A-Level Mathematics · Cambridge International · Pearson Edexcel · AQA · OCR · Equivalent A-Levels

Free A-Level Mathematics Practice, Built Like a Proper Syllabus

Begin with free topic-based Mathematics revision, structured problems, calculations, proofs, and practice tests across all major A-Level domains, then move to premium timed, mock-exam-style practice when you need a larger question bank and worked solutions.

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Sections10
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Cambridge InternationalPearson EdexcelAQAOCREquivalent A-Levels
Free Mathematics Practice

Start With Free A-Level Mathematics Tests

Use the free version to begin immediately, practise one Mathematics topic at a time, diagnose weak areas, and strengthen algebraic fluency, graph interpretation, calculus, modelling, proof, and multi-step mathematical reasoning.

  • No access code needed
  • Ten focused Mathematics topics
  • Targeted revision pathway
  • Start practising immediately
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Premium Mathematics Practice

Turn Practice Into Exam Confidence

1,000practice questions & exercises with worked solutions

Move beyond occasional revision into a complete preparation system covering the full A-Level Mathematics syllabus with timed, exam-style practice.

  • 1,000 practice questions
  • Worked solutions explanations
  • Timed exam-style practice
  • Full syllabus reinforcement
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One premium pathway. Ten Mathematics domains. One thousand opportunities to replace uncertainty with exam-ready confidence.

Course coverage

What the Free A-Level Mathematics Version Covers

Alternate between number and algebra topics and geometry, mensuration, statistics and probability so procedural fluency and problem-solving confidence develop together.

