Chapter 13 Practice Paper: Proportion and rates of change — question paper (print)

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QQ/GCSE-MATHS/CH13

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

Chapter 13 Practice Paper

Proportion and rates of change

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.
Include units in your final answers to compound-measure questions.
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 13: speed, density and pressure, converting compound units, direct and inverse proportion with the unitary method and y = kx / y = k/x equations, rates of change from graphs, and capture–recapture estimation.

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 cyclist rides 100 km in 2 hours. Her average speed is
1. A50 km/h
2. B200 km/h
3. C25 km/h
4. D102 km/h
( )
2
72 km/h expressed in m/s is
1. A7200 m/s
2. B7.2 m/s
3. C20 m/s
4. D0.02 m/s
( )
3
Ore of mass 540 g occupies 200 cm³. Its density in g/cm³ is
1. A0.37 g/cm³
2. B2.7 g/cm³
3. C27 g/cm³
4. D740 g/cm³
( )
4
A force of 250 N acts over an area of 0.5 m². The pressure is
1. A125 Pa
2. B0.002 Pa
3. C250.5 Pa
4. D500 Pa
( )
5
Four kilograms of flour cost £4.80. Six kilograms cost
1. A£7.20
2. B£4.80
3. C£9.60
4. D£6.60
( )
6
For the equation y = 3x, find y at x = 12.
1. A45
2. B15
3. C36
4. D60
( )
7
Ten workers build a wall in 12 days. Eight workers, at the same rate, take
1. A9.6 days
2. B15 days
3. C96 days
4. D14 days
( )
8
y = 6/x. When x = 3, y is
1. A18
2. B9
3. C3
4. D2
( )
9
One cubic metre is the same volume as
1. A1 000 000 cm³
2. B1000 cm³
3. C100 cm³
4. D10 cm³
( )
10
The graph of two quantities in direct proportion is
1. Aa curve through the origin
2. Bany straight line
3. Ca straight line through the origin
4. Da horizontal line
( )

Section B: Structured questions[20 marks]

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

11
Compound measures.
1. (a)
  Convert 36 km/h into m/s.
  [2]
2. (b)
  A liquid has density 0.8 g/cm³. Find the volume of 2 kg (2000 g) of the liquid.
  [2]
12
Fruit tea in direct proportion.
1. (a)
  250 g of fruit tea makes 6 cups. How many grams are needed for 15 cups?
  [2]
2. (b)
  How many whole cups can be made from a 1 kg (1000 g) packet?
  [2]
13
Machines and hours.
1. (a)
  Five identical machines fill an order in 16 hours. How long would eight machines take?
  [2]
2. (b)
  How many machines would be needed to finish the order in 4 hours?
  [2]
14
A delivery van’s fuel.
1. (a)
  The van uses 18 litres of diesel to travel 153 miles. Find its rate in miles per litre.
  [1]
2. (b)
  How many litres are needed for a 255-mile journey?
  [2]
3. (c)
  How far could the van travel on a full 60-litre tank?
  [1]
15
Badgers in a park. (Higher)
1. (a)
  A ranger tags 25 badgers and releases them. The next week she traps 40 badgers, of which 5 carry tags. Estimate the park’s badger population.
  [3]
2. (b)
  State one assumption your estimate depends on.
  [1]

— End of paper —