Ratio, Proportion and Rates of Change (Applied)Edexcel GCSE Maths: Topic test

20 questions, 52 marks

Edexcel GCSE Maths

Ratio, Proportion and Rates of Change (Applied) topic test

Total 52 marks

Name

Class

Date

1
A delivery company is reviewing three figures from its weekly report: a van's average speed, a 12% rise in fuel prices, and a scale drawing of its warehouse.
(a)
A van travels 180 km in 2 hours 15 minutes. What is its average speed, in km/h?
[1 mark]
A72 km/h
B80 km/h
C90 km/h
D100 km/h
(b)
Fuel priced at £1.55 per litre rises by 12%. What is the new price per litre, to the nearest penny?
[1 mark]
A£1.67
B£1.73
C£1.74
D£1.83
(c)
A scale drawing of the warehouse uses a scale of 1:250. A wall measures 8 cm on the drawing. What is the real length of the wall, in metres?
[1 mark]
A20 m
B2 m
C200 m
D0.2 m
Total for question 1: 3 marks
2
A cartographer is drawing a map of a nature reserve using a scale of 1:20,000. A ranger patrols a straight path at a steady pace, covering 3.6 km in 45 minutes.
(a)
A footpath is 2,400 m long in real life. What length, in cm, should it be drawn on the map?
[2 marks]
(b)
Work out the ranger's speed, in km/h.
[2 marks]
Total for question 2: 4 marks
3
A conservation charity's membership was 640 last year and grew by 15% this year. This year's members are grouped for site visits in the ratio 3:5 between Reserve A and Reserve B.
(a)
Work out the charity's membership this year.
[3 marks]
(b)
This year's membership of 736 is split between Reserve A and Reserve B in the ratio 3:5 for site visits. Work out the number of members allocated to Reserve B.
[3 marks]
Total for question 3: 6 marks
4
A haulage firm's lorry has a mass of 3.5 tonnes when empty. Its cargo has a density of $0.8$ g/cm $^3$ and fills a volume of 6 m $^3$ ( $1$ g/cm $^3 = 1000$ kg/m $^3$ ). The firm's annual fuel bill of £42,000 is expected to fall by 6% next year, and then by a further 4% the year after. The firm also makes 900 deliveries a month, split between three regions in the ratio 2:3:4, and Region 3 charges an average delivery fee of £18.50.
(a)
Work out the total mass of the lorry (empty mass plus cargo), in tonnes.
[4 marks]
(b)
Work out the firm's fuel bill two years from now, giving your answer to the nearest penny.
[4 marks]
(c)
The firm's 900 monthly deliveries are split between three regions in the ratio 2:3:4. Region 3 charges an average delivery fee of £18.50. Work out the total fee income from Region 3's deliveries that month.
[5 marks]
Total for question 4: 13 marks
5
A logistics company is reviewing three figures from its monthly report: a courier's average speed, an 18% rise in packaging costs, and a scale drawing of its depot.
(a)
A courier travels 63 km in 1 hour 24 minutes. What is the courier's average speed, in km/h?
[1 mark]
A52.5 km/h
B63 km/h
C50 km/h
D45 km/h
(b)
Packaging costs of £2.40 per parcel rise by 18%. What is the new cost per parcel, to the nearest penny?
[1 mark]
A£2.83
B£2.90
C£2.75
D£2.62
(c)
A scale drawing of the depot uses a scale of 1:150. A loading bay measures 6 cm on the drawing. What is the real length of the loading bay, in metres?
[1 mark]
A0.9 m
B9 m
C90 m
D15 m
Total for question 5: 3 marks
6
A town planner is drawing a map of a new estate using a scale of 1:5,000. A cyclist rides along a straight cycle path at a steady pace, covering 2.4 km in 32 minutes.
(a)
A cycle path is 1,600 m long in real life. What length, in cm, should it be drawn on the map?
[2 marks]
(b)
Work out the cyclist's speed, in km/h.
[2 marks]
Total for question 6: 4 marks
7
A wildlife trust's membership was 520 last year and grew by 25% this year. This year's members are grouped for site visits in the ratio 2:3 between Reserve C and Reserve D.
(a)
Work out the trust's membership this year.
[3 marks]
(b)
This year's membership of 650 is split between Reserve C and Reserve D in the ratio 2:3 for site visits. Work out the number of members allocated to Reserve D.
[3 marks]
Total for question 7: 6 marks
8
A shipping firm's container has a mass of 2.2 tonnes when empty. Its cargo has a density of $1.2$ g/cm $^3$ and fills a volume of 5 m $^3$ ( $1$ g/cm $^3 = 1000$ kg/m $^3$ ). The firm's annual insurance bill of £28,000 is expected to fall by 5% next year, and then rise by 3% the year after. The firm also makes 480 shipments a month, split between three ports in the ratio 3:4:5, and Port 3 charges an average handling fee of £24.50.
(a)
Work out the total mass of the container (empty mass plus cargo), in tonnes.
[4 marks]
(b)
Work out the firm's insurance bill two years from now, giving your answer to the nearest penny.
[4 marks]
(c)
The firm's 480 monthly shipments are split between three ports in the ratio 3:4:5. Port 3 charges an average handling fee of £24.50. Work out the total fee income from Port 3's shipments that month.
[5 marks]
Total for question 8: 13 marks

End of questions