Worksheet library · IGCSE

IGCSE Maths Exam Questions by Topic

Practise IGCSE Maths one topic at a time with original Edexcel-style questions. The 19 topic sets below contain 109 printable pages, with the mark scheme beside the questions so you can check the method before moving on.

Edexcel

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: Differentiation: Gradients and Turning Points

A curve has equation y = x^3 - 6x^2 + 9x. Find the coordinates of the two turning points and determine the nature of each.

Differentiate term by term: dy/dx = 3x^2 - 12x + 9.
Set the gradient to zero: 3x^2 - 12x + 9 = 0. Divide through by 3 to get x^2 - 4x + 3 = 0, then factorise to (x - 1)(x - 3) = 0, so x = 1 or x = 3.
Substitute into the original equation for the y values: when x = 1, y = 1 - 6 + 9 = 4, and when x = 3, y = 27 - 54 + 27 = 0.
Differentiate again for the nature: the second derivative is 6x - 12.
At x = 1 the second derivative is 6 - 12 = -6, which is negative, so (1, 4) is a maximum. At x = 3 it is 18 - 12 = 6, which is positive, so (3, 0) is a minimum.
Final answer: a maximum at (1, 4) and a minimum at (3, 0).

5.1 Differentiation: Gradients and Turning Points5p + answers · 50 marks · PDF

1.1 Sets and Venn Notation5p + answers · 43 marks · PDF

2.1 Linear Programming4p + answers · 40 marks · PDF

2.2 Functions: Composite and Inverse Functions4p + answers · 40 marks · PDF

2.3 Matrices and Matrix Transformations4p + answers · 35 marks · PDF

3.1 Vector Geometry: Proof and Ratio Problems3p + answers · 40 marks · PDF

3.2 The Sine Rule, Cosine Rule and Area of a Triangle4p + answers · 40 marks · PDF

3.3 Similarity: Length, Area and Volume Scale Factors4p + answers · 37 marks · PDF

2.4 Arithmetic and Geometric Sequences and Series4p + answers · 33 marks · PDF

2.5 Direct and Inverse Proportion With Non-Linear Powers3p + answers · 37 marks · PDF

2.6 Transformations of Graphs of Functions5p + answers · 28 marks · PDF

3.4 Vectors in Two Dimensions: Notation, Magnitude and Arithmetic4p + answers · 40 marks · PDF