01 Foundations of Pure Mathematics (Core Algebra and Number) Build a strong A-Level Mathematics foundation by mastering algebraic methods, proof basics, equations, inequalities, and the core symbolic fluency that supports higher pure mathematics.
  • Sets, intervals, notation, logical implication, contradiction, contrapositive, and introductory proof methods
  • Indices, surds, and logarithms, including negative and fractional powers, rationalising denominators, and solving exponential or logarithmic equations
  • Polynomial expansion, factorisation, completing the square, remainder and factor ideas, and algebraic division
  • Algebraic fractions and partial fractions, including linear and repeated factors, with extension to irreducible quadratic forms where relevant
  • Linear, quadratic, simultaneous, and modulus equations and inequalities, with clear interpretation of solution sets
  • Function notation, domain and range, restrictions, composite functions, inverses, and graph transformations
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02 Functions, Graphs, and Transformations Strengthen graph interpretation and functional reasoning by working with standard families of functions, transformations, inverses, compositions, and piecewise or parametric forms.
  • Sketching and interpreting linear, quadratic, cubic, reciprocal, exponential, and logarithmic graphs
  • Recognising intercepts, asymptotes, turning points, end behaviour, and other key graphical features
  • Translations, stretches, compressions, and reflections, including combined transformations and their effect on graph behaviour
  • Inverse and composite functions, with domain restrictions and one-to-one conditions for invertibility
  • Piecewise-defined functions, continuity at boundaries, and solving equations or inequalities across different intervals
  • Parametric representation, conversion to Cartesian form, and basic sketching of parametric curves
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03 Coordinate Geometry and Straight Lines Develop confident coordinate reasoning through gradients, line equations, intersections, geometric interpretation, and the use of algebra to solve plane geometry problems.
  • Distance and midpoint formulae, gradient interpretation, and coordinate geometry fundamentals
  • Straight-line forms including slope-intercept, point-slope, and two-point form
  • Parallel and perpendicular line relationships, including gradient conditions and geometric meaning
  • Intersection of lines, angle between lines, and algebraic methods for coordinate geometry questions
  • Regions defined by linear inequalities, half-planes, and feasible regions in optimisation-style questions
  • Applications involving loci, distance constraints, and problems translated from geometry into coordinate form
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04 Trigonometry and Trigonometric Identities Prepare for advanced trigonometry by studying trig graphs, identities, equations, and triangle applications in both algebraic and contextual settings.
  • Degree and radian measure, graphs of sine, cosine, and tangent, and their transformations
  • Amplitude, period, phase shift, vertical shift, and interpretation of transformed trig functions
  • Pythagorean, reciprocal, compound-angle, and double-angle identities, with half-angle extensions where included
  • Using identities to simplify expressions, prove results, and transform equations into solvable forms
  • Solving trigonometric equations and inequalities in specified intervals and giving multiple or general solutions where required
  • Sine rule, cosine rule, area formula, ambiguous case questions, and bearings or navigation-style applications
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05 Exponentials, Logarithms, and Growth or Decay Modelling Use exponential and logarithmic techniques to solve equations, compare growth patterns, and model real processes such as half-life, doubling time, and continuous change.
  • Properties and graph behaviour of exponential and logarithmic functions, including asymptotes and domains
  • Solving equations that combine exponentials and logarithms, with change-of-base and algebraic transformation methods
  • Checking the validity of solutions against domain restrictions and expression conditions
  • Growth and decay models, including half-life, doubling-time, and interpretation of parameters
  • Linearising relationships with logarithms where appropriate for modelling and analysis
  • Solving inequalities involving exponential or logarithmic expressions with careful attention to valid intervals
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06 Differentiation (Single-Variable Calculus) Build strong calculus technique by learning the meaning of the derivative, standard differentiation rules, and advanced methods used in pure mathematics questions.
  • Differentiation from first principles as a conceptual introduction to gradient and tangent ideas
  • Core rules including the power rule, constant multiple, sum and difference rules, product rule, quotient rule, and chain rule
  • Differentiation of exponential, logarithmic, and trigonometric functions, including composite forms
  • Implicit differentiation for relations not written explicitly as y equals a function of x
  • Parametric differentiation using dy/dx as dy/dt divided by dx/dt
  • Higher derivatives, tangent and normal gradients, and second derivative interpretation
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07 Applications of Differentiation (Optimisation and Curve Analysis) Apply calculus to analyse curves, classify stationary points, optimise quantities, and interpret changing behaviour in mathematical and real-world contexts.
  • Stationary points, local maxima and minima, and points of inflection
  • Classification using first derivative sign changes and second derivative tests where included
  • Curve sketching using intercepts, asymptotes, increasing and decreasing intervals, and concavity
  • Optimisation in geometry, algebra, and modelling contexts by forming objective functions under constraints
  • Checking endpoints, domains, and the practical meaning of optimisation answers
  • Related rates, numerical methods such as Newton-Raphson iteration, and awareness of convergence or approximation accuracy
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08 Integration (Techniques and Definite Integrals) Develop integration fluency through antiderivatives, standard methods, definite integrals, area problems, and links between calculus and kinematics.
  • Indefinite integration using reverse power rules and the constant of integration
  • Integration of exponentials, basic trigonometric functions, and algebraic expressions
  • Techniques such as substitution, integration by parts, and partial fractions where required
  • Use of trigonometric identities to simplify integrands before integration
  • Definite integrals, the fundamental theorem of calculus, and properties such as linearity or reversed limits
  • Area under curves, area between curves, sign changes across the x-axis, and displacement, velocity, or acceleration links
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09 Sequences and Series Master ordered patterns and summation methods through arithmetic and geometric sequences, sigma notation, recurrence, binomial expansion, and convergence ideas.
  • Arithmetic sequences and series, including nth-term formulas and sums of the first n terms
  • Geometric sequences and series, including finite sums and sums to infinity under convergence conditions
  • Recurrence relations and interpretation of sequence generation where included
  • Sigma notation, splitting sums, index shifts, and telescoping ideas in suitable contexts
  • Binomial expansion, general terms, coefficient finding, and approximations for small values where included
  • Basic convergence and divergence reasoning, especially for geometric series
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10 Vectors and Advanced Pure Extensions Strengthen spatial and abstract reasoning through vectors in two and three dimensions, line representations, dot product methods, and advanced extensions that appear in some A-Level routes.
  • Vector notation, magnitude, unit vectors, vector addition, subtraction, and scalar multiplication
  • Position vectors and geometric relationships involving collinearity or line intersection
  • Vector equations of lines in parametric or vector form, including interpretation of coordinates and direction
  • Dot product methods for angles, perpendicularity, and basic projection ideas where included
  • Further pure extensions such as induction on identities, first-order separable differential equations, or Maclaurin and Taylor ideas in advanced routes
  • Awareness that some A-Level Mathematics variants may also include complex numbers, while others reserve them for Further Mathematics
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Begin revising

Choose a Free Mathematics Practice Section

Each free section opens in a new tab. Premium Mathematics practice is available separately and requires an access code.

