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Chapter 3 Practice Paper: Linear Law — question paper

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QQ/S4AM/CH3

Secondary 4 · Additional Mathematics (G3)

Chapter 3 Practice Paper

Linear Law

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
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 3 (G2 linear law: transforming relations to linear form).

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. Throughout this paper, lg x means log₁₀ x, and you may use lg 2 = 0.30, lg 3 = 0.48, lg 5 = 0.70.

  1. 1

    The variables x and y are connected by y = axⁿ, where a and n are constants.

    1. (a)

      Taking logarithms, show that the relation can be written as lg y = n lg x + lg a.

      [2]
    2. (b)

      State what must be plotted on each axis to obtain a straight line, and identify its gradient and vertical intercept.

      [3]
  2. 2

    The table gives experimental values of x and y for a relation y = kbˣ, where k and b are constants.

    Data for Question 2

    x1234
    y61854162
    1. (a)

      Complete the table of lg y, correct to 2 decimal places, using lg 2 = 0.30, lg 3 = 0.48, lg 6 = 0.78.

      [2]
    2. (b)

      Explain why these values support a straight-line graph of lg y against x, and state the gradient of that line.

      [3]
    3. (c)

      Find the values of k and b.

      k, b =[2]
  3. 3

    The variables x and y are believed to satisfy y = axⁿ. The table gives values of x and y.

    Data for Question 3

    x1416
    y540320
    1. (a)

      Complete the table of lg x and lg y, correct to 3 decimal places, using lg 4 = 0.602, lg 5 = 0.699, lg 16 = 1.204, lg 40 = 1.602, lg 320 = 2.505.

      [2]
    2. (b)

      Show that these points lie on a straight line and find its gradient.

      [3]
    3. (c)

      Hence find the values of a and n.

      a, n =[2]
  4. 4

    The variables x and y satisfy y = A√x + B, where A and B are constants. Values of x and y are given below.

    Data for Question 4

    x1925
    y71115
    1. (a)

      State what to plot to obtain a straight line, and find A and B.

      [4]
    2. (b)

      Estimate the value of y when x = 16.

      y =[1]
    3. (c)

      Find the value of x for which y = 17.

      x =[1]
  5. 5

    A student suggests that plotting lg y against lg x will produce a straight line for the relationship y = x² + 3x.

    1. (a)

      Explain why the student is wrong.

      [3]
    2. (b)

      Describe the shape of the graph of y against x for this relationship.

      [2]

— End of paper —