Completing the square

Mark scheme and answers · Total marks: 45

Question 1 [1 mark]

x = -5 ± 9

Mark scheme
  • A [1] — cao x = -5 ± √9

Accept algebraically equivalent correct forms.

Question 2 [1 mark]

x = 3 or x = -7

Mark scheme
  • A [1] — cao x = 3 or x = -7

Accept algebraically equivalent correct forms.

Question 3 [1 mark]

(x - 3.5)² - 2.25

Mark scheme
  • A [1] — cao (x - 3.5)² - 2.25

Accept algebraically equivalent correct forms.

Question 4 [1 mark]

2(x + 2)² - 2

Mark scheme
  • A [1] — cao 2(x + 2)² - 2

Accept algebraically equivalent correct forms.

Question 5 [1 mark]

3(x - 2)² - 2

Mark scheme
  • A [1] — cao 3(x - 2)² - 2

Accept algebraically equivalent correct forms.

Question 6 [1 mark]

(x + 0.75)² - 2.5625

Mark scheme
  • A [1] — cao (x + 0.75)² - 2.5625

Accept algebraically equivalent correct forms.

Question 7 [1 mark]

(3, 2)

Mark scheme
  • A [1] — cao (3, 2)

Accept algebraically equivalent correct forms.

Question 8 [1 mark]

(x + 3)² - 1

Mark scheme
  • A [1] — cao (x + 3)² - 1

Accept algebraically equivalent correct forms.

Question 9 [1 mark]

(x - 2)² - 3

Mark scheme
  • A [1] — cao (x - 2)² - 3

Accept algebraically equivalent correct forms.

Question 10 [1 mark]

(x - 4)² - 9

Mark scheme
  • A [1] — cao (x - 4)² - 9

Accept algebraically equivalent correct forms.

Question 11 [1 mark]

(x + 1)² - 6

Mark scheme
  • A [1] — cao (x + 1)² - 6

Accept algebraically equivalent correct forms.

Question 12 [1 mark]

(x + 5)²

Mark scheme
  • A [1] — cao (x + 5)²

Accept algebraically equivalent correct forms.

Question 13 [1 mark]

(x + 2.5)² - 0.25

Mark scheme
  • A [1] — cao (x + 2.5)² - 0.25

Accept algebraically equivalent correct forms.

Question 14 [1 mark]

(x + 0.5)² - 6.25

Mark scheme
  • A [1] — cao (x + 0.5)² - 6.25

Accept algebraically equivalent correct forms.

Question 15 [1 mark]

x = 2.5 ± 3.25

Mark scheme
  • A [1] — cao x = 2.5 ± √3.25

Accept algebraically equivalent correct forms.

Question 16 [2 marks]

k ≤ 4

Mark scheme
  • A [2] — cao k ≤ 4

Accept algebraically equivalent correct forms.

Question 17 [2 marks]

8

Mark scheme
  • A [2] — cao 8

Accept algebraically equivalent correct forms.

Question 18 [2 marks]

(-2, -3)

Mark scheme
  • A [2] — cao (-2, -3)

Accept algebraically equivalent correct forms.

Question 19 [2 marks]

x = [-b ± b² - 4ac]/(2a)

Mark scheme
  • A [2] — cao x = [-b ± √(b² - 4ac)]/(2a)

Accept algebraically equivalent correct forms.

Question 20 [2 marks]

4(x + 3)² - 1

Mark scheme
  • A [2] — cao 4(x + 3)² - 1

Accept algebraically equivalent correct forms.

Question 21 [2 marks]

x = -1 or x = -5

Mark scheme
  • A [2] — cao x = -1 or x = -5

Accept algebraically equivalent correct forms.

Question 22 [2 marks]

x = 5 or x = -3

Mark scheme
  • A [2] — cao x = 5 or x = -3

Accept algebraically equivalent correct forms.

Question 23 [2 marks]

x = 0.67 or x = -3.00

Mark scheme
  • A [2] — cao x = 0.67 or x = -3.00

Accept algebraically equivalent correct forms.

Question 24 [2 marks]

x = 2 or x = 6

Mark scheme
  • A [2] — cao x = 2 or x = 6

Accept algebraically equivalent correct forms.

Question 25 [2 marks]

x = 2 ± 2.25

Mark scheme
  • A [2] — cao x = 2 ± √2.25

Accept algebraically equivalent correct forms.

Question 26 [2 marks]

p = -4, q = -1

Mark scheme
  • A [2] — cao p = -4, q = -1

Accept algebraically equivalent correct forms.

Question 27 [2 marks]

2(x + 0.75)² - 5.125

Mark scheme
  • A [2] — cao 2(x + 0.75)² - 5.125

Accept algebraically equivalent correct forms.

Question 28 [2 marks]

x = -3 or x = -4

Mark scheme
  • A [2] — cao x = -3 or x = -4

Accept algebraically equivalent correct forms.

Question 29 [2 marks]

x = -1 or x = -5

Mark scheme
  • A [2] — cao x = -1 or x = -5

Accept algebraically equivalent correct forms.

Question 30 [2 marks]

6(x - 1)² + 1

Mark scheme
  • A [2] — cao 6(x - 1)² + 1

Accept algebraically equivalent correct forms.