01Foundations of Pure Mathematics (Core Algebra and Number) 02Functions, Graphs, and Transformations 03Coordinate Geometry and Straight Lines 04Trigonometry and Trigonometric Identities 05Exponentials, Logarithms, and Growth or Decay Modelling 06Differentiation (Single-Variable Calculus) 07Applications of Differentiation (Optimisation and Curve Analysis) 08Integration (Techniques and Definite Integrals) 09Sequences and Series 10Vectors and Advanced Pure Extensions
A-Level Mathematics preparation overview

Why the Free and Premium Mathematics Pathways Work Together

“A disciplined, manageable, globally understandable study path for A-Level Mathematics.”

This page provides both an immediate free-practice pathway and a clear premium upgrade route for learners preparing for A-Level Mathematics across multiple examination systems. Candidates can first diagnose weaknesses through free topic-based tests, then progress to premium timed and solution-rich practice when greater depth is needed.

The layout uses clearer topic separation, stronger mathematics-focused visual structure, and improved navigation — making the page easier to scan and more useful for learners who want to identify exactly which topic to tackle next.

This section-based structure is especially valuable for learners preparing for Cambridge International, Pearson Edexcel, AQA, OCR and equivalent A-Level examinations who need a disciplined, manageable, and globally understandable study path for Mathematics.

Learners building a broader A-Level study plan can also continue with Physics practice, Chemistry practice, Biology practice, and Economics practice.

Better diagnosisTopic separation makes it easier to see whether problems come from number, algebra, geometry, mensuration, trigonometry, statistics, probability, or graphs.
Efficient revision flowAlternate between calculation-based, conceptual, and practical-style topics for balanced preparation.
Stronger exam readinessFocused practice supports better control, speed, and consistency in A-Level Mathematics examinations.
Have questions?

Frequently Asked Questions

Short answers that explain how to use the A-Level Mathematics page effectively.

What is the purpose of this A-Level Mathematics page?

This page provides a structured overview of the major A-Level Mathematics sections so learners understand what each topic involves before beginning practice. It connects syllabus awareness with focused exam preparation.

Is this page suitable for Cambridge International, Pearson Edexcel, AQA, OCR, and equivalent A-Level learners?

Yes. The page supports major A-Level and equivalent school-leaving Mathematics examinations while covering the shared core knowledge and skills learners are expected to master.

Are the 10 sections arranged in a useful study order?

Yes. The sections move through the major A-Level Mathematics domains in a logical sequence, although learners can begin with whichever topic requires the most attention.

Can I use this page for targeted A-Level revision?

Yes. The page is designed for focused topic practice, helping learners work specifically on weak areas such as number, algebra, geometry, mensuration, trigonometry, statistics, probability, or graphs instead of revising everything at once.

Are the A-Level Mathematics practice tests free?

Yes. Learners can begin with the free topic-based Mathematics practice sections immediately without an access code. The free version is suitable for identifying weak topics and building confidence progressively.

What is the difference between the free version and the 1,000-question premium Mathematics version?

The free version lets learners practise immediately by topic. The premium version contains 1,000 structured practice questions and exercises, timed exam-style preparation, worked solutions, and access-code protection.

Can I use this page for Mathematics mock-exam preparation?

Yes. The free sections support topic revision, while the premium pathway is intended for timed, exam-style practice that can form part of a structured mock-examination routine.

What kinds of questions and skills does the practice cover?

The ten-topic structure supports algebraic fluency, graph interpretation, calculus, modelling, proof, and multi-step mathematical reasoning across the main A-Level Mathematics areas.

How should I move from free to premium Mathematics practice?

Begin with the free sections to identify weak topics. Move to premium when you are ready to complete 1,000 practice questions and exercises, train under timed conditions, and use worked solutions to correct mistakes systematically.

Can teachers and parents use the page to organise revision?

Yes. Teachers and parents can use the ten-section structure to identify weak domains, assign focused practice, and monitor improvement across algebraic fluency, graph interpretation, calculus, modelling, proof, and multi-step mathematical reasoning.