Skip to content
QuizQuip
Sign up
Back to WA1
Mark schemePDF

WA1 Practice Paper: Weighted Assessment 1 — question paper

QuizQuipPractice Series
QQ/S3AM/WA1

Secondary 3 · 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 (some schools include the start of Chapter 3).

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 unless told otherwise.

  1. 1

    The function f is defined by f(x) = 2x² − 12x + 7.

    1. (a)

      Express f(x) in the form a(x + b)² + c.

      [3]
    2. (b)

      State the minimum value of f(x) and the value of x at which it occurs.

      minimum =[2]
    3. (c)

      Write down the coordinates of the point where the curve y = f(x) crosses the y-axis.

      point =[1]
  2. 2

    The line y = 2x + k is a tangent to the curve y = x² − 4x + 5, where k is a constant.

    1. (a)

      Show that the x-coordinates of the intersection points satisfy x² − 6x + (5 − k) = 0, and hence form an equation in k.

      [4]
    2. (b)

      Find the coordinates of the point of tangency.

      [2]
    3. (c)

      State the number of intersection points between the line y = 2x − 2 and the curve.

      [1]
  3. 3

    Answer this question without a calculator where exact values are required.

    1. (a)

      Solve the inequality x² − 5x + 4 < 0.

      [3]
    2. (b)

      Find the range of values of c for which x² + 2x + c is always positive.

      [3]
    3. (c)

      Hence write down the smallest integer value of c.

      c =[1]
  4. 4

    Do not use a calculator in this question.

    1. (a)

      Simplify (3√2 + 1)(√2 − 4), giving your answer in the form p + q√2.

      [3]
    2. (b)

      Rationalise the denominator of 6/(√5 − 1).

      [3]
  5. 5

    Solve the equation √(2x + 3) − √(x − 2) = 2.

    1. Show all steps, including the check of every candidate in the original equation.

      [6]
  6. 6

    The height of a model rocket above the ground is modelled by h = 24t − 6t², where h is in metres and t is the time in seconds after launch.

    1. (a)

      Express h in the form a(t − b)² + c, and hence find the maximum height reached.

      [4]
    2. (b)

      Find the time at which the rocket returns to the ground.

      [2]
    3. (c)

      Find the two times at which the rocket is 18 m above the ground.

      t =[2]

— End of paper —