Worksheet library · A Level

A Level Further Maths Exam Questions by Topic

Practise A Level Further Maths one topic at a time with original Edexcel, AQA, OCR and WJEC-style questions. The 33 topic sets below contain 305 printable pages, with the mark scheme beside the questions so you can check the method before moving on.

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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: Complex Numbers

Solve the equation z^2 - 2z + 5 = 0, giving each root in the form a + bi, then find the modulus and argument of the root with positive imaginary part.

Use the quadratic formula: z = [2 +- sqrt((-2)^2 - 4(1)(5))] / (2(1)).
Simplify inside the root: 4 - 20 = -16, so sqrt(-16) = 4i.
z = (2 +- 4i)/2 = 1 +- 2i, so the roots are z = 1 + 2i and z = 1 - 2i.
For z = 1 + 2i, the modulus is sqrt(1^2 + 2^2) = sqrt(5).
The argument is arctan(2/1) = 1.107 radians, since the point (1,2) lies in the first quadrant.
Final answer: z = 1 + 2i or z = 1 - 2i; the root 1 + 2i has modulus sqrt(5) and argument 1.107 radians.

1.1 Complex Numbers7p + answers · 114 marks · PDF

1.2 Matrices4p + answers · 114 marks · PDF

1.3 Further Algebra and Roots3p + answers · 117 marks · PDF

1.4 Further Calculus4p + answers · 114 marks · PDF

1.5 Further Vectors3p + answers · 98 marks · PDF

1.6 Polar Coordinates3p + answers · 111 marks · PDF

1.7 Hyperbolic Functions3p + answers · 114 marks · PDF

1.8 Differential Equations4p + answers · 149 marks · PDF

1.9 Proof by Induction3p + answers · 91 marks · PDF

1.10 Series and Summation4p + answers · 100 marks · PDF

1.11 Maclaurin Series4p + answers · 109 marks · PDF

1.12 Core Pure: Complex Numbers Depth4p + answers · 131 marks · PDF