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WJEC GCSE Maths

Topic questions Pure mathematics Trigonometric ratios

Trigonometric ratios

36 questions · 179 marks · about 4 hours

Trigonometric ratios questions

TopicTrigonometric ratios

WJEC 3300 Trigonometric ratios 36 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 November 2023 Higher tier, Question 18 8 marks

Figure for question 18
(a)

Calculate the length of CE.

You must show all your working.

[6]
Reveal mark scheme Mark scheme for question 18(a)
(b)

Hence, calculate the area of triangle CGE.

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

Unit 2: Calculator-allowed June 2023 Higher tier, Question 6 7 marks

In the diagram below, AD is a straight line.

BACmaths symbol = 90°, BDEmaths symbol = 90° and CBEmaths symbol = 90°.

AC = 7·7 cm, BC = 11·3 cm and BD = 13·1 cm.

Figure for question 6
(a)

Calculate the value of x.

[3]
Reveal mark scheme Mark scheme for question 6(a)
(b)

Hence find the length DE.

[4]
Reveal mark scheme Mark scheme for question 6(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 15, also on the Higher paper 3 marks

Calculate the length of the side YZ in the triangle XYZ shown below.

Figure for question 15
[3]
Reveal mark scheme Mark scheme for question 15

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 5, also on the Intermediate paper 3 marks

Calculate the length of the side YZ in the triangle XYZ shown below.

Figure for question 5
[3]
Reveal mark scheme Mark scheme for question 5

Unit 2: Calculator-allowed June 2022 Intermediate tier, Question 13, also on the Higher paper 6 marks

(a)

The diagram below shows a right-angled triangle.

Figure for question 13

Calculate the value of x.

[3]
Reveal mark scheme Mark scheme for question 13(a)
(b)

The diagram below shows a different right-angled triangle.

Figure for question 13

Calculate the value of y.

[3]
Reveal mark scheme Mark scheme for question 13(b)

Unit 2: Calculator-allowed June 2022 Higher tier, Question 7, also on the Intermediate paper 6 marks

(a)

The diagram below shows a right-angled triangle.

Figure for question 7

Calculate the value of x.

[3]
Reveal mark scheme Mark scheme for question 7(a)
(b)

The diagram below shows a different right-angled triangle.

Figure for question 7

Calculate the value of y.

[3]
Reveal mark scheme Mark scheme for question 7(b)

Unit 2: Calculator-allowed November 2020 Intermediate tier, Question 15 5 marks

In the diagram below, AB, BC and CD are three sides of a regular polygon.

The polygon has 15 sides. The length of each side is 8 cm. The exterior angle of the polygon is x°. BRC is a right-angled triangle.

Figure for question 15

Calculate the length of BR.

[5]
Reveal mark scheme Mark scheme for question 15

Unit 2: Calculator-allowed November 2020 Intermediate tier, Question 19, also on the Higher paper 6 marks

The diagram below shows a circle with centre at point O.

A, B, C and D are all points on the circumference of the circle. AB = 7·5 cm and BC = 4·7 cm.

Figure for question 19
(a)(i)
Figure for question 19
[1]
Reveal mark scheme Mark scheme for question 19(a)(i)
(a)
(a)(ii)

Calculate the size of angle x.

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

Write down the size of angle y.

State the circle theorem you have used to find your answer.

Circle theorem used:........

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

Unit 2: Calculator-allowed November 2020 Higher tier, Question 10, also on the Intermediate paper 6 marks

The diagram below shows a circle with centre at point O.

A, B, C and D are all points on the circumference of the circle. AB = 7·5 cm and BC = 4·7 cm.

Figure for question 10
(a)(i)
Figure for question 10
[1]
Reveal mark scheme Mark scheme for question 10(a)(i)
(a)
(a)(ii)

Calculate the size of angle x.

[3]
Reveal mark scheme Mark scheme for question 10(a)(ii)
(b)

Write down the size of angle y.

State the circle theorem you have used to find your answer.

Circle theorem used:........

[2]
Reveal mark scheme Mark scheme for question 10(b)

Unit 2: Calculator-allowed November 2018 Higher tier, Question 9 7 marks

The diagram below shows two right-angled triangles ABC and APQ.

= 8.2 cm, = 6.4 cm and = 7.9 cm. AB BC PQ CAQmaths symbol = 90°.

Figure for question 9
(a)

Calculate the size of angle x.

[3]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Calculate the length AQ.

[4]
Reveal mark scheme Mark scheme for question 9(b)

Unit 2: Calculator-allowed June 2018 Higher tier, Question 9 6 marks

ABC and CDE are two right-angled triangles.

In triangle ABC, AB = 6.5 cm and BC = 10.4 cm. In triangle CDE, CE = 9.4 cm. BCEmaths symbol = 22°. ACBmaths symbol = x°.

Figure for question 9
(a)

Calculate the value of x.

[3]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Hence find the length of DE.

[3]
Reveal mark scheme Mark scheme for question 9(b)

Unit 2: Calculator-allowed November 2017 Intermediate tier, Question 15, also on the Higher paper 6 marks

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

SPQmaths symbol = 90°, SQRmaths symbol = 90°, SQPmaths symbol = 38°, PS = 8 cm and QR = 15 cm.

Figure for question 15

Calculate the size of angle x.

[6]
Reveal mark scheme Mark scheme for question 15

Unit 2: Calculator-allowed November 2017 Higher tier, Question 7, also on the Intermediate paper 6 marks

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

SPQmaths symbol = 90°, SQRmaths symbol = 90°, SQPmaths symbol = 38°, PS = 8 cm and QR = 15 cm.

Figure for question 7

Calculate the size of angle x.

[6]
Reveal mark scheme Mark scheme for question 7

Unit 2: Calculator-allowed June 2017 Intermediate tier, Question 16, also on the Higher paper 3 marks

Calculate the length of the side QR in the triangle PQR shown below.

Figure for question 16
[3]
Reveal mark scheme Mark scheme for question 16

Unit 2: Calculator-allowed June 2017 Intermediate tier, Question 21 5 marks

The area of triangle ABD, shown in the diagram below, is 35 cm2.

AD = 5 cm and BC = 32 cm. D is on the line AC, and BD is perpendicular to AC.

Figure for question 21

Calculate the size of angle x.

You must show all your working.

[5]
Reveal mark scheme Mark scheme for question 21

Unit 2: Calculator-allowed June 2017 Higher tier, Question 6, also on the Intermediate paper 3 marks

Calculate the length of the side QR in the triangle PQR shown below.

Figure for question 6
[3]
Reveal mark scheme Mark scheme for question 6

Unit 2: Calculator-allowed June 2017 Higher tier, Question 11 7 marks

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

The area of triangle ABD, shown in the diagram below, is 35 cm2. AD = 5 cm and BC = 32 cm. D is on the line AC, and BD is perpendicular to AC.

Figure for question 11

Calculate the size of angle x.

You must show all your working.

[7]
Reveal mark scheme Mark scheme for question 11

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