Rates (Copy)

IGCSE Mathematics Core Practice Exam

Topic: Rates, Speed, Density, Pressure, Exchange Rates & Proportion
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)

Section A: Common Measures of Rate (No Calculator)

Total Marks: 20

1. A worker earns $96 for 8 hours of work.
What is their hourly rate of pay? (2 marks)

2. Convert £250 to USD if £1 = $1.28. (2 marks)

3. A car travels 180 km in 3 hours.
Calculate the average speed in km/h. (2 marks)

4. A fuel tank holds 60 litres of petrol. The car travels 720 km on a full tank.
Calculate the fuel consumption in km per litre. (2 marks)

5. A pipe fills 150 