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Chapter 11 Practice Paper: Properties of Circles — question paper

QuizQuipPractice Series
QQ/S3EM/CH11

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 11 Practice Paper

Properties of Circles

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 11 (G3 Properties of Circles: angle properties, chord properties, tangent properties, multi-step chains).

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. State the circle property used for each angle found.

  1. 1

    O is the centre of a circle. Points A and B lie on the circle with angle AOB = 60° at the centre, and C lies on the major arc AB.

    1. (a)

      Find angle ACB.

      [2]
    2. (b)

      State the size of the angle at the circumference standing on arc AB from any other point of the major arc.

      [1]
  2. 2

    The chord AB is a diameter; C is a point on the circle where angle CAB measures 41°.

    1. (a)

      Write down angle ACB, with a reason.

      [1]
    2. (b)

      Find angle ABC.

      [2]
    3. (c)

      State the size of the angle subtended by AB at any other point D of the semicircle containing C.

      [1]
  3. 3

    The four points P, Q, R and S lie on a circle, joined in that order to form a quadrilateral. Angle P is 87° and angle Q is 74°.

    1. (a)

      Find angle R.

      [2]
    2. (b)

      Find angle S.

      [2]
  4. 4

    A chord of length 24 cm lies in a circle of radius 13 cm.

    1. (a)

      Find the distance from the centre of the circle to the chord.

      [2]
    2. (b)

      A second chord of the same circle also measures 24 cm. Write down its distance from the centre, with a reason.

      [2]
  5. 5

    Two tangents drawn from the point P outside a circle touch it at A and B; the centre is O. Given angle APB = 64° and PA = 9 cm.

    1. (a)

      Write down the length of PB, with a reason.

      [1]
    2. (b)

      Find angle PAB.

      [2]
    3. (c)

      Find angle AOB.

      [2]
  6. 6

    O is the centre of a circle. Points A, B, C and D lie on the circle, with C and D on the same segment standing on chord AB. Angle ACB = 34°.

    1. (a)

      Write down angle ADB, with a reason.

      [1]
    2. (b)

      Find angle AOB.

      [2]
    3. (c)

      A fifth point E lies on the opposite (minor) segment standing on AB. Explain why angle AEB cannot equal 34°.

      [2]
  7. 7

    AB is a diameter of a circle with centre O, and C lies on the circle. TC is a tangent to the circle at C, and angle CAB = 36°.

    1. (a)

      Find angle ABC.

      [2]
    2. (b)

      Find angle AOC.

      [2]
    3. (c)

      Write down the angle between the tangent TC and the radius OC.

      [1]

— End of paper —