Edexcel IAL

IAL Mathematics

Pure Mathematics — building essential A-Level skills in algebra, coordinate geometry, calculus, sequences, and trigonometry.

P2
P3
P4

Choose a Module

Select a module to access study resources, past papers, and revision tools.

P2 8 Topics

Pure Mathematics 2

Algebraic methods, coordinate geometry, exponentials, binomial expansion, sequences, trigonometry, differentiation, and integration.

Algebraic Methods Coordinate Geometry Exponentials + 5 more
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Mark Mate
P3 8 Topics

Pure Mathematics 3

Algebraic methods, functions and graphs, trigonometry, parametric equations, differentiation, integration, numerical methods, and vectors.

Trigonometry Integration Vectors + 5 more
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Mark Mate
P4 7 Topics

Pure Mathematics 4

Pure Mathematics 4 — advanced pure mathematics covering proof, partial fractions, parametric equations, binomial expansion, differentiation, integration, and vectors.

Proof Partial Fractions Vectors + 4 more
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Mark Mate
P2

Pure Mathematics 2

Algebraic methods, coordinate geometry, exponentials, binomial expansion, sequences, trigonometry, differentiation, and integration.

Mind Map

Interactive mind map covering all topics in the module — explore connections between key concepts visually.

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Textbook

The complete course textbook covering every topic in the syllabus, with clear explanations, worked examples, and exercises to build confidence and fluency.

Browse Topics

Questions by Topic

Exam-style questions by topic, arranged by difficulty with full mark schemes and worked solutions to sharpen your technique.

Browse Topics

Past Papers

Full worked solutions to all Edexcel IAL past paper questions, taught by experienced instructors with clear step-by-step explanations for every mark.

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Planner & Checklist

A structured study planner and checklist to track your progress through every topic, ensuring complete and confident exam preparation.

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Flashcards

Develop your understanding using custom-built flashcards covering key definitions, identities, and results — perfect for quick daily revision sessions.

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P2

Pure Mathematics 2

Textbook — Select a chapter to read in the notebook.

Formula Book
01 Textbook

Algebraic Methods

Algebraic fractions, dividing polynomials, factor theorem, remainder theorem, mathematical proof and methods of proof.

02 Textbook

Coordinate Geometry

Midpoints, perpendicular bisectors, equation of a circle, intersections of lines and circles, tangent and chord properties.

03 Textbook

Exponentials and Logarithms

Exponential functions, logarithms, laws of logarithms, solving equations using logarithms, and changing the base.

04 Textbook

The Binomial Expansion

Pascal's triangle, factorial notation, binomial expansion, solving binomial problems, and binomial estimation.

05 Textbook

Sequences and Series

Arithmetic and geometric sequences, sum to infinity, sigma notation, recurrence relations, and modelling with series.

06 Textbook

Trigonometric Identities and Equations

Angles in all four quadrants, exact values, trig identities, solving simple and harder trig equations, equations and identities.

07 Textbook

Differentiation

Increasing and decreasing functions, stationary points, sketching gradient functions, and modelling with differentiation.

08 Textbook

Integration

Definite integrals, areas under curves, areas under the x-axis, areas between curves and lines, and the trapezium rule.

P2

Questions by Topic

Select a topic to practise exam-style questions with worked solutions.

Formula Book
CH 01

Algebraic Methods

Algebraic fractions, dividing polynomials, factor theorem, remainder theorem, mathematical proof and methods of proof.

Fractions Factor Theorem Proof
Trend Analysis Mark Scheme
Subtopic A Factor Theorem, Remainder Theorem & Algebraic Division
Mark Scheme
Subtopic B Proof: Deduction, Counter-Example & Exhaustion
Mark Scheme
CH 02

Coordinate Geometry

Midpoints, perpendicular bisectors, equation of a circle, intersections of lines and circles, tangent and chord properties.

Circles Tangent Bisector
Trend Analysis Mark Scheme
Subtopic A Circle Equation Forms & Completing the Square
Mark Scheme
Subtopic B Tangent & Normal Questions
Mark Scheme
Subtopic C Chord, Diameter & Geometric Reasoning
Mark Scheme
Subtopic D Discriminant & Intersection Conditions
Mark Scheme
CH 03

Exponentials and Logarithms

Exponential functions, logarithms, laws of logarithms, solving equations using logarithms, and changing the base.

