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WA2 Practice Paper: Weighted Assessment 2 — question paper

QuizQuipPractice Series
QQ/S3AM/WA2

Secondary 3 · Additional Mathematics (G3)

WA2 Practice Paper

Weighted Assessment 2

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 3–5 (polynomials and partial fractions; binomial expansions; exponential and logarithmic functions).

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. Throughout this paper, lg x means log₁₀ x.

  1. 1

    The polynomial f(x) = 2x³ + ax² − 5x + 6 has (x − 1) as a factor.

    1. (a)

      Use the factor theorem to find the value of a.

      [3]
    2. (b)

      Factorise f(x) completely.

      [3]
  2. 2

    Split (9x + 8)/((2x + 1)(x + 3)) into its partial fractions.

    1. Show the values you substitute and check your coefficients before writing the answer.

      [5]
  3. 3

    Given that lg 2 = p and lg 3 = q, express each of the following in terms of p and q.

    1. (a)

      lg 24.

      lg 24 =[1]
    2. (b)

      lg(9/2).

      lg(9/2) =[1]
  4. 4

    Write down, in ascending powers of x, the first four terms of the expansion of (1 + 2x)⁵.

    1. Give the coefficient of each power of x.

      [3]
  5. 5

    Using your expansion of (1 + 2x)⁵, or otherwise, find the coefficient of x² in the expansion of (1 + 2x)⁵(1 + x)².

    1. Identify every product of terms that contributes to the x² term.

      [4]
  6. 6

    The first three terms, in ascending powers of x, of the expansion of (1 + kx)⁶ are 1 − 12x + 60x².

    1. (a)

      Find the value of the constant k.

      [2]
    2. (b)

      Hence estimate the value of (0.98)⁶, giving your answer to 4 decimal places.

      [4]
  7. 7

    Solve the equation 3^(2x + 1) = 20, leaving lg 20 and lg 3 in your working and giving x correct to 3 significant figures.

    1. Take logarithms and show every step of the algebra.

      [4]
  8. 8

    Solve the equation lg(x + 4) + lg x = lg 12.

    1. Combine the logarithms first, and reject any invalid solution with a stated reason.

      [7]
  9. 9

    The number of bacteria in a culture is modelled by N = 800 × 2^(t/3), where t is the time in hours after the culture is observed.

    1. (a)

      Find the number of bacteria after 9 hours.

      [2]
    2. (b)

      State, with a reason, how long the culture takes to double in number.

      [1]

— End of paper —