A-level · Algebra & functions

The modulus functionExam-style questions

The modulus as a distance, and what follows from that. The graph of y = |x − a| and how to sketch y = |f(x)|; modulus equations, with two cases or by squaring; modulus inequalities, one stretch or two; why a solution must be checked when the other side contains x; and counting solutions with a horizontal line across the V.

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37 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Solve $|x^{2} - 4| = 3$ . (4 marks)
Level 3 · 4 marksTry it
2
(a) Sketch the graph of $y = |3x - 4|$ , stating the coordinates of the points where the graph meets the axes. (2 marks)
(b) Solve the equation $|3x-4| = 2x + 7$ . (4 marks)
(c) Hence write down the solution of the inequality $|3x-4| < 2x + 7$ . (1 mark)
Level 3 · 7 marksTry it
3
Solve $|2x + 1| > 7$ . (3 marks)
Level 3 · 3 marksTry it
4
(a) Sketch the graph of $y = |2x + 5|$ .

(1 mark)
(b) Solve the inequality $4 - x > |2x + 5|$ .

(3 marks)
Level 3 · 4 marksTry it
5
In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

The graph with equation $y = |9 - 4x|$ is V-shaped, with its vertex on the $x$ -axis.

Solve

$|9 - 4x| = 6 + 2x$

(4 marks)
Level 3 · 4 marksTry it

6 more questions on the modulus function

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