2.12 Completing the square Quiz: AQA Further Maths, Unit 2

The 20 questions

1. Write x^2 + 6x in the form (x + a)^2 + b.

   • (x + 3)^2 + 9
   • (x + 3)^2 − 9
   • (x − 3)^2 − 9
   • (x + 6)^2 − 36

2. What number must be added to x^2 − 8x to make a perfect square?

   • 16
   • 64
   • 4
   • 8

3. Write x^2 + 4x + 7 in the form (x + a)^2 + b.

   • (x + 2)^2 − 3
   • (x + 2)^2 + 3
   • (x + 2)^2 + 7
   • (x + 4)^2 + 7

4. What are the coordinates of the turning point of y = (x − 3)^2 + 5?

   • (−3, 5)
   • (3, 5)
   • (−3, −5)
   • (3, −5)

5. What is the minimum value of x^2 − 6x + 11?

   • 3
   • −2
   • 2
   • 11

6. Write 3x^2 − 12x + 5 in the form a(x + b)^2 + c.

   • a = 3, b = 2, c = −7
   • a = 3, b = −2, c = 5
   • a = 3, b = −2, c = −7
   • a = −3, b = −2, c = −7

7. Solve x^2 + 6x + 5 = 0 by completing the square.

   • x = −1 or x = −5
   • x = −3 or x = 3
   • x = 1 or x = 5
   • x = −2 or x = −3

8. Solve x^2 − 4x − 1 = 0 by completing the square.

   • x = 2 ± √3
   • x = −2 ± √5
   • x = 2 ± √5
   • x = 4 ± √5

9. What are the coordinates of the minimum point of f(x) = 2x^2 − 8x + 3?

   • (2, −5)
   • (2, 3)
   • (−2, 3)
   • (−2, −5)

10. What is the maximum value of f(x) = −x^2 + 4x − 1?

    • 1
    • 3
    • 4
    • −3

11. Solve (x + 4)^2 = 9.

    • x = −1 or x = −7
    • x = 1 or x = 7
    • x = −7 or x = −4
    • x = −1 or x = 7

12. Write x^2 + 5x − 3 in the form (x + p)^2 + q.

    • (x − 5/2)^2 − 37/4
    • (x + 5/2)^2 − 37/4
    • (x + 5/2)^2 + 37/4
    • (x + 5)^2 − 28

13. How many real solutions does x^2 + 4x + 6 = 0 have?

    • Infinitely many
    • None
    • One
    • Two

14. Write 2x^2 + 8x in the form a(x + b)^2 + c.

    • 2(x + 2)^2 − 8
    • 2(x + 4)^2 − 32
    • 2(x + 2)^2 + 8
    • 2(x − 2)^2 − 8

15. Solve 2(x − 1)^2 = 18.

    • x = 1 or x = 10
    • x = 4 or x = −2
    • x = 3 or x = −3
    • x = −4 or x = 2

16. What is the minimum value of x^2 + 2x + 3?

    • 1
    • 2
    • 3
    • −1

17. Given x^2 + px + q = (x − 3)^2 − 4, what are p and q?

    • p = −6, q = −4
    • p = −3, q = 5
    • p = 6, q = 5
    • p = −6, q = 5

18. What is the maximum value of f(x) = 10 − 2(x − 5)^2?

    • −10
    • 5
    • 20
    • 10

19. Solve 3x^2 − 6x − 9 = 0 by completing the square.

    • x = 9 or x = −3
    • x = −3 or x = 1
    • x = 3 or x = −1
    • x = 3 or x = 1

20. For x^2 − 10x + 30, what is the minimum value?

    • 5
    • 30
    • −5
    • −25

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