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WJEC GCSE Maths

Topic questions Geometry and measures Pythagoras' theorem

Pythagoras' theorem

35 questions · 190 marks · about 4 hours

Pythagoras' theorem questions

TopicPythagoras' theorem

WJEC 3300 Pythagoras' theorem 35 questions

Unit 2: Calculator-allowed June 2025 Intermediate tier, Question 15, also on the Higher paper 6 marks

(a)

Calculate the length of PQ.

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

Calculate the size of angle x.

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

Unit 2: Calculator-allowed June 2025 Higher tier, Question 4, also on the Intermediate paper 6 marks

(a)

Calculate the length of PQ.

Figure for question 4
[3]
Reveal mark scheme Mark scheme for question 4(a)
(b)

Calculate the size of angle x.

Figure for question 4
[3]
Reveal mark scheme Mark scheme for question 4(b)

Unit 2: Calculator-allowed November 2024 Intermediate tier, Question 14, also on the Higher paper 6 marks

(a)

Calculate the length of AC.

Figure for question 14
[3]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Calculate the value of x.

Figure for question 14
[3]
Reveal mark scheme Mark scheme for question 14(b)

Unit 2: Calculator-allowed November 2024 Higher tier, Question 5, also on the Intermediate paper 6 marks

(a)

Calculate the length of AC.

Figure for question 5
[3]
Reveal mark scheme Mark scheme for question 5(a)
(b)

Calculate the value of x.

Figure for question 5
[3]
Reveal mark scheme Mark scheme for question 5(b)

Unit 2: Calculator-allowed June 2024 Intermediate tier, Question 16, also on the Higher paper 6 marks

In the diagram below, A B D and B C D are both right-angled triangles.

Figure for question 16

A B = 7·3 cm, A D = 13·8 cm and C D = 5·5 cm.

Calculate the value of y.

[6]
Reveal mark scheme Mark scheme for question 16

Unit 2: Calculator-allowed June 2024 Higher tier, Question 6, also on the Intermediate paper 6 marks

In the diagram below, A B D and B C D are both right-angled triangles.

Figure for question 6

A B = 7·3 cm, A D = 13·8 cm and C D = 5·5 cm.

Calculate the value of y.

[6]
Reveal mark scheme Mark scheme for question 6

Unit 2: Calculator-allowed June 2024 Higher tier, Question 12 6 marks

The pyramid below has a horizontal rectangular base A B C D.

The point O is the top of the pyramid. It is vertically above the point A. O C = 113 cm, A B = 72 cm and C B = 84 cm.

Figure for question 12
(a)

Calculate the length of O A, the vertical height of the pyramid.

[4]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Calculate the volume of this pyramid.

[2]
Reveal mark scheme Mark scheme for question 12(b)

Unit 1: Non-calculator November 2022 Intermediate tier, Question 21, also on the Higher paper 2 marks

(a)

Which complete method, using Pythagoras’s Theorem, can be used to find x ?

Circle your answer.

Figure for question 21
Question 21, shown as an image
Question 21, shown as an image
[1]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Which of the following calculations can be used to find y?

Circle your answer.

Figure for question 21
Question 21, shown as an image
Question 21, shown as an image
[1]
Reveal mark scheme Mark scheme for question 21(b)

Unit 2: Calculator-allowed November 2022 Intermediate tier, Question 13 7 marks

A, B and C are points on the circumference of a circle with centre O.

The length of BC is 10 cm. The diameter of the circle is 18 cm.

Figure for question 13

Calculate the shaded area.

You must show all your working.

[7]
Reveal mark scheme Mark scheme for question 13

Unit 1: Non-calculator November 2022 Higher tier, Question 8, also on the Intermediate paper 2 marks

(a)

Which complete method, using Pythagoras’s Theorem, can be used to find x ?

Circle your answer.

Figure for question 8
Question 8, shown as an image
Question 8, shown as an image
[1]
Reveal mark scheme Mark scheme for question 8(a)
(b)

Which of the following calculations can be used to find y?

Circle your answer.

Figure for question 8
Question 8, shown as an image
Question 8, shown as an image
[1]
Reveal mark scheme Mark scheme for question 8(b)

Unit 2: Calculator-allowed November 2022 Higher tier, Question 4 9 marks

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A, B and C are points on the circumference of a circle with centre O. The length of BC is 10 cm. The diameter of the circle is 18 cm.

Figure for question 4

Calculate the shaded area.

You must show all your working.

[9]
Reveal mark scheme Mark scheme for question 4

Unit 2: Calculator-allowed November 2020 Intermediate tier, Question 11 5 marks

The diagram shows two right-angled triangles, joined together along a common side.

AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.

Figure for question 11

Calculate the area of triangle ACD.

You must show all your working.

[5]
Reveal mark scheme Mark scheme for question 11

Unit 2: Calculator-allowed November 2020 Higher tier, Question 2 7 marks

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram shows two right-angled triangles, joined together along a common side. AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.

