Lesson B5

B5 Linear and quadratic inequalities Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson B5, Linear and quadratic inequalities: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

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The 20 questions

  1. Solve x^2 - 5x + 6 < 0.

    • -3 < x < -2
    • x <= 2 or x >= 3
    • x < 2 or x > 3
    • 2 < x < 3

  2. Solve x^2 - x - 6 >= 0.

    • x <= 2 or x >= -3
    • -2 <= x <= 3
    • x >= -2 and x <= 3
    • x <= -2 or x >= 3

  3. Solve 3(x - 1) > 2x + 4.

    • x < 7
    • x > 7
    • x > -7
    • x > 1/5

  4. Solve (x - 1)/(x + 2) >= 0.

    • x <= -2 or x >= 1
    • -2 < x <= 1
    • x > -2 and x <= 1
    • x < -2 or x >= 1

  5. Which set notation describes x > 2 or x < -1?

    • [-1, 2]
    • (-1, 2)
    • (-infinity, 2) intersection (-1, infinity)
    • (-infinity, -1) union (2, infinity)

  6. For a quadratic with no real roots and a positive leading coefficient, when is it positive?

    • For all real x
    • Only when x > 0
    • For no real x
    • Only between its roots

  7. Find the range of k for which x^2 + kx + 4 > 0 for all real x.

    • -2 < k < 2
    • k < -4 or k > 4
    • k > 4
    • -4 < k < 4

  8. Which region represents y > x + 1?

    • Below the line y = x + 1, drawn dashed
    • Below the line y = x + 1, drawn solid
    • Above the line y = x + 1, drawn solid
    • Above the line y = x + 1, drawn dashed

  9. How many integers satisfy 2 < x^2 < 20?

    • 3
    • 8
    • 4
    • 6

  10. A rectangle has length x + 3 and width x, and its area is less than 40. Which range of x applies?

    • x < 5
    • x > 5
    • 0 < x < 5
    • -8 < x < 5

  11. Profit P = -x^2 + 10x - 16 is positive for which values of x?

    • 0 < x < 10
    • x < 2 or x > 8
    • 2 < x < 8
    • x > 8

  12. Solve x/(x - 1) < 2.

    • x < 1 or x > 2
    • 1 < x < 2
    • x < 2
    • x > 2

  13. For which x does y = x^2 - 2x + 3 lie above y = 2x?

    • x < 1 or x > 3
    • x < 3
    • x > 1
    • 1 < x < 3

  14. Which statement about x^2 < 0 is correct?

    • Only x = 0 satisfies it
    • All real x satisfy it
    • No real x satisfies it
    • Only negative values of x satisfy it

  15. Solve x^2 - 4 >= 0 and x < 3 together.

    • -2 <= x <= 2
    • x >= 2 only
    • x <= -2 or x >= 3
    • x <= -2 or 2 <= x < 3

  16. Which set of values of x satisfies 2x - 1 < 5 and 3x + 2 > -4?

    • -3 < x < 2
    • -2 < x < 3
    • x < 3 and x < -2
    • x < 3 or x > -2

  17. Solve 2x^2 + 3x - 2 > 0.

    • x < -2 or x > 1/2
    • x < 1/2 or x > 2
    • x > -2 only
    • -2 < x < 1/2

  18. Which expression is positive for all real x?

    • x^2 - 6x + 5
    • x^2 + 2x + 5
    • x^2 - 2x - 5
    • -x^2 + 2x + 5

  19. How many integer values of x satisfy x^2 - 2x - 8 < 0?

    • 4
    • 6
    • 3
    • 5

  20. For (x - a)(x - b) < 0 with a < b, what is the solution set?

    • a < x < b
    • x > a only
    • b < x < a
    • x < a or x > b

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