Chapter 16 Practice Paper: Pythagoras and trigonometry — question paper (print)

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QQ/GCSE-MATHS/CH16

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 16 Practice Paper

Pythagoras and trigonometry

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Answer all questions.
Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
Section B contains structured questions. Write your answers in the spaces provided.
Give lengths to 3 significant figures and angles to 1 decimal place unless told otherwise.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 16: Pythagoras’ theorem for hypotenuses and shorter sides, SOH CAH TOA for sides and angles, exact trigonometric values, the sine rule, cosine rule and ½ab sin C, the ambiguous case, and 3D diagonal problems.

For Examiner’s Use
Section A	/ 10
Section B	/ 20
Total	/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

1
The legs of a right-angled triangle are 9 cm and 12 cm long. The length of the hypotenuse is
1. A15 cm
2. B21 cm
3. C10.8 cm
4. D7.9 cm
( )
2
tan 60° written in exact surd form is
1. A√3⁄2
2. B1⁄√3
3. C√3
4. D1
( )
3
Given a hypotenuse of 17 cm together with one leg of 8 cm, the other leg is
1. A19 cm
2. B15 cm
3. C12 cm
4. D9 cm
( )
4
The ratio opposite⁄hypotenuse defines
1. Atan θ
2. Bcos θ
3. Cthe reciprocal of cos θ
4. Dsin θ
( )
5
A hypotenuse of 8 cm makes an angle of 25° with the base. The side opposite the 25° angle is
1. A3.38 cm
2. B7.25 cm
3. C8.91 cm
4. D1.85 cm
( )
6
The exact value of sin 45° is
1. A½
2. B√3⁄2
3. C√2⁄2
4. D0
( )
7
A right-angled triangle has opposite side 3 cm and adjacent side 4 cm. The angle opposite the 3 cm side is
1. A53.1°
2. B36.9°
3. C48.6°
4. D30.0°
( )
8
To find the third side of a triangle from two sides and the angle between them, use
1. Athe sine rule
2. BPythagoras’ theorem
3. Cthe area formula
4. Dthe cosine rule
( )
9
A triangle has sides 5 cm and 8 cm enclosing an angle of 40°. Its area is
1. A12.9 cm²
2. B40 cm²
3. C25.7 cm²
4. D20 cm²
( )
10
The longest straight line that fits inside a 2 cm × 3 cm × 6 cm box measures
1. A11 cm
2. B3.6 cm
3. C7 cm
4. D6.7 cm
( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer.

11
Pythagoras both ways.
1. (a)
  Work out the hypotenuse of a right-angled triangle whose legs are 12 cm and 16 cm.
  [2]
2. (b)
  A right triangle has a 26 cm hypotenuse and a 10 cm leg. How long is the remaining side?
  [2]
12
Sides from ratios.
1. (a)
  A right-angled triangle has an opposite side of 7 cm at an angle of 34°. Find the hypotenuse, to 1 decimal place.
  [2]
2. (b)
  A right-angled triangle has an adjacent side of 4.5 cm at an angle of 28°. Find the opposite side, to 2 decimal places.
  [2]
13
A ship’s bearing.
1. (a)
  After sailing 12 km west and then 5 km south, how far has a ship ended up from where it began?
  [2]
2. (b)
  Work out the ship’s bearing measured at the port, to 1 decimal place.
  [2]
14
Exact values. (Higher)
1. (a)
  Evaluate sin 30° + cos 60°.
  [2]
2. (b)
  Evaluate tan 45° × tan 60°, leaving your answer in surd form.
  [2]
15
A triangle from two sides. (Higher)
1. (a)
  Two sides of a triangle measure 6 cm and 9 cm, and the angle between them is 47°. Calculate the side facing that angle, to 2 decimal places.
  [3]
2. (b)
  Calculate the triangle’s area, to 1 decimal place.
  [1]

— End of paper —