Cambridge IGCSE · Mathematics - Additional (0606)

Equations, inequalities and graphs: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Equations, inequalities and graphs.

10 questions22 marksFree, no account
Question 1
1 mark

Solve the equation \(|3x + 2| = 8\).

Question 2
1 mark

Find the set of values of \(x\) for which \((x + 2)(x - 1)(x - 3) > 0\).

Question 3
1 mark

In the diagram, a sketch of the function \(f(x) = (x + 2)(x - 1)(x - 3)\) is shown. Use the sketch to determine the set of values of \(x\) for which \(f(x) > 0\).

Question 4
1 mark

Solve the equation \(4|x - 1| = 12\).

Question 5
1 mark

Solve the equation \(x - 5\sqrt{x} + 6 = 0\) by using a suitable substitution.

Question 6
2 marks

Solve the equation:
\(|3x + 2| = 11\)

Write your answer out first, then check it against the worked solution.

Question 7
4 marks

Solve the equation \(x^4 - 13x^2 + 36 = 0\) by using an appropriate substitution.

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Question 8
5 marks

The graph of \(y = |(x-2)(x-4)(x+3)|\) is drawn. State the coordinates of all the points where the graph intersects the x-axis and the y-axis.

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Question 9
2 marks

Solve the equation \(|2x - 3| = 5\).

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Question 10
4 marks

Solve the equation \(|x^2 - 6x + 5| = 4\).

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