Topic 3 Practice Paper: Ratio, proportion and rates — question paper (print)

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QQ/IGCSE-MATHS/T3

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

Topic 3 Practice Paper

Ratio, proportion and rates

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 3: simplifying ratios, dividing quantities in a ratio, recipes, map scales and best buys, direct and inverse proportion, speed and average speed, density, pressure, population density, pay and fuel rates.

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
The ratio 84 : 36 in its simplest form is
1. A21 : 9
2. B7 : 3
3. C3 : 7
4. D42 : 18
( )
2
A rope 91 cm long is cut in the ratio 4 : 3. The longer piece measures
1. A39 cm
2. B13 cm
3. C56 cm
4. D52 cm
( )
3
A runner completes 400 m in 50 seconds. The average speed is
1. A8 m/s
2. B12.5 m/s
3. C20 m/s
4. D0.125 m/s
( )
4
If 4 identical notebooks cost 5.40, then 10 notebooks cost
1. A12.40
2. B21.60
3. C13.50
4. D10.80
( )
5
A force of 900 N acts over an area of 0.6 m². The pressure is
1. A1500 N/m²
2. B540 N/m²
3. C900.6 N/m²
4. D0.000667 N/m²
( )
6
On a scale drawing, 1 cm represents 2.5 m. A hall of length 32 m measures
1. A12.8 cm
2. B8 cm
3. C64 cm
4. D1.28 cm
( )
7
p is inversely proportional to q. When p = 6, q = 4. When q = 8, p equals (Extended)
1. A12
2. B2
3. C3
4. D48
( )
8
A tap flows at 12 litres per minute. The time to fill a 300-litre tank is
1. A3600 min
2. B0.04 min
3. C3.6 min
4. D25 min
( )
9
A block of density 2.5 g/cm³ has volume 36 cm³. Its mass is
1. A14.4 g
2. B90 g
3. C38.5 g
4. D0.069 g
( )
10
The first stage of a journey covers 100 km in 1 h 15 min and the second 60 km in 45 min. The average speed is
1. A75 km/h
2. B90 km/h
3. C160 km/h
4. D80 km/h
( )

Section B: Structured questions[20 marks]

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

11
A charity splits its donations between three appeals in the ratio 6 : 5 : 4.
1. (a)
  In one month, 7 500 was donated. Find how much each appeal received.
  [3]
2. (b)
  In a different month the smallest appeal received 1 320. Find the total donated that month.
  [3]
12
Wire of the same thickness is sold by weight. A 50 g coil of wire has resistance 3.2 ohms. (Extended)
1. (a)
  The resistance R is directly proportional to the length, which is proportional to the weight w. Write an equation for R in terms of w.
  [2]
2. (b)
  Find the resistance of an 85 g coil.
  [2]
3. (c)
  A circuit needs a coil of resistance 9.6 ohms. Find its weight.
  [3]
13
A delivery van makes a two-part journey.
1. (a)
  It covers 132 km at an average speed of 88 km/h. Find this stage’s time, in hours and minutes.
  [2]
2. (b)
  After a 25-minute break it travels 57 km in 45 min. Find the average speed for the whole journey, including the break, correct to 3 significant figures.
  [3]
3. (c)
  The van uses 8.4 litres of diesel per 100 km. Find the diesel used on the 189 km journey, correct to 2 decimal places.
  [2]

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