A18 Solving quadratic equations Quiz: AQA Maths, Unit 2

The 20 questions

1. Solve x^2 + 5x + 6 = 0.

   • x = 2 or x = 3
   • x = -5 or x = -6
   • x = 5 or x = 6
   • x = -2 or x = -3

2. Solve x^2 - 7x + 12 = 0.

   • x = -3 or x = -4
   • x = 7 or x = 12
   • x = 1 or x = 12
   • x = 3 or x = 4

3. Solve x^2 - 16 = 0.

   • x = 16 only
   • x = 4 or x = -4
   • x = 4 only
   • x = 8 or x = -8

4. Solve x^2 + 3x = 0.

   • x = 0 or x = 3
   • x = 3 or x = -3
   • x = 0 or x = -3
   • x = -3 only

5. Solve 2x^2 - 8x = 0.

   • x = 0 or x = -4
   • x = 4 only
   • x = 0 or x = 4
   • x = 8 only

6. Solve (x - 2)^2 = 9.

   • x = 5 or x = 1
   • x = -5 or x = 1
   • x = 5 or x = -1
   • x = 11 or x = -7

7. Solve x^2 + 4x - 5 = 0.

   • x = -1 or x = 5
   • x = 5 or x = 1
   • x = 1 or x = -5
   • x = 4 or x = -5

8. (H) Solve x^2 + 2x - 2 = 0 using the quadratic formula.

   • x = -1 plus or minus sqrt(3)
   • x = -2 plus or minus sqrt(3)
   • x = 1 plus or minus sqrt(3)
   • x = -1 plus or minus sqrt(2)

9. (H) Solve x^2 + 6x + 4 = 0 to 2 decimal places.

   • x = 0.76 or x = 5.24
   • x = -0.24 or x = -5.76
   • x = -1.76 or x = -4.24
   • x = -0.76 or x = -5.24

10. (H) Solve x^2 + 4x = 5 by completing the square.

    • x = -1 or x = 5
    • x = 9 or x = -1
    • x = 2 or x = -6
    • x = 1 or x = -5

11. (H) Solve x^2 = 3x + 10.

    • x = -5 or x = 2
    • x = 5 or x = -2
    • x = 10 or x = -3
    • x = 3 or x = 10

12. (H) Solve x^2 - 6x + 9 = 0.

    • x = -3 only
    • x = 6 only
    • x = 9 or x = -3
    • x = 3 only

13. A rectangle has length 3 cm more than its width and area 40 cm squared. What is the width?

    • 5 cm
    • -8 cm
    • 3 cm
    • 8 cm

14. A number added to its square gives 56. What are the possible values of the number?

    • 7 or -8
    • 14 or -4
    • 6 or -9
    • 8 or -7

15. The product of two consecutive positive whole numbers is 132. What is the smaller number?

    • 10
    • 11
    • 12
    • 66

16. (H) Solve 2x^2 + 3x - 2 = 0.

    • x = 1 or x = -4
    • x = -1/2 or x = 2
    • x = 1/2 or x = -2
    • x = 2 or x = -1/2

17. (H) What is the first step when solving x^2 + 6x = 2 by completing the square?

    • Factorise the left-hand side as 2x(x + 3)
    • Add 9 to both sides to make a perfect square
    • Subtract 2 from both sides only
    • Divide both sides by x

18. (H) Solve x^2 + 4x + 1 = 0 using the quadratic formula.

    • x = -2 plus or minus sqrt(5)
    • x = -4 plus or minus sqrt(3)
    • x = 2 plus or minus sqrt(3)
    • x = -2 plus or minus sqrt(3)

19. (H) Solve (x + 1)(x - 3) = 5.

    • x = 4 or x = -2
    • x = 5 or x = -3
    • x = -4 or x = 2
    • x = 3 or x = -1

20. What is the standard form of a quadratic equation?

    • ax^3 + bx^2 + c = 0
    • ax^2 + bx + c = 0 with a not equal to 0
    • a/x + b = c
    • ax + b = 0 with a not equal to 0

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