Chapter 15 Practice Paper: Congruence, similarity and transformations — question paper (print)

Back to Chapter 15

Mark scheme PDF

QuizQuipPractice Series

QQ/GCSE-MATHS/CH15

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

Chapter 15 Practice Paper

Congruence, similarity and transformations

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 full descriptions of transformations: centre, angle, direction, line or vector as required.
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 15: congruence criteria (SSS, SAS, ASA, RHS), similar shapes with length, area and volume scale factors, rotations, reflections, translations and enlargements (including negative scale factors), invariant points and column-vector arithmetic.

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
Two triangles share two sides of 5 cm and 7 cm with a 40° angle between them. The congruence criterion is
1. ASSS
2. BSAS
3. CASA
4. DRHS
( )
2
A side of 2.5 cm is enlarged by scale factor 4. Its new length is
1. A10 cm
2. B6.5 cm
3. C1 cm
4. D8 cm
( )
3
The column vector ( −3 over 2 ) translates a shape
1. A3 right, 2 up
2. B3 up, 2 left
3. C3 left, 2 up
4. D3 left, 2 down
( )
4
The point (3, −1) reflected in the x-axis lands at
1. A(−3, −1)
2. B(−1, 3)
3. C(−3, 1)
4. D(3, 1)
( )
5
Similar shapes have length scale factor 10. Each area is multiplied by
1. A100
2. B20
3. C1000
4. D10
( )
6
Similar solids have volumes in the ratio 1 : 8. Their length scale factor is
1. A8
2. B4
3. C2
4. D24
( )
7
A complete description of a rotation states
1. Athe angle only
2. Bthe centre, the angle and the direction
3. Cthe direction only
4. Dthe centre and the angle
( )
8
A 6 cm side is enlarged by scale factor ½. The image side is
1. A12 cm
2. B2 cm
3. C9 cm
4. D3 cm
( )
9
The vector journey AB followed by BC equals
1. AAC
2. BCA
3. CAB again
4. DBC again
( )
10
Under a reflection in a line, the invariant points are
1. Athe endpoints of the shape
2. Bevery point of the shape
3. Cthe points on the mirror line
4. Dno points at all
( )

Section B: Structured questions[20 marks]

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

11
Congruence checks.
1. (a)
  A student claims that two triangles with a 50° angle and sides 6 cm and 9 cm around some other arrangement must be congruent. Explain why the claim needs more care.
  [2]
2. (b)
  Two triangles have sides 5 cm, 6 cm, 8 cm and 5 cm, 6 cm, 8 cm. Name the congruence criterion.
  [2]
12
Sides of similar triangles.
1. (a)
  A triangle has sides 4 cm, 7 cm and 9 cm. A similar triangle has the side corresponding to 4 cm measuring 12 cm. Find the scale factor.
  [2]
2. (b)
  Find the length of the side corresponding to 7 cm.
  [2]
13
Transformations on a grid.
1. (a)
  A 90° anticlockwise turn about the origin is applied to the point (2, 1). Find where it lands.
  [2]
2. (b)
  Reflect the point (−3, 4) in the x-axis. Give the image.
  [2]
14
Translations.
1. (a)
  Translate the point (1, 4) by the vector (2, −5). Give the image.
  [2]
2. (b)
  A translation moves a shape 2 units left and 6 units up. Write it as a column vector.
  [2]
15
Similar cylinders. (Higher)
1. (a)
  Two cylinders are similar with length scale factor 2. State the volume scale factor.
  [2]
2. (b)
  Given that the smaller cylinder holds 150 cm³, work out the volume of the larger one.
  [2]

— End of paper —