Exponentials Log Laws Equations
Trend Analysis Mark Scheme
Subtopic A Logarithmic Equations (Laws of Logarithms)
Mark Scheme
Subtopic B Exponential Equations
Mark Scheme
Subtopic C Exponential Modelling & Real-World Contexts
Mark Scheme
Subtopic D Graph Sketching & Transformations
Mark Scheme
Subtopic E Abstract Log Manipulation & "Express in Terms of"
Mark Scheme
CH 04

The Binomial Expansion

Pascal's triangle, factorial notation, binomial expansion, solving binomial problems, and binomial estimation.

Pascal nCr Estimation
Trend Analysis Mark Scheme
Subtopic A Standard Expansion ("Find the First n Terms")
Mark Scheme
Subtopic B Product Expansion ("Hence Find the Coefficient")
Mark Scheme
Subtopic C Reverse Problems ("Find the Unknown Constant")
Mark Scheme
Subtopic D Approximation Applications
Mark Scheme
Subtopic E Relationship Between Coefficients
Mark Scheme
CH 05

Sequences and Series

Arithmetic and geometric sequences, sum to infinity, sigma notation, recurrence relations, and modelling with series.

Arithmetic Geometric Sigma
Trend Analysis Mark Scheme
Subtopic A Recurrence Relations
Mark Scheme
Subtopic B Arithmetic Series
Mark Scheme
Subtopic C Geometric Series
Mark Scheme
CH 06

Trigonometric Identities and Equations

Angles in all four quadrants, exact values, trig identities, solving simple and harder trig equations, equations and identities.

Identities Equations Exact Values
Trend Analysis Mark Scheme
Subtopic A "Show That" Quadratic Format
Mark Scheme
Subtopic B Solving Trigonometric Equations (Direct Format)
Mark Scheme
Subtopic C Identity Manipulation (sin²+cos²=1, tan=sin/cos)
Mark Scheme
Subtopic D Double-Angle & Compound Argument Substitution
Mark Scheme
CH 07 ~ 08

Differentiation & Integration

Increasing and decreasing functions, stationary points, definite integrals, areas under curves, areas between curves and lines, and the trapezium rule.

Stationary Points Areas Trapezium
Trend Analysis Mark Scheme
Subtopic A Differentiation
Mark Scheme
Subtopic B Integration & Area
Mark Scheme
Subtopic C Trapezium Rule
Mark Scheme
CH 01

Proof

Proof by contradiction, including proofs of irrationality and infinity of primes.

Contradiction Irrationality
Trend Analysis Mark Scheme
CH 02

Partial Fractions

Partial fractions with linear factors, repeated factors, and improper fractions.

Linear Repeated Improper
Trend Analysis Mark Scheme
CH 03

Coordinate Geometry in the (x,y) Plane

Parametric equations, converting between parametric and Cartesian forms, trig identities in parametric problems, and curve sketching.

Parametric Cartesian Curve Sketching
Trend Analysis Mark Scheme
CH 04

Binomial Expansion

Expanding (1+x)^n for any rational n, expanding (a+bx)^n, and using partial fractions with the binomial expansion.

(1+x)^n (a+bx)^n Partial Fractions
Trend Analysis Mark Scheme
CH 05

Differentiation

Parametric differentiation, implicit differentiation, and connected rates of change.

Parametric Implicit Rates of Change
Trend Analysis Mark Scheme
CH 06

Integration

Areas parametrically, volumes of revolution, integration by substitution, by parts, using partial fractions, differential equations, and modelling.

Substitution Parts Volumes Diff. Eq.
Trend Analysis Mark Scheme
CH 07

Vectors

2D and 3D vectors, magnitude, direction, geometric problems, position vectors, 3D coordinates, equations of lines, intersections, and the scalar product.

3D Vectors Lines Scalar Product
Trend Analysis Mark Scheme
P2

Planner & Checklist

Tools to organise your revision, track topics, and log past paper progress.

Weekly Planner

Plan your study week with daily goals and time blocks — stay on track with a clear, structured revision schedule.

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Topic Checklist

Tick off every syllabus point as you master it — see your progress at a glance and identify gaps before the exam.

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Past Paper Tracker

Log every paper you complete with scores and timing — spot trends, track improvement, and target weak areas.

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Worked Solution
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