Topic 9 Practice Paper: Graphs of functions — question paper (print)

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QQ/IGCSE-MATHS/T9

IGCSE · Cambridge IGCSE Mathematics (Extended (Core + Extended))

Topic 9 Practice Paper

Graphs of functions

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

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 9: conversion and distance–time graphs, speed–time graphs with distance as area, plotting curves from tables of values, solving equations graphically, and sketching quadratics, cubics, reciprocals and exponentials.

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
A conversion line joins (0, 0) to (10, 8). The value paired with 25 on the horizontal axis is
1. A16
2. B20
3. C25
4. D33
( )
2
On a distance–time graph, the steepness of a straight section measures the
1. Adistance travelled
2. Bacceleration
3. Cspeed
4. Dtime taken
( )
3
A bus covers 45 km in 1 hour 15 minutes. Its average speed is
1. A36 km/h
2. B45 km/h
3. C33.75 km/h
4. D60 km/h
( )
4
A speed rises steadily from 4 m/s to 16 m/s in 6 s. The acceleration is
1. A1 m/s²
2. B2.7 m/s²
3. C20 m/s²
4. D2 m/s²
( )
5
The area under a speed–time rectangle of height 8 m/s and width 15 s represents a distance of
1. A120 m
2. B23 m
3. C60 m
4. D240 m
( )
6
Substituting x = −1 into y = x² − 2x gives
1. A1
2. B−3
3. C3
4. D−1
( )
7
The roots of y = (x − 1)(x − 5) are
1. A−1 and −5
2. B1 and 5
3. C1 and −5
4. D−1 and 5
( )
8
To solve x² − 2x = 7 from the graph of y = x² − 2x, you draw
1. Ax = 7
2. By = 2
3. Cy = −7
4. Dy = 7
( )
9
The turning point of y = (x + 3)² − 4 is at
1. A(3, −4)
2. B(−3, −4)
3. C(3, 4)
4. D(−3, 4)
( )
10
The graph of y = 3ˣ crosses the y-axis at (Extended)
1. A(1, 3)
2. B(3, 1)
3. C(0, 1)
4. D(1, 0)
( )

Section B: Structured questions[20 marks]

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

11
A cyclist’s distance–time graph shows 0 to 40 km covered in the first 2 hours, a flat section from 2 to 3 hours, and a return to 0 km between 3 and 5 hours.
1. (a)
  Find the speed during the first stage.
  [1]
2. (b)
  Write down the length of the stop.
  [1]
3. (c)
  Find the speed of the return journey.
  [1]
4. (d)
  Work out the mean speed over the entire ride.
  [2]
12
The curve y = x² + x − 6 is drawn for −4 ⩽ x ⩽ 3.
1. (a)
  Show that y = 6 when x = −4 and when x = 3.
  [2]
2. (b)
  Write down the roots of x² + x − 6 = 0 from the graph.
  [1]
3. (c)
  Use a suitable straight line to solve x² + x − 4 = 0, giving your answers to 2 decimal places.
  [2]
13
The speed–time graph of a motorbike rises to 15 m/s after 10 s, stays flat for 30 s, and returns to zero after a further 5 s. (Extended)
1. (a)
  Find the acceleration and the deceleration.
  [2]
2. (b)
  Work out how far the motorbike travels in total.
  [2]
3. (c)
  State the mean speed across the 45 seconds.
  [1]
14
Sketch work on y = x² − 2x − 3. (Extended)
1. (a)
  Write down the roots of y = (x + 1)(x − 3) and the y-intercept.
  [2]
2. (b)
  Find the coordinates of the minimum point of the curve.
  [2]
3. (c)
  State what happens to the arms of the curve for large positive and large negative x.
  [1]

— End of paper —