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Topic 12 Practice Paper: Geometry, angles and polygons — question paper

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QQ/IGCSE-MATHS/T12

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 12 Practice Paper

Geometry, angles and polygons

Duration: 40 minutes
Total: 30 marks
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Class:
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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.
  • 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 against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 12: angle facts on lines and around points, triangle and quadrilateral sums, parallel-line rules with reasons, interior and exterior angles of polygons, similarity scale factors, symmetry, and three-figure bearings.

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. 1

    One angle on a straight line is 143°. The other is

    1. A47°
    2. B57°
    3. C143°
    4. D37°
    ( )
  2. 2

    A right-angled triangle has a second angle of 31°. The third angle is

    1. A121°
    2. B59°
    3. C149°
    4. D31°
    ( )
  3. 3

    The co-interior partner of a 68° angle between parallel lines is

    1. A112°
    2. B68°
    3. C22°
    4. D292°
    ( )
  4. 4

    The alternate partner of a 76° angle between parallel lines is

    1. A104°
    2. B14°
    3. C76°
    4. D284°
    ( )
  5. 5

    Turning one corner of a regular octagon swings through

    1. A45°
    2. B135°
    3. C40°
    4. D8°
    ( )
  6. 6

    Inside a regular hexagon, every corner angle measures

    1. A60°
    2. B108°
    3. C135°
    4. D120°
    ( )
  7. 7

    A regular polygon has exterior angle 12°. The number of sides is

    1. A12
    2. B30
    3. C15
    4. D60
    ( )
  8. 8

    All ten interior angles of a decagon total

    1. A1080°
    2. B1260°
    3. C1440°
    4. D1620°
    ( )
  9. 9

    Similar shapes have lengths scaled by 5. A small area of 4 cm² becomes

    1. A20 cm²
    2. B100 cm²
    3. C16 cm²
    4. D500 cm²
    ( )
  10. 10

    Navigating south-west calls for the bearing

    1. A225°
    2. B135°
    3. C315°
    4. D045°
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    Angle facts.

    1. (a)

      Angles of 210° and 55° meet at a point with a third angle x. Find x.

      [2]
    2. (b)

      Three angles of a quadrilateral are 130°, 80° and 75°. Find the fourth.

      [2]
    3. (c)

      The apex of an isosceles triangle measures 36°. Work out a base angle.

      [1]
  2. 12

    A regular nonagon (9 sides).

    1. (a)

      Find the total of all the interior angles.

      [2]
    2. (b)

      Find the exterior angle.

      [1]
    3. (c)

      Hence find the size of each interior angle.

      [2]
  3. 13

    A ship leaves port on a bearing of 090° and sails 24 km, then turns onto a bearing of 180° and sails 32 km. (Extended)

    1. (a)

      How far is the ship now from the port?

      [2]
    2. (b)

      On what bearing should the ship now sail to return to port? Give it to 1 decimal place.

      [3]
  4. 14

    A small cylinder has radius 2 cm and height 6 cm. A similar large cylinder has scale factor 3. (Extended)

    1. (a)

      Write down the radius and height of the large cylinder.

      [2]
    2. (b)

      The small cylinder has volume 24π cm³. Find the volume of the large cylinder, in terms of π.

      [3]

— End of paper —