Skip to content
QuizQuip
Sign up
Back to Chapter 6
Mark schemePDF

Chapter 6 Practice Paper: Congruence and Similarity — question paper

QuizQuipPractice Series
QQ/S2MATH/CH6

Secondary 2 · Lower Secondary Mathematics (G2 / G3)

Chapter 6 Practice Paper

Congruence and Similarity

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Section A: write the letter (A, B, C or D) of the correct answer in the brackets provided.
  • Section B: write your answers in the spaces provided.
  • Show all working. Marks may be awarded for correct working even if the final answer is wrong.
  • Give units with your answers where appropriate.
  • The number of marks is given in brackets [ ] at the end of each question or part question.

Original practice material written for the MOE Lower Secondary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 6.

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

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

  1. 1

    Congruent shapes always have

    1. Aequal areas only
    2. Bequal corresponding sides and angles
    3. Cthe same orientation on the page
    4. Ddifferent perimeters
    ( )
  2. 2

    A figure is reflected in a line. The figure and its image are

    1. Asimilar only
    2. Bneither similar nor congruent
    3. Ccongruent
    4. Denlarged
    ( )
  3. 3

    In a pair of similar triangles, the matching angles are

    1. Aequal
    2. Bdoubled
    3. Cproportional to the sides
    4. Dhalved
    ( )
  4. 4

    A triangle with sides 5, 12, 13 is enlarged by scale factor 4. The longest side of the image is

    1. A17
    2. B30
    3. C48
    4. D52
    ( )
  5. 5

    A 7 cm side becomes 21 cm after an enlargement. The scale factor is

    1. A14
    2. B3
    3. C1/3
    4. D21
    ( )
  6. 6

    A map has scale 1 : 20 000. A distance of 5 cm on the map represents

    1. A100 m
    2. B10 km
    3. C1 km
    4. D4 km
    ( )
  7. 7

    Rectangle F measures 3 by 8, and rectangle G measures 4.5 by 12. The scale factor from F to G is

    1. A1.5
    2. B2
    3. C2.5
    4. D5
    ( )
  8. 8

    Two similar triangles have corresponding sides in ratio 2 : 7. The smaller triangle has perimeter 20 cm. The larger has perimeter

    1. A35 cm
    2. B90 cm
    3. C27 cm
    4. D70 cm
    ( )
  9. 9

    A bridge model uses scale 1 : 50. The real bridge is 120 m long. The model’s length is

    1. A24 m
    2. B2.4 m
    3. C0.6 m
    4. D6 m
    ( )
  10. 10

    An enlargement with scale factor ¾ produces

    1. Aan enlargement in every direction
    2. Ba congruent figure
    3. Ca reduced figure with three-quarters of each length
    4. Da figure with smaller angles
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly.

  1. 1

    A rectangular banner measures 40 cm by 90 cm and is sent to a printer for enlargement.

    1. (a)

      The enlarged banner has length 270 cm. Find the scale factor.

      scale factor =[1]
    2. (b)

      Find the width of the enlarged banner.

      width =[1]
    3. (c)

      The printer’s board is 250 cm long. Explain whether the enlarged banner fits on it.

      [2]
    4. (d)

      The printer can only enlarge by whole-number scale factors. Which factor should be used so the banner fits the board?

      factor =[1]
  2. 2

    Triangle ABC has AB = 4 cm, BC = 6 cm and CA = 8 cm. Triangle PQR is similar to ABC, and PQ (matching AB) is 10 cm.

    1. (a)

      PQ matches AB. Work out the enlargement factor.

      scale factor =[1]
    2. (b)

      Find QR (matching BC).

      QR =[1]
    3. (c)

      Find RP (matching CA).

      RP =[1]
    4. (d)

      Find the perimeter of triangle PQR.

      [2]
  3. 3

    An orienteering map is drawn to scale 1 : 50 000.

    1. (a)

      The map distance between two checkpoints is 4.6 cm. Calculate the actual distance in kilometres.

      [2]
    2. (b)

      A river is 6.8 km long in reality. How long is it on the map?

      [2]
    3. (c)

      Explain why a scale of 1 : 5 000 would be impractical for a 20 km route on one sheet.

      [1]
  4. 4

    A museum builds a statue model at scale 1 : 12. The real statue is 2.4 m tall.

    1. (a)

      Find the height of the model in centimetres.

      [2]
    2. (b)

      The model’s base is 6 cm wide. Find the width of the real base.

      width =[1]
    3. (c)

      A second, larger model of the same statue is built at scale 1 : 8. Find its height in centimetres.

      [2]

— End of paper —