Pure Mathematics — Year 2

The full Year 2 Pure Maths topic list for Year 13, structured to the Edexcel specification — functions, sequences and series, further trigonometry, parametric equations, exponentials and calculus.

Pure Maths Year 2 Topics

Each topic page will include step-by-step worked examples, graded practice questions and full answers — in the same format as our GCSE Maths resources.

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Algebraic Methods

Algebraic division, partial fractions and further algebraic proof.

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𝑓(𝑥)
Functions & Graphs

Composite and inverse functions, the modulus function and graph transformations.

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Σ
Sequences & Series

Arithmetic and geometric sequences, series and sigma notation.

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ⁿCᵣ
Binomial Expansion

Expanding expressions with negative and fractional powers, and validity conditions.

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𝜋
Radians

Radian measure, arc length, sector area and small angle approximations.

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sec
Trigonometric Functions

Secant, cosecant, cotangent and inverse trigonometric functions.

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𝑅sin
Trigonometry & Modelling

Compound and double angle formulae, and the R sin(θ ± α) form.

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(𝑥,𝑦)
Parametric Equations

Converting between parametric and Cartesian forms, and parametric curve sketching.

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ln
Exponentials, Logarithms & Modelling

Natural logarithms, exponential models and growth/decay differential equations.

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d/dx
Differentiation

Differentiating trigonometric, exponential and logarithmic functions.

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d²y/dx²
Further Differentiation

Chain, product and quotient rules, and connected rates of change.

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Numerical Methods

Locating roots, iteration and the Newton-Raphson method.

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Integration

Integrating trigonometric, exponential and logarithmic functions, and finding areas.

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Further Integration & Differential Equations

Integration by substitution, by parts, and forming and solving differential equations.

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Vectors

3D vectors, magnitude, direction and equations of lines in vector form.

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