Figure for question 2

Calculate the area of triangle ACD.

You must show all your working.

[7]
Reveal mark scheme Mark scheme for question 2

Unit 1: Non-calculator November 2019 Higher tier, Question 10 9 marks

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagrams below show a solid cone and a solid hemisphere.

Figure for question 10

The cone has a base radius of 9 cm and a vertical height of 12 cm. The hemisphere has a radius of 8 cm.

Which of the two solids has the greater curved surface area? You should express any areas in terms of maths symbol.

You must show all your working.

[9]
Reveal mark scheme Mark scheme for question 10

Unit 2: Calculator-allowed November 2019 Higher tier, Question 9 6 marks

The right-angled triangle ABC has an area of 84 cm2.

AB = 24 cm.

Figure for question 9

Calculate the perimeter of the triangle ABC.

You must show all your working.

[6]
Reveal mark scheme Mark scheme for question 9

Unit 2: Calculator-allowed June 2019 Intermediate tier, Question 10 4 marks

Is it possible to draw a right-angled triangle with the measurements shown below?

You must use calculations (not a scale drawing) to support your answer.

You must show all your working.

Figure for question 10
[4]
Reveal mark scheme Mark scheme for question 10

Unit 2: Calculator-allowed June 2019 Higher tier, Question 2 6 marks

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Is it possible to draw a right-angled triangle with the measurements shown below? You must use calculations (not a scale drawing) to support your answer.

You must show all your working.

Figure for question 2
[6]
Reveal mark scheme Mark scheme for question 2

Unit 2: Calculator-allowed November 2018 Higher tier, Question 7 6 marks

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The perimeter of a square is 76.4 m.

Calculate the length of its diagonal.

You must show all your working.

[6]
Reveal mark scheme Mark scheme for question 7

Unit 2: Calculator-allowed November 2018 Higher tier, Question 14 4 marks

The diagram below shows a cuboid with HG = 3 cm, AE = 5 cm and EH = 7 cm.

Figure for question 14

Calculate the length of the line AG.

Give your answer correct to 2 decimal places.

[4]
Reveal mark scheme Mark scheme for question 14

Unit 2: Calculator-allowed June 2018 Intermediate tier, Question 15, also on the Higher paper 3 marks

PQR is a right-angled triangle, as shown below.

PQ = 1.41 m and PR = 0.89 m.

Figure for question 15

Calculate the length of QR.

[3]
Reveal mark scheme Mark scheme for question 15

Unit 2: Calculator-allowed June 2018 Higher tier, Question 5, also on the Intermediate paper 3 marks

PQR is a right-angled triangle, as shown below.

PQ = 1.41 m and PR = 0.89 m.

Figure for question 5

Calculate the length of QR.

[3]
Reveal mark scheme Mark scheme for question 5

Unit 2: Calculator-allowed November 2017 Intermediate tier, Question 12 8 marks

A triangular prism of length 2 metres is shown below.

Figure for question 12

AC = 21 cm, BC = 35 cm and BACmaths symbol = 90°.

(a)

Calculate the area of triangle ABC. Give your answer in cm2.

You must show all your working.

[5]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Calculate the volume of the prism.

You must give the units of your answer.

[3]
Reveal mark scheme Mark scheme for question 12(b)

Unit 2: Calculator-allowed November 2017 Higher tier, Question 4 10 marks

A triangular prism of length 2 metres is shown below.

Figure for question 4

AC = 21 cm, BC = 35 cm and BACmaths symbol = 90°.

(a)

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing. Calculate the area of triangle ABC. Give your answer in cm2.

You must show all your working.

[7]
Reveal mark scheme Mark scheme for question 4(a)
(b)

Calculate the volume of the prism.

You must give the units of your answer.

[3]
Reveal mark scheme Mark scheme for question 4(b)

Unit 2: Calculator-allowed June 2017 Intermediate tier, Question 14, also on the Higher paper 3 marks

A right-angled triangle LMN is shown below.

LN = 16.9 cm and LM = 6.5 cm.

Figure for question 14

Calculate the length MN.

[3]
Reveal mark scheme Mark scheme for question 14

Unit 2: Calculator-allowed June 2017 Higher tier, Question 4, also on the Intermediate paper 3 marks

A right-angled triangle LMN is shown below.

LN = 16.9 cm and LM = 6.5 cm.

Figure for question 4

Calculate the length MN.

[3]
Reveal mark scheme Mark scheme for question 4

Unit 2: Calculator-allowed June 2017 Higher tier, Question 21 4 marks

The cube below has an internal diagonal of length 20 cm. Each edge of the cube is of length xcm.

Figure for question 21

Calculate the value of x.

You must use an algebraic method and show all your working.

[4]
Reveal mark scheme Mark scheme for question 21

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