GCSE Further Maths

Practice papers with model solutions

Original practice sets for GCSE Further Maths, drawn from our own question bank. Each has a stable link, a printable PDF and a full worked mark scheme.

GCSE Further Maths - Grades 1-9

GCSE Further Maths Paper 1

Covers Algebraic Manipulation, Surds and Indices, Simultaneous Equations and Inequalities and 9 more.

13 questions - 60 marks

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GCSE Further Maths - Grades 1-9

GCSE Further Maths Paper 2

Covers Algebraic Manipulation, Surds and Indices, Simultaneous Equations and Inequalities and 9 more.

14 questions - 60 marks

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GCSE Further Maths - Grades 1-9

GCSE Further Maths Paper 3

Covers Algebraic Manipulation, Surds and Indices, Simultaneous Equations and Inequalities and 9 more.

16 questions - 60 marks

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GCSE Further Maths - Grades 1-9

GCSE Further Maths Paper 4

Covers Algebraic Manipulation, Surds and Indices, Simultaneous Equations and Inequalities and 9 more.

14 questions - 60 marks

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GCSE Further Maths - Grades 1-9

GCSE Further Maths Short Paper A

Covers Algebraic Manipulation, Surds and Indices, Simultaneous Equations and Inequalities and 3 more.

9 questions - 40 marks

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GCSE Further Maths - Grades 1-9

GCSE Further Maths Short Paper B

Covers Differentiation, Applications of Differentiation, Trigonometric Identities and Equations and 3 more.

9 questions - 40 marks

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Papers scoped to what has been taught

The papers above are scoped by grade band. These are scoped by teaching point instead: each one leaves out content a student at that stage has not met yet, so a mock in the middle of the course tests what has actually been covered.

These bands are a typical teaching order, not a syllabus rule. No exam board defines what belongs to Year 10, and schools sequence the course differently. Check the split against your own scheme of work before using it to decide what a class has covered. Unlike an AS/A2 split, there is no specification document that defines "Year 10 content" for GCSE Further Maths - this is a scheme-of-work convention and it genuinely varies by school: some centres compress the whole qualification into Year 11, some start it in Year 9, and the order topics are introduced in depends on staffing, timetabling and cohort confidence. Treat this as a reasonable default sequencing based on typical prerequisite structure, not as a fact about any specific school's curriculum. I am least confident about matrices, which some schemes introduce early since it needs little GCSE background and is sometimes used to vary the Year 10 diet, and about functions-graphs as a whole, since basic function notation is often taught early but harder content like composite and inverse functions can be deferred to Year 11 - here the entire topic is treated as Year 10 calculus groundwork, which may not hold at every centre.

Year 10

GCSE Further Maths - Year 10

Year 10 Paper 1: Core Skills

Covers the full Year 10 further maths topic list: algebraic manipulation, surds and indices, simultaneous equations and inequalities, functions and their graphs, coordinate geometry, and sequences.

14 questions - 60 marks

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GCSE Further Maths - Year 10

Year 10 Paper 2: Algebra and Equations

Covers algebraic manipulation, surds and indices, simultaneous equations and inequalities, functions and their graphs, and coordinate geometry.

13 questions - 60 marks

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GCSE Further Maths - Year 10

Year 10 Paper 3: Graphs and Geometry

Covers algebraic manipulation, simultaneous equations and inequalities, functions and their graphs, coordinate geometry, and sequences.

19 questions - 80 marks

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GCSE Further Maths - Year 10

Year 10 Paper 4: Algebra and Sequences

Covers algebraic manipulation, surds and indices, simultaneous equations and inequalities, coordinate geometry, and sequences.

14 questions - 60 marks

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GCSE Further Maths - Year 10

Year 10 Paper 5: Equations, Graphs and Sequences

Covers surds and indices, simultaneous equations and inequalities, functions and their graphs, coordinate geometry, and sequences.

19 questions - 80 marks

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GCSE Further Maths - Year 10

Year 10 Paper 6: Mixed Review

Brings together algebraic manipulation, surds and indices, simultaneous equations and inequalities, functions and their graphs, and sequences in one longer paper.

24 questions - 100 marks

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Year 11

GCSE Further Maths - Year 11

Year 11 Paper 1: Algebra and Graphs Recap

Revisits algebraic manipulation, surds and indices, simultaneous equations and inequalities, functions and their graphs, coordinate geometry, and sequences before the Year 11 topics are added.

15 questions - 60 marks

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GCSE Further Maths - Year 11

Year 11 Paper 2: Matrices and Coordinate Methods

Covers algebraic manipulation, simultaneous equations and inequalities, functions and their graphs, coordinate geometry, and matrices and transformations.

13 questions - 60 marks

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GCSE Further Maths - Year 11

Year 11 Paper 3: Differentiation and Its Applications

Covers algebraic manipulation, functions and their graphs, coordinate geometry, differentiation, applications of differentiation, and sequences.

20 questions - 80 marks

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GCSE Further Maths - Year 11

Year 11 Paper 4: Trigonometric Methods

Covers surds and indices, simultaneous equations and inequalities, trigonometric identities and equations, non-right-angled triangle trigonometry, and sequences.

13 questions - 60 marks

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GCSE Further Maths - Year 11

Year 11 Paper 5: Sequences, Trigonometry and Proof

Covers algebraic manipulation, sequences, matrices and transformations, non-right-angled triangle trigonometry, and geometric proof.

18 questions - 80 marks

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GCSE Further Maths - Year 11

Year 11 Paper 6: Mixed Practice

Brings together algebraic manipulation, functions and their graphs, coordinate geometry, differentiation, applications of differentiation, trigonometric identities and equations, non-right-angled triangle trigonometry, and sequences in one longer paper.

25 questions - 100 marks

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