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Chapter 11 Practice Paper: Graphs of functions and real-life graphs — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH11

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 11 Practice Paper

Graphs of functions and real-life graphs

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.
  • Sketches need shape and labelled key points.
  • 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 for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 11: recognising and sketching linear, quadratic, cubic, reciprocal, exponential and trig graphs, transformations of functions (Higher), distance–time graphs, gradients of curves and areas under graphs (Higher), and the circle equation with tangents (Higher).

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

    Which is the graph of a cubic function?

    1. AA U-shape
    2. BA straight line
    3. CAn S-shape through the origin
    4. DTwo separate branches
    ( )
  2. 2

    The graph of y = 1⁄x never touches

    1. Athe line y = x
    2. Bthe x-axis or y-axis
    3. Cthe origin only
    4. Dany point with x = 1
    ( )
  3. 3

    y = 3ˣ passes through (2, y). Here y equals

    1. A6
    2. B8
    3. C3
    4. D9
    ( )
  4. 4

    The curve y = (½)ˣ shows

    1. Agrowth
    2. Ba straight line
    3. Ca wave
    4. Ddecay
    ( )
  5. 5

    At x = 90°, sin x equals

    1. A0
    2. B1
    3. C−1
    4. D90
    ( )
  6. 6

    The graph of y = f(x) + 2 compared with y = f(x) is shifted (Higher)

    1. Aright 2
    2. Bleft 2
    3. Cdown 2
    4. Dup 2
    ( )
  7. 7

    The graph of y = f(x + 5) compared with y = f(x) is shifted (Higher)

    1. Aleft 5
    2. Bright 5
    3. Cup 5
    4. Ddown 5
    ( )
  8. 8

    A distance–time graph gets steeper and steeper. The speed is (Higher)

    1. Aconstant
    2. Bzero
    3. Cincreasing
    4. Ddecreasing
    ( )
  9. 9

    The area under a velocity–time graph from 0 to 6 s, at a constant 5 m/s, is (Higher)

    1. A30 m
    2. B11 m
    3. C1.2 m
    4. D5 m
    ( )
  10. 10

    State the radius of the circle with equation x² + y² = 49. (Higher)

    1. A49
    2. B7
    3. C24.5
    4. D√49 as a surd form
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer.

  1. 11

    Matching and features.

    1. (a)

      State whether each graph is linear, quadratic, cubic or reciprocal: y = 4 − x², y = x³ − 3x, y = 1⁄x, y = 2x + 7.

      [2]
    2. (b)

      Write down the coordinates of the y-intercept of y = x² − 4x − 5.

      [2]
  2. 12

    Distance–time graph.

    1. (a)

      A delivery van travels 30 km in the first 40 minutes at a steady speed, then rests for 20 minutes. Sketch the graph.

      [2]
    2. (b)

      Find the speed for the first stage in km/h.

      [2]
  3. 13

    Transformations. (Higher)

    1. (a)

      The curve y = (x − 1)² + 3 is a translation of y = x². Where does the point (4, 16) of the original curve land? Give the new coordinates.

      [2]
    2. (b)

      Describe the reflection that maps y = x² onto y = −x².

      [2]
  4. 14

    Area under a graph. (Higher)

    1. (a)

      A train accelerates uniformly from 0 to 30 m/s over 20 s, then holds 30 m/s for 30 s. Find the total distance.

      [4]
    2. (b)

      State the acceleration during the first stage.

      [1]
  5. 15

    Tangents to circles. (Higher)

    1. (a)

      A circle has equation x² + y² = 169. Show that the point (5, 12) lies on it, and find the equation of the tangent there.

      [3]

— End of paper —