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Topic 4 Practice Paper: Indices, surds and standard form — question paper

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QQ/IGCSE-MATHS/T4

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 4 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.
  • 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 against the Cambridge IGCSE Mathematics syllabus. It is not an official Cambridge examination paper. Topic 4: index laws with zero, negative and fractional indices, standard form conversions and arithmetic, simplifying surds, and rationalising denominators.

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 5² × 5⁻⁴.

    1. A1/25
    2. B25
    3. C5⁻⁸
    4. D625
    ( )
  2. 2

    Which number is written in standard form?

    1. A12.5 × 10³
    2. B8.04 × 10⁵
    3. C0.7 × 10⁶
    4. D804 × 10³
    ( )
  3. 3

    Evaluate 8^(2/3). (Extended)

    1. A2
    2. B16
    3. C4
    4. D32
    ( )
  4. 4

    Write 0.0009 in standard form.

    1. A9 × 10⁻⁴
    2. B9 × 10⁴
    3. C9 × 10⁻³
    4. D0.9 × 10⁻³
    ( )
  5. 5

    Simplify √75. (Extended)

    1. A3√5
    2. B25√3
    3. C15
    4. D5√3
    ( )
  6. 6

    What is 9⁰ × 9¹?

    1. A82
    2. B9
    3. C1
    4. D10
    ( )
  7. 7

    Work out (5 × 10⁶) × (3 × 10⁻²).

    1. A1.5 × 10⁵
    2. B15 × 10⁴
    3. C1.5 × 10⁴
    4. D8 × 10⁴
    ( )
  8. 8

    Simplify √27 + √12. (Extended)

    1. A√39
    2. B6√3
    3. C5√3
    4. D13√2
    ( )
  9. 9

    Evaluate 4⁻².

    1. A−16
    2. B8
    3. C−1/16
    4. D1/16
    ( )
  10. 10

    Express 4/√8 in the form k√n, where k and n are integers. (Extended)

    1. A4√2
    2. B√2
    3. C2√2/4
    4. D2√2
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show all your working.

  1. 11

    Answer this question without a calculator.

    1. (a)

      Simplify 3⁵ × 3⁻² ÷ 3.

      [2]
    2. (b)

      Evaluate 25^(3/2).

      [2]
    3. (c)

      Write 1/16 as a power of 2.

      [2]
  2. 12

    Standard form in context.

    1. (a)

      A grain of pollen has mass 0.0000058 g. Write this mass in standard form.

      [1]
    2. (b)

      A library holds 4 × 10⁶ books, each with an average mass of 6 × 10⁻¹ kg. Find the total mass in kilograms, in standard form.

      [3]
    3. (c)

      A second archive holds 1.2 × 10⁷ kg of books. How many times heavier is the second archive than the library in part (b)?

      [3]
  3. 13

    This question is about surds. (Extended)

    1. (a)

      Simplify √300.

      [2]
    2. (b)

      Simplify √72 + √50 − √18.

      [3]
    3. (c)

      Rationalise the denominator of 12/√3, simplifying fully.

      [2]

— End of paper —