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Chapter 4 Practice Paper: Binomial Expansions — question paper

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QQ/S3AM/CH4

Secondary 3 · Additional Mathematics (G3)

Chapter 4 Practice Paper

Binomial Expansions

Duration: 40 minutes
Total: 30 marks
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Class:
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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. Chapter 4 (A5 Binomial expansions).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give exact answers unless told otherwise.

  1. 1

    This question is about binomial notation.

    1. (a)

      Evaluate (7 3).

      (7 3) =[1]
    2. (b)

      Simplify 9!/7!, showing your working.

      [2]
    3. (c)

      State the number of terms in the expansion of (a + b)⁹.

      number of terms =[1]
  2. 2

    Answer the whole of this question on the expansion of (1 + 3x)⁴.

    1. (a)

      Expand (1 + 3x)⁴, writing your answer as a polynomial in x with each coefficient simplified.

      [4]
    2. (b)

      State the coefficient of x³ in the expansion.

      coefficient =[1]
    3. (c)

      Explain why, for a positive value of x, every term of the expansion is positive.

      [1]
  3. 3

    This question is about the expansions of (2 + x)⁶ and (2 − x)⁶.

    1. (a)

      State, in terms of r, the part of the expansion of (2 + x)⁶ that contains xʳ, for 0 ≤ r ≤ 6.

      [2]
    2. (b)

      Use your answer to part (a) to determine the number that multiplies x⁴ when (2 + x)⁶ is expanded.

      coefficient =[2]
    3. (c)

      What happens to that number in the expansion of (2 − x)⁶? Explain why the sign is what it is.

      coefficient =[2]
  4. 4

    Answer the whole of this question on the expansion of (3 + 2x)⁵.

    1. (a)

      Expand (3 + 2x)⁵ up to and including the term in x³, in ascending powers of x.

      [4]
    2. (b)

      Identify the x² term from your expansion.

      term =[1]
    3. (c)

      State the total number of terms in the full expansion.

      number of terms =[1]
  5. 5

    This question is about the expansion of (x² − 3/x)⁶.

    1. (a)

      Obtain, in simplified form, the part of the expansion that contains x raised to the power 12 − 3r.

      [3]
    2. (b)

      Find the term independent of x.

      [3]
    3. (c)

      Find the coefficient of x⁶.

      coefficient =[1]
    4. (d)

      State the coefficient of x⁵, with a reason.

      [1]

— End of paper —