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Chapter 5 Practice Paper: Integration and Applications — question paper

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QQ/S4AM/CH5

Secondary 4 · Additional Mathematics (G3)

Chapter 5 Practice Paper

Integration and Applications

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 5 (C1 Integration: standard integrals, definite integrals, areas).

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 non-exact numerical answers correct to 3 significant figures unless told otherwise.

  1. 1

    Find each of the following indefinite integrals.

    1. (a)

      ∫(8x³ − 6x + 4) dx.

      [2]
    2. (b)

      ∫3/x⁴ dx.

      [2]
    3. (c)

      ∫sec²x dx.

      integral =[1]
  2. 2

    Find each of the following indefinite integrals.

    1. (a)

      ∫(3x − 2)⁴ dx.

      [2]
    2. (b)

      ∫e^(5x) dx.

      [2]
    3. (c)

      ∫cos 4x dx.

      [2]
  3. 3

    Evaluate ∫₁³(2x² + 1/x²) dx.

    1. (a)

      Rewrite the integrand with all terms as powers of x.

      [2]
    2. (b)

      Integrate the expression in (a).

      [2]
    3. (c)

      Hence evaluate the integral, showing the bracketed substitution.

      [2]
  4. 4

    The curve y = x² − 2x − 3 crosses the x-axis at A and B, and C is the point on the curve with x-coordinate 4.

    1. (a)

      Find the coordinates of A and B.

      [2]
    2. (b)

      Show that ∫₋₁³(x² − 2x − 3) dx = −32/3, and explain what the negative sign tells you.

      [3]
    3. (c)

      Find the total area of the region bounded by the curve and the x-axis from A to C.

      [2]
  5. 5

    The curve y = 8 − x² and the line y = 2x intersect at the points L and M.

    1. (a)

      Find the x-coordinates of L and M.

      [2]
    2. (b)

      Calculate the area of the region between the parabola and the line.

      [4]

— End of paper —