Worksheet library · GCSE

GCSE Further Maths Exam Questions by Topic

Practise GCSE Further Maths one topic at a time with original AQA Level 2-style questions. The 37 topic sets below contain 350 printable pages, with the mark scheme beside the questions so you can check the method before moving on.

AQA Level 2

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Algebra (16)Geometry, Calculus, Matrices and Surds (21)

How to practise exam questions by topic

Choose the topic that cost marks in classwork or a past paper. Try the questions without notes so the first attempt shows what the student can actually recall.
Use the mark scheme to compare the method as well as the final answer. For written subjects, check that each credited point is stated clearly; for calculations, identify the first step that went wrong.
Revisit the same topic after a gap, then mix it into a full paper. Topic practice repairs one weakness at a time, while a timed paper checks whether the method can still be recognised among other questions.

See the method: Algebraic Fractions: Simplifying, Multiplying and Dividing

Simplify fully (x^2 + x - 6)/(x^2 - 9).

Factorise the numerator: x^2 + x - 6 = (x + 3)(x - 2).
Factorise the denominator using the difference of two squares: x^2 - 9 = (x - 3)(x + 3).
Rewrite the fraction as [(x + 3)(x - 2)] / [(x - 3)(x + 3)].
Cancel the common factor of (x + 3) from the numerator and denominator.
Final answer: (x - 2)/(x - 3).

2.1 Algebraic Fractions: Simplifying, Multiplying and Dividing6p + answers · 85 marks · PDF

2.1d Algebraic Fractions: Simplifying, Multiplying and Dividing: Fluency and Exam Drill4p + answers · 40 marks · PDF

2.2 Algebraic Fractions: Adding, Subtracting and Solving Equations6p + answers · 84 marks · PDF

2.2d Algebraic Fractions: Adding, Subtracting and Solving Equations: Fluency and Exam Drill4p + answers · 40 marks · PDF

2.3 Quadratic Equations: Factorising, the Formula and Completing the Square6p + answers · 70 marks · PDF

2.3d Quadratic Equations: Factorising, the Formula and Completing the Square: Fluency and Exam Drill4p + answers · 40 marks · PDF

2.4 Quadratic Inequalities6p + answers · 70 marks · PDF

2.4d Quadratic Inequalities: Fluency and Exam Drill4p + answers · 40 marks · PDF

2.5 Simultaneous Equations: Linear and Quadratic7p + answers · 109 marks · PDF

2.5d Simultaneous Equations: Linear and Quadratic: Fluency and Exam Drill4p + answers · 40 marks · PDF

2.6 Functions: Composite and Inverse Functions8p + answers · 104 marks · PDF

2.6d Functions: Composite and Inverse Functions: Fluency and Exam Drill4p + answers · 40 marks · PDF