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Chapter 6 Practice Paper: Functions and Graphs — question paper

QuizQuipPractice Series
QQ/S3EM/CH6

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 6 Practice Paper

Functions and Graphs

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.
  • Geometrical instruments and an approved calculator may be used.
  • 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 Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 6 (N6 Functions and Graphs: linear graphs and gradients, quadratic sketches, power and exponential curves, tangent gradients).

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 where appropriate.

  1. 1

    A line passes through the points (1, 1) and (5, 9).

    1. (a)

      Find the gradient of the line.

      [1]
    2. (b)

      Find the equation of the line, giving your answer in the form y = ax + b.

      [2]
  2. 2

    The equation of a line is y = 4 − x/2.

    1. (a)

      State the gradient and the y-intercept of the line.

      [2]
    2. (b)

      Write down the coordinates of the x-intercept.

      [1]
    3. (c)

      Determine whether the point (6, 1) lies on the line, showing your reasoning.

      [1]
  3. 3

    A quadratic curve has equation y = x² − 6x + 5.

    1. (a)

      Find the x-intercepts of the curve.

      [2]
    2. (b)

      Express x² − 6x + 5 in the form (x − p)² + q and state the coordinates of the turning point.

      [2]
    3. (c)

      Describe the shape of the curve, using your answers to (a) and (b).

      [1]
  4. 4

    A curve has equation y = (x + 3)² − 2.

    1. (a)

      State the coordinates and nature of the turning point.

      [1]
    2. (b)

      Write down the y-intercept of the curve.

      [1]
    3. (c)

      Find the x-intercepts, giving your answers correct to 3 significant figures.

      [2]
  5. 5

    A curve has equation y = 5 × 2ˣ.

    1. (a)

      Copy and complete the table of values for x = 0, 1, 2, 3.

      [2]
    2. (b)

      Find the value of x for which y = 80.

      [2]
  6. 6

    Tangents are drawn to a curve at points P and Q. The tangent at P(1, 3) passes through (4, 12). The tangent at Q passes through (0, 5) and (2, 5).

    1. (a)

      Estimate the gradient of the curve at P.

      [2]
    2. (b)

      Find the gradient of the tangent at Q and state what this means about the curve at Q.

      [2]
  7. 7

    A quadratic curve has equation y = −2x² + 8x + 10.

    1. (a)

      Show that −2x² + 8x + 10 = −2(x − 5)(x + 1) and hence state the x-intercepts of the curve.

      [2]
    2. (b)

      Write down the y-intercept of the curve.

      [1]
    3. (c)

      Find the coordinates and nature of the turning point of the curve.

      [2]
    4. (d)

      Describe the shape of the curve.

      [1]

— End of paper —