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Chapter 3 Practice Paper: Indices, surds and standard form — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH3

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 3 Practice Paper

Indices, surds and standard form

Duration: 40 minutes
Total: 30 marks
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • Give exact answers unless a question tells you to round.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 3: index laws and the zero index, negative and fractional indices (Higher), simplifying and rationalising surds (Higher), exact calculations with surds and π, and standard form conversions, products and quotients.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    Work out 3² × 3³.

    1. A3⁶
    2. B9⁵
    3. C3⁵
    4. D6⁵
    ( )
  2. 2

    Work out (2³)².

    1. A64
    2. B256
    3. C12
    4. D512
    ( )
  3. 3

    Work out 9⁰ + 9¹.

    1. A18
    2. B10
    3. C9
    4. D2
    ( )
  4. 4

    Simplify a¹⁰ ÷ a⁴.

    1. Aa¹⁴
    2. Ba⁵
    3. C4a⁶
    4. Da⁶
    ( )
  5. 5

    The surd √32 simplifies to

    1. A2√8
    2. B4√2
    3. C8√2
    4. D16√2
    ( )
  6. 6

    Work out 2⁻³. (Higher)

    1. A−8
    2. B⅛
    3. C6
    4. D−6
    ( )
  7. 7

    Work out √9 + ∛8.

    1. A11
    2. B4
    3. C7
    4. D5
    ( )
  8. 8

    Rationalising 6⁄√3 gives (Higher)

    1. A2√3
    2. B6√3
    3. C2
    4. D√3⁄2
    ( )
  9. 9

    Write 720 000 in standard form.

    1. A72 × 10⁴
    2. B7.2 × 10⁻⁵
    3. C7.2 × 10⁵
    4. D0.72 × 10⁶
    ( )
  10. 10

    Work out (2 × 10⁴) × (6 × 10⁻³).

    1. A12 × 10¹
    2. B1.2 × 10⁸
    3. C1.2 × 10²
    4. D8 × 10¹
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer. Give exact answers unless told to round.

  1. 11

    Index laws.

    1. (a)

      Simplify (x⁴)³ × x⁵.

      [2]
    2. (b)

      Simplify 15p⁷q² ÷ 5p²q².

      [2]
  2. 12

    Exact geometry.

    1. (a)

      A circle has radius 9 cm. Write down the exact circumference.

      [2]
    2. (b)

      A square tile covers 75 cm². Write the exact side length of the tile as a simplified surd.

      [2]
  3. 13

    Standard form.

    1. (a)

      Write 5 600 000 in standard form.

      [1]
    2. (b)

      Convert 4.02 × 10⁻³ from standard form into an ordinary decimal number.

      [1]
    3. (c)

      Divide (4 × 10⁹) by (8 × 10³) and write the result in standard form.

      [2]
  4. 14

    Fractional indices. (Higher)

    1. (a)

      Work out 32^(2/5).

      [2]
    2. (b)

      Work out 4^(−3/2).

      [2]
  5. 15

    Rationalising. (Higher)

    1. (a)

      Write 12⁄√6 with a rational (surd-free) denominator, in its simplest form.

      [2]
    2. (b)

      Show that 4⁄(√7 − 3) = −2(√7 + 3).

      [2]

— End of paper —