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Topic 10 Practice Paper: Functions and differentiation — question paper

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QQ/IGCSE-MATHS/T10

IGCSE · Cambridge IGCSE Mathematics (Extended (Extended only))

Topic 10 Practice Paper

Functions and differentiation

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 10: function notation, domain and range, inverse and composite functions, differentiating powers of x, stationary points and their classification, and tangents and normals to curves — all Extended content.

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

    If f(x) = x + 7, then f(−2) is

    1. A9
    2. B−5
    3. C5
    4. D−9
    ( )
  2. 2

    With f(x) = x² and g(x) = x − 4, working out gf(3) gives

    1. A13
    2. B5
    3. C2
    4. D7
    ( )
  3. 3

    For f(x) = 6 − x, the inverse function is

    1. A6 − x
    2. Bx − 6
    3. C−6 − x
    4. D1⁄(6 − x)
    ( )
  4. 4

    Differentiate 3x⁴.

    1. A3x³
    2. B7x³
    3. C4x³
    4. D12x³
    ( )
  5. 5

    The derivative of y = 5x − x³ is

    1. A5 − 3x²
    2. B5 − x³
    3. C−3x²
    4. D5x − 3x²
    ( )
  6. 6

    At x = 2, the slope of the curve y = x³ equals

    1. A6
    2. B8
    3. C12
    4. D3
    ( )
  7. 7

    Where does the curve y = x² + 4x flatten out?

    1. A(2, 4)
    2. B(−2, −4)
    3. C(2, −4)
    4. D(−2, 4)
    ( )
  8. 8

    The second derivative of y = x⁴ is

    1. A4x³
    2. B4x²
    3. C12x³
    4. D12x²
    ( )
  9. 9

    f(x) = x + 1 and g(x) = 3x. The composite gf(x) is

    1. A3x + 1
    2. Bx + 3
    3. C3x + 3
    4. D3x + 4
    ( )
  10. 10

    Which input is banned for y = 1⁄(x + 5)?

    1. Ax ≠ −5
    2. Bx ≠ 5
    3. Cx < −5
    4. Dall real x
    ( )

Section B: Structured questions[20 marks]

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

  1. 11

    f(x) = 4x − 3.

    1. (a)

      Find f(2).

      [1]
    2. (b)

      Find f⁻¹(x).

      [2]
    3. (c)

      Find ff(1), showing both stages.

      [2]
  2. 12

    f(x) = x² + 1 and g(x) = 3x.

    1. (a)

      Find gf(2).

      [2]
    2. (b)

      Find fg(2).

      [2]
    3. (c)

      Solve gf(x) = 51.

      [1]
  3. 13

    The curve is y = x³ − 3x².

    1. (a)

      Find dy⁄dx.

      [2]
    2. (b)

      Write down the coordinates of each stationary point.

      [2]
    3. (c)

      Classify each stationary point, showing your reasoning.

      [2]
  4. 14

    The curve is y = x² − 4x.

    1. (a)

      Find the gradient of the curve at x = 5.

      [1]
    2. (b)

      Write down the coordinates of the point on the curve at x = 5.

      [1]
    3. (c)

      Find the equation of this tangent, in the form y = mx + c.

      [2]

— End of paper —