Cambridge OCR A Level · Mathematics A - H240

Inequalities: Practice Questions

5 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Inequalities.

9 questions19 marksFree, no account

Question 1

1 mark

What is the solution to the inequality \( 4 - x > 2(x - 1) \)?

Question 2

1 mark

A rectangular garden has a length of \( (x + 5) \) m and a width of \( (x - 2) \) m. If the area of the garden must be at least \( 30 \text{ m}^2 \), find the range of possible values for \( x \).

Question 3

1 mark

Solve the inequality \( (x + 4)(x - 1) \ge 0 \).

Question 4

1 mark

Find the values of \( x \) that satisfy the simultaneous inequalities:
\( 2x + 1 > 5 \)
\( x^2 - 10x + 21 < 0 \)

Question 5

1 mark

Find the set of values of \( k \) for which the quadratic equation \( x^2 + kx + 9 = 0 \) has real distinct roots.

Question 6

3 marks

Find the set of values of \(x\) for which \(x^{2} - 7x + 10 > 0\).

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

Question 7

2 marks

Solve the inequality \(3(x - 4) < 15\) and express your answer in set notation.

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Question 8

4 marks

Find the set of values of \( k \) for which the quadratic equation \( 3x^2 - 6x + k = 0 \) has no real roots. Express your answer using interval notation.

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

Question 9

5 marks

(a) Solve the linear inequality:
\( 5x - 3 < 2(x + 6) \)

(b) Solve the quadratic inequality:
\( x^2 - 2x - 15 \geq 0 \)

(c) Find the set of values of \( x \) that satisfy both the inequality in part (a) and the inequality in part (b). Express your answer using set notation.

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

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