IGCSE Further Pure Mathematics
Logarithms, quadratics, series, calculus, trigonometry and more.
Mind Map
Interactive mind map covering all topics in the module — explore connections between key concepts visually.
Coming SoonTextbook
The complete course textbook covering every topic in the syllabus, with clear explanations, worked examples, and exercises to build confidence and fluency.
Questions by Topic
Exam-style questions by topic, arranged by difficulty with full mark schemes and worked solutions to sharpen your technique.
Past Papers
Full worked solutions to all Edexcel IGCSE past paper questions, taught by experienced instructors with clear step-by-step explanations for every mark.
Coming SoonPlanner & Checklist
A structured study planner and checklist to track your progress through every topic, ensuring complete and confident exam preparation.
Flashcards
Develop your understanding using custom-built flashcards covering key definitions, identities, and results — perfect for quick daily revision sessions.
Coming SoonCourse Structure and Content
The Edexcel International GCSE (9-1) Further Pure Mathematics qualification provides a solid foundation in advanced mathematical techniques. The course covers ten interconnected chapters ranging from logarithmic functions and indices through to calculus and trigonometry, building the analytical skills needed for A-Level study.
At the end of the course, all students sit two written examinations. Paper 1 is a calculator-permitted paper lasting 2 hours, worth 100 marks (50%). Paper 2 is also calculator-permitted, lasting 1 hour 45 minutes, worth 80 marks (50%).
A calculator is permitted on both papers. Students are encouraged to use it to verify intermediate results, freeing attention for the deeper mathematical reasoning and justification that earn the most marks.
Questions range from short procedural exercises to multi-step problems that connect different parts of the syllabus — for example, applying calculus techniques alongside trigonometric identities, or combining series with binomial expansions.
There is no coursework or internal assessment component. Achievement is determined entirely by the final written examinations, rewarding consistent algebraic fluency, careful presentation, and a structured approach to problem-solving.
Tips for Success
- Accurate and concise mathematical communication is vital — show all your steps of working clearly.
- Always simplify as much as possible — it often makes next steps easier, non-simplified answers can lose marks and it is good practice for your algebraic manipulation!
- Particularly in long questions with multiple parts, look for information or solutions from previous parts to help you.
IGCSE Further Pure Mathematics
Textbook — Select a chapter to read in the notebook.
Surds and Logarithmic Functions
Surds, laws of logarithms, change of base, exponential equations, and index laws applied to solve problems.
The Quadratic Function
Completing the square, quadratic formula, discriminant, simultaneous equations, and applications involving quadratic models.
Inequalities and Identities
Factor theorem, remainder theorem, algebraic identities, solving polynomial inequalities, and modulus functions.
Sketching Polynomials
Sketching polynomial and rational functions, asymptotes, transformations, and modulus graphs.
Sequences and Series
Arithmetic and geometric sequences and series, sigma notation, sum to infinity, and convergence.
The Binomial Series
Binomial expansion for positive integer and fractional powers, approximations, and validity conditions.
Scalar and Vector Quantities
Position vectors, magnitude, direction, scalar product, applications to geometry, and vector equations.
Rectangular Cartesian Coordinates
Distance, midpoint, gradient, equation of a line, parallel and perpendicular lines, circle equations.
Differentiation
Differentiation from first principles, rules for differentiation, tangents, normals, and applications.
Integration
Indefinite and definite integrals, area under curves, area between curves, and applications of integration.
Trigonometry
Radian measure, arc length, sector area, trigonometric equations, identities and proofs.
Questions by Topic
Select a topic to practise exam-style questions with worked solutions.
Surds and Logarithmic Functions
Surds, laws of logarithms, change of base, exponential equations, and index laws applied to solve problems.
The Quadratic Function
Completing the square, quadratic formula, discriminant, simultaneous equations, and applications involving quadratic models.
Inequalities and Identities
Factor theorem, remainder theorem, algebraic identities, solving polynomial inequalities, and modulus functions.
Sketching Polynomials
Sketching polynomial and rational functions, asymptotes, transformations, and modulus graphs.
Sequences and Series
Arithmetic and geometric sequences and series, sigma notation, sum to infinity, and convergence.
The Binomial Series
Binomial expansion for positive integer and fractional powers, approximations, and validity conditions.
Scalar and Vector Quantities
Position vectors, magnitude, direction, scalar product, applications to geometry, and vector equations.
Rectangular Cartesian Coordinates
Distance, midpoint, gradient, equation of a line, parallel and perpendicular lines, circle equations.
Differentiation
Differentiation from first principles, rules for differentiation, tangents, normals, and applications.
Integration
Indefinite and definite integrals, area under curves, area between curves, and applications of integration.
Trigonometry
Radian measure, arc length, sector area, trigonometric equations, identities and proofs.
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.
Topic Checklist
Tick off every syllabus point as you master it — see your progress at a glance and identify gaps before the exam.
Past Paper Tracker
Log every paper you complete with scores and timing — spot trends, track improvement, and target weak areas.