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Term 2G3

Sec 3 A-Math WA2 practice paper

WA2 is usually the Term 2 assessment. In the common scheme it covers the middle of the Sec 3 algebra strand: factor and remainder theorems, partial fractions, the binomial theorem, and exponential and logarithmic functions.

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Total marks
40
Time
55 min
Covers
Chapters 3–5 (polynomials and partial fractions; binomial expansions; exponential and logarithmic functions)
Format
9 structured questions

The paper and mark scheme

Set out like a school paper, with a separate mark scheme for checking.

Question paper

WA2 Practice Paper

40 marks · 55 min · 5 pages

9 multiple-choice questions and structured questions with answer lines. Chapters 3–5 (polynomials and partial fractions; binomial expansions; exponential and logarithmic functions).

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Mark scheme

PRO

WA2 Practice Paper — mark scheme

Answers · Marking points · 3 pages

Model answers with a mark for each creditworthy point — for marking at home or in class.

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What’s tested

Commonly Chapters 3–5 (polynomials and partial fractions, binomial expansions, exponential and logarithmic functions). Some schools begin Term 2 with trigonometry instead, so check your school’s outline.

  1. 3Polynomials & Partial FractionsTheme 1 · AlgebraNotes & quiz
  2. 4Binomial ExpansionsTheme 1 · AlgebraNotes & quiz
  3. 5Exponential & Logarithmic FunctionsTheme 1 · AlgebraNotes & quiz

How to use this paper

  1. 1Print the paper, or open the PDF and write on paper.
  2. 2Set a timer for 55 min and work without notes.
  3. 3Mark your answers with the mark scheme, one point at a time.
  4. 4Redo every question you lost marks on, then revise that topic.

Preview

The first questions of Section A, as they appear on the paper.

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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]

Revision checklist

  • Use the factor theorem to find unknown coefficients and factorise cubics completely.
  • Set up partial fractions with repeated and distinct linear factors, and check by covering the denominator.
  • Write binomial expansions in ascending powers and pick out specific coefficients from products.
  • Use binomial expansions of (1 + kx)ⁿ for small-x estimates.
  • Solve exponential equations by taking logarithms and logarithmic equations by combining with the product law.
  • Reject invalid solutions where logarithm arguments would be negative — with a stated reason.

Exam tips

  • State the factor theorem explicitly before substituting.
  • In partial fractions, substitute the root of each factor first — it is faster than comparing every coefficient.
  • Keep values exact until the final rounding step, then round to 3 significant figures.
  • Check logarithm answers: every argument of a log must end up positive.

Questions about the WA2

What is tested in Sec 3 A-Math WA2?

Typically Chapter 3 (factor and remainder theorems, partial fractions), Chapter 4 (binomial expansions and coefficients) and Chapter 5 (exponential and logarithmic equations and models). Confirm with your school’s assessment outline.

Do I need to memorise the binomial coefficients?

The formula list gives the binomial expansion, but fluency with nCr values for small n and with the (ax + b)ⁿ form saves time. Practise until the first four terms are routine.

Is this paper based on a real school paper?

No. QuizQuip papers are original material written against the syllabus. QuizQuip is not affiliated with MOE or SEAB.