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Chapter 13 Practice Paper: Mensuration — question paper

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QQ/S3EM/CH13

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 13 Practice Paper

Mensuration

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.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 13 (G5 Mensuration: composite plane figures, arc/sector/segment, radians, volumes and surface areas of solids, composite solids, unit conversions).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

  1. 1

    This question tests plane-figure areas.

    1. (a)

      Trapezium ABCD has parallel sides AB = 9 cm and DC = 15 cm, with a perpendicular distance of 8 cm between them. Find the area of ABCD.

      [1]
    2. (b)

      A parallelogram PQRS stands on base PS = 11 cm, and the perpendicular distance between PS and QR is 6 cm. Find the area of PQRS.

      [1]
    3. (c)

      Explain why the slanted side of a parallelogram (length 9 cm in part (b)’s shape) must not be used as the height in the area formula.

      [1]
  2. 2

    A circle has radius 7 cm.

    1. (a)

      Find the arc length of a sector with angle 130°, to 3 significant figures.

      [2]
    2. (b)

      Find the area of the same sector, to 3 significant figures.

      [2]
  3. 3

    Convert (a) 150° into radians, in terms of π, and (b) 0.9 radians into degrees, correct to 1 decimal place.

    1. (a)

      150° in radians.

      [2]
    2. (b)

      0.9 rad in degrees.

      [1]
  4. 4

    A window is a rectangle 1.2 m wide by 2 m high with a semicircle of radius 0.6 m on top of the 1.2 m side.

    1. (a)

      Find the total area of the window, in m², to 3 significant figures.

      [3]
    2. (b)

      Find the perimeter of the window (the outer boundary), to 3 significant figures.

      [3]
  5. 5

    A solid metal cylinder has radius 6 cm and height 20 cm.

    1. (a)

      Find its volume, to 3 significant figures.

      [2]
    2. (b)

      Find its total surface area, to 3 significant figures.

      [3]
  6. 6

    A sphere of radius 9 cm is melted and recast into a cone of radius 6 cm and height h cm. No metal is lost.

    1. (a)

      Find the volume of the sphere, to 3 significant figures.

      [2]
    2. (b)

      Find h.

      [3]
  7. 7

    A toy block is a cuboid 10 cm by 6 cm by 4 cm with a cylindrical hole of radius 1.5 cm drilled straight through from top to bottom.

    1. (a)

      Find the volume of the block after drilling, to 3 significant figures.

      [2]
    2. (b)

      Find the total surface area after drilling, to 3 significant figures. (The two circular holes are new surfaces; the cuboid faces keep their areas with two circular holes removed.)

      [2]

— End of paper —