2.17 Solution of linear and quadratic inequalities Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Solve x + 3 > 7.

   • x ≥ 4
   • x < 4
   • x > 4
   • x > 10

2. What is the set of values of x satisfying the inequality x^2 < 9?

   • x < 3
   • x > 3
   • -3 < x < 3
   • x < -3

3. Solve x^2 < 16.

   • 0 < x < 16
   • x < 4
   • −4 < x < 4
   • x < −4 or x > 4

4. Solve 2x − 5 ≤ 1.

   • x ≥ 3
   • x ≤ 6
   • x ≤ −2
   • x ≤ 3

5. Which value does NOT satisfy 3x − 1 ≥ 8?

   • 4
   • 3
   • 2.5
   • 5

6. Solve 5(x − 7) > 2(x + 1).

   • x > 37/3
   • x < 37/3
   • x > 11
   • x > −37/3

7. Solve x^2 ≥ 25.

   • −5 ≤ x ≤ 5
   • x ≤ 5
   • x ≤ −5 or x ≥ 5
   • x ≥ 5 only

8. Solve 3x^2 − 5x − 2 > 0.

   • x > −1/3
   • −1/3 < x < 2
   • x < −2 or x > 1/3
   • x < −1/3 or x > 2

9. Solve (x − 1)(x + 4) ≤ 0.

   • −1 ≤ x ≤ 4
   • x ≤ −4 or x ≥ 1
   • −4 ≤ x ≤ 1
   • x ≥ −4

10. How many integers satisfy 2 < 3x − 1 ≤ 11?

    • 2
    • 3
    • 1
    • 4

11. Solve x + 3 > 2x − 1 and 4x − 2 ≤ 10 together. Which is the solution set?

    • x ≤ 3
    • x < 4
    • x < 3
    • x ≥ 3

12. What is the smallest integer n satisfying 7 − 2x < 1?

    • 2
    • 5
    • 3
    • 4

13. For which real values of x is the inequality x^2 + 2x + 5 > 0 satisfied?

    • No real values
    • All real values
    • x > -1
    • x > 2

14. Solve x^2 − 4x ≤ 0.

    • −4 ≤ x ≤ 0
    • 0 ≤ x ≤ 4
    • x ≤ 0 or x ≥ 4
    • x ≥ 4

15. Solve 2(x + 1) − (x − 3) ≥ 3x − 4.

    • x ≤ 4
    • x ≤ 1/2
    • x ≤ 9/2
    • x ≥ 9/2

16. For what values of k does x^2 + kx + 4 = 0 have real roots?

    • k ≥ 4 only
    • k ≤ 2
    • −4 ≤ k ≤ 4
    • k ≤ −4 or k ≥ 4

17. What is the smallest positive integer n such that n^2 > 50?

    • 9
    • 8
    • 7
    • 25

18. Solve x^2 − 7x + 10 < 0.

    • x > 5
    • x < −2 or x > −5
    • x < 2 or x > 5
    • 2 < x < 5

19. A rectangle has length 2x + 3 and width x. Its area is at most 35. What is the largest possible positive value of x?

    • 7
    • 2.5
    • 3.5
    • 5

20. Solve 4 − x > 2x − 5.

    • x > 9
    • x < −3
    • x > 3
    • x < 3

Related quizzes

• The basic processes of algebra Quiz · 2.1 · 20 questions
• Definition of a function Quiz · 2.2 · 20 questions
• Domain and range of a function Quiz · 2.3 · 20 questions
• Composite functions Quiz · 2.4 · 20 questions
• Inverse functions Quiz · 2.5 · 20 questions
• Expanding brackets and collecting like terms Quiz · 2.6 · 20 questions
• Expand (a + b)^n for positive integer n Quiz · 2.7 · 20 questions
• Factorising Quiz · 2.8 · 20 questions
• Manipulation of rational expressions: Use of + – × ÷ for algebraic fractions with denominators being numeric, linear or quadratic Quiz · 2.9 · 20 questions
• Use and manipulation of formulae and expressions Quiz · 2.10 · 20 questions