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EOY Practice Paper: End-of-Year Examination — question paper

QuizQuipPractice Series
QQ/S3EM/EOY

Secondary 3 · Elementary Mathematics (G2 / G3)

EOY Practice Paper

End-of-Year Examination

Duration: 90 minutes
Total: 60 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.
  • An approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. The full Sec 3 year (Chapters 1–13).

For Examiner’s Use
Section A/ 60
Total/ 60

Section A: Structured questions[60 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, or 1 decimal place for angles in degrees, unless told otherwise.

  1. 1

    Answer all parts of this question.

    1. (a)

      Express 0.0000382 in standard form.

      Answer =[1]
    2. (b)

      Evaluate √48.5, correct to 2 decimal places.

      [1]
    3. (c)

      By writing each number correct to 1 significant figure, estimate the value of (39.8 × 4.12) ÷ 0.198.

      [2]
  2. 2

    A sum of money is divided between Kai and Lin in the ratio 4 : 7. Lin receives $63 more than Kai.

    1. (a)

      Find the total sum of money.

      [2]
    2. (b)

      Express Kai’s share as a percentage of the total sum, correct to 3 significant figures.

      [1]
    3. (c)

      The total sum is increased by 15%. Find the new total.

      [1]
  3. 3

    A saver places $5,000 in an account. Interest rates are unchanged over the period considered.

    1. (a)

      Find the simple interest earned in 2½ years at 3.2% per year.

      [2]
    2. (b)

      Find the value of the investment after 2 years if interest is instead 3.2% per year, compounded yearly.

      [2]
  4. 4

    Answer all parts of this question.

    1. (a)

      Factorise 3x² − 75 completely.

      [2]
    2. (b)

      Expand and simplify (2x − 3)(x + 5) − 2(x² − 4x).

      [2]
  5. 5

    Solve the following equations.

    1. (a)

      Solve x² − 5x − 14 = 0.

      [2]
    2. (b)

      Solve the simultaneous equations x + 2y = 7 and 3x − y = 7.

      [3]
  6. 6

    Answer all parts of this question.

    1. (a)

      Solve the inequality 7 − 3x > 1.

      [2]
    2. (b)

      List all the integer values of x satisfying −1 ≤ 2x + 3 < 9.

      [2]
  7. 7

    A curve has equation y = 2x² − 8x + 3.

    1. (a)

      Express 2x² − 8x + 3 in the form a(x + b)² + c.

      [2]
    2. (b)

      State the minimum value of y and the value of x at which it occurs.

      [1]
    3. (c)

      Hence solve 2x² − 8x + 3 = 0, giving each root correct to 2 decimal places.

      [2]
  8. 8

    A gym has 80 members. 55 swim, 41 use the weights room, and 12 do neither activity.

    1. (a)

      Find the number of members who do both activities.

      [2]
    2. (b)

      Find the number of members who swim only.

      [1]
    3. (c)

      A member is chosen at random. Find the probability that the member uses the weights room but does not swim.

      [1]
  9. 9

    Matrices P = [[1, 2], [3, −1]] and Q = [[4, 0], [−2, 5]].

    1. (a)

      Find 2P − Q.

      [2]
    2. (b)

      Find PQ.

      [2]
  10. 10

    Answer all parts of this question on polygon geometry.

    1. (a)

      A regular pentagon is drawn. Find its exterior angle.

      [1]
    2. (b)

      Hence find the interior angle of the regular pentagon.

      [1]
    3. (c)

      A different regular polygon has an interior angle of 156°. Find the number of sides it has.

      [2]
  11. 11

    A model building is made to a scale of 1 : 50.

    1. (a)

      The model is 34 cm tall. Find the actual height of the building, in metres.

      [2]
    2. (b)

      The floor area of the actual building is 125 m². Find the floor area of the model, in cm².

      [3]
  12. 12

    A, B and C lie on a circle with centre O. Angle AOB = 140°, and A, O and C are arranged so that C lies on the major arc AB.

    1. (a)

      Find angle ACB, stating the circle property used.

      [2]
    2. (b)

      Find angle OAB, explaining your method.

      [2]
  13. 13

    In triangle ABC, AB = 8 cm, BC = 11 cm and angle ABC = 72°.

    1. (a)

      Use the cosine rule to find AC, correct to 1 decimal place.

      [3]
    2. (b)

      Find the area of triangle ABC, correct to 3 significant figures.

      [2]
  14. 14

    A closed cylinder has a base radius of 5 cm and a height of 12 cm.

    1. (a)

      Find the volume of the cylinder, correct to 3 significant figures.

      [2]
    2. (b)

      Find the total surface area of the cylinder, correct to 3 significant figures.

      [2]

— End of paper —