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OCR GCSE Maths

Topic questions Pure mathematics Completing the square

Completing the square

13 questions · 86 marks · about 1.5 hours

Completing the square questions

TopicCompleting the square

OCR J560 Completing the square 13 questions

Paper 5 June 2025 Higher tier, Question 15 5 marks

(a)

Write x2 - 6x + 5 in the form (x - a)2 - b.

[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Write down the coordinates of the turning point of y = x2 - 6x + 5.

[2]
Reveal mark scheme Mark scheme for question 15(b)

Paper 4 June 2024 Higher tier, Question 15 10 marks

(a)

Solve by factorisation.

Question 15, shown as an image
[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Write x2 + 8x + 11 in the form (x + a)2 - b.

[3]
Reveal mark scheme Mark scheme for question 15(b)
(c)(i)

Write down the coordinates of the turning point of the graph y = (x - 3)2 + 8.

[2]
Reveal mark scheme Mark scheme for question 15(c)(i)
(c)(ii)

Describe the single transformation which maps the graph of y = x2 onto the graph of y = (x - 3)2 + 8.

[2]
Reveal mark scheme Mark scheme for question 15(c)(ii)

Paper 5 November 2023 Higher tier, Question 21 6 marks

The graph of y = x2 is shown below for -2 ⩽ x ⩽ 2.

Figure for question 21
(a)

Find the equation of the image when y = x2 is reflected in the line y = 2.

[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Describe the single transformation that maps the graph of y = x2 onto the graph of y = x2 + 6x - 5.

[4]
Reveal mark scheme Mark scheme for question 21(b)

Paper 6 June 2023 Higher tier, Question 20 7 marks

(a)

Write (2x - 5)(x + 4) in the form 2(x + a)2 - b.

You must show your working.

[5]
Reveal mark scheme Mark scheme for question 20(a)
(b)

Charlie, Dev and Eve all attempt to sketch the graph of y = (2 x - 5)(x + 4).

Charlie‛s sketch
Dev‛s sketch Eve‛s sketch

Figure for question 20

Whose sketch is the most accurate? Write down the properties of the graph that you used in making your decision.

[2]
Reveal mark scheme Mark scheme for question 20(b)

Paper 5 November 2022 Higher tier, Question 18 8 marks

(a)

By factorising, find the roots of y = x2 + 18x + 77.

(a) x =........ and x =........

[3]
Reveal mark scheme Mark scheme for question 18(a)
(b)(i)

Write y = x2 + 18x + 77 in the form y = (x + a)2 - b.

[3]
Reveal mark scheme Mark scheme for question 18(b)(i)
(b)(ii)

Write down the coordinates of the turning point of the graph of y = x2 + 18x + 77.

[2]
Reveal mark scheme Mark scheme for question 18(b)(ii)

Paper 6 June 2022 Higher tier, Question 19 5 marks

Also involves Surds

(a)

Write x2 - 8x + 9 in the form maths symbolx - amaths symbol2 - b.

[3]
Reveal mark scheme Mark scheme for question 19(a)
(b)

Use your answer from part (a) to solve.

x2 - 8x + 9 = 0

Give your answers in exact form. You must show your working.

[2]
Reveal mark scheme Mark scheme for question 19(b)

Paper 5 November 2020 Higher tier, Question 19 7 marks

(a)

Write x2 - 10x + 22 in the form (x - a)2 - b.

[3]
Reveal mark scheme Mark scheme for question 19(a)
(b)

Sketch the graph of y = x2 - 10x + 22. Show clearly the coordinates of any turning points and the value of the y-intercept.

Figure for question 19
[4]
Reveal mark scheme Mark scheme for question 19(b)

Paper 5 November 2019 Higher tier, Question 20 6 marks

(a)

Write x2 - 6x + 11 in the form maths symbolx - amaths symbol2 + b.

[3]
Reveal mark scheme Mark scheme for question 20(a)
(b)

Sketch the graph of y = x2 - 6x + 11. Show clearly the coordinates of any turning points.

Figure for question 20
[3]
Reveal mark scheme Mark scheme for question 20(b)

Paper 5 June 2019 Higher tier, Question 17 7 marks

(a)

Write x2 + 8x + 3 in the form maths symbolx + amaths symbol2 - b.

[3]
Reveal mark scheme Mark scheme for question 17(a)
(b)

Sketch the graph of y = x2 + 8x + 3. Show clearly the coordinates of any turning points and the y-intercept.

Figure for question 17
[4]
Reveal mark scheme Mark scheme for question 17(b)

Paper 5 November 2018 Higher tier, Question 18 10 marks

Also involves Surds

(a)(i)

Write x2 + 4x - 16 in the form (x + a)2 - b.

[3]
Reveal mark scheme Mark scheme for question 18(a)(i)
(a)(ii)

Solve the equation x2 + 4x - 16 = 0. Give your answers in surd form as simply as possible.

(ii) x =........ or x =........

[4]
Reveal mark scheme Mark scheme for question 18(a)(ii)
(b)

Sketch the graph of y = x2 + 4x - 16, showing clearly the coordinates of any turning points.

Figure for question 18
[3]
Reveal mark scheme Mark scheme for question 18(b)

Paper 4 June 2018 Higher tier, Question 15 7 marks

(a)

Write x2 – 8x + 25 in the form (x – a)2 + b.

[3]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Write down the coordinates of the turning point of the graph of y = x2 – 8x + 25.

[2]
Reveal mark scheme Mark scheme for question 15(b)
(c)

Hence describe the single transformation which maps the graph of y = x2 onto the graph of y = x2 – 8x + 25.

[2]
Reveal mark scheme Mark scheme for question 15(c)

Paper 4 November 2017 Higher tier, Question 16 5 marks

(a)

Write x2 - 6x + 20 in the form (x - a)2 + b.

[3]
Reveal mark scheme Mark scheme for question 16(a)
(b)

Write down the turning point of the graph of y = x2 - 6x + 20.

[2]
Reveal mark scheme Mark scheme for question 16(b)

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