

• Quantities and Units: S.I. units for length, mass, time, velocity, acceleration, force, weight, moment.
• Kinematics: Displacement, velocity, acceleration, SUVAT equations, motion graphs, calculus in kinematics (2D vectors).
• Forces and Newton's Laws: Forces, Newton's laws, resolving forces, connected particles, friction (F ≤ μR).
• Moments: Equilibrium of rigid bodies, parallel and non-parallel coplanar forces.

Assessment Objectives

The exam papers assess three main skills:

• AO1 (48–52%): Use and apply standard techniques, accurately recall facts, terminology and definitions.
• AO2 (23–27%): Reason, interpret and communicate mathematically, construct rigorous arguments (including proofs).
• AO3 (23–27%): Solve problems within mathematics and in other contexts, use mathematical models, evaluate outcomes.