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WA1 Practice Paper: Weighted Assessment 1 — question paper

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QQ/S4AM/WA1

Secondary 4 · Additional Mathematics (G3)

WA1 Practice Paper

Weighted Assessment 1

Duration: 55 minutes
Total: 40 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.
  • 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 Additional Mathematics syllabus. It is not an official MOE or school examination paper. Chapters 1–2 (further trigonometry; proofs in plane geometry), with a linear-law item.

For Examiner’s Use
Section A/ 40
Total/ 40

Section A: Structured questions[40 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. You may use lg 5 = 0.70.

  1. 1

    It is given that 3 cos θ + 4 sin θ can be written in the form R cos(θ − α), where R > 0 and 0° < α < 90°.

    1. (a)

      State the value of R and the value of α, giving α correct to 1 decimal place.

      [4]
    2. (b)

      Write down the maximum and minimum values of 3 cos θ + 4 sin θ.

      max, min =[2]
    3. (c)

      Hence find the two values of θ in 0° ≤ θ ≤ 360° for which 3 cos θ + 4 sin θ = 2, correct to 1 decimal place.

      θ =[1]
  2. 2

    Do not use a calculator in this question.

    1. (a)

      Show that cos 15° = (√6 + √2)/4.

      [3]
    2. (b)

      Write down the exact value of cos 105°.

      [3]
  3. 3

    It is given that tan A = 3/4, where A is an acute angle.

    1. (a)

      Find the exact value of tan 2A, as a fraction in its lowest terms.

      [3]
    2. (b)

      Hence find all the angles x in 0° ≤ x ≤ 360° that satisfy tan 2x = 24/7, correct to 1 decimal place.

      [3]
  4. 4

    In triangle ABC, D lies on AB with AD = 6 cm and DB = 3 cm, and E lies on AC with AE = 4 cm and EC = 2 cm.

    1. (a)

      Show that triangles ADE and ABC are similar.

      [3]
    2. (b)

      Given BC = 12 cm, find DE.

      [2]
    3. (c)

      Given that the area of triangle ADE is 10 cm², find the area of triangle ABC.

      [3]
  5. 5

    The points P, Q, R and S lie on a circle with centre O. PR is a diameter and angle QPR = 28°, with Q and S on the same semicircle and S lying on the arc PQ.

    1. (a)

      Explain why angle PQR = 90°.

      [2]
    2. (b)

      Find angle QRP.

      [2]
    3. (c)

      Write down angle QSR, giving a reason.

      [2]
    4. (d)

      The tangent to the circle at P is drawn. Find the angle between this tangent and the chord PQ.

      [2]
  6. 6

    Experimental data for variables x and y satisfy y = axⁿ. A graph of lg y against lg x is drawn and the line of best fit has gradient 1.5 and passes through the point (0, 0.699). You may use lg 5 = 0.70.

    1. (a)

      Find the values of a and n.

      [4]
    2. (b)

      Estimate the value of y when x = 4, correct to 3 significant figures.

      y =[1]

— End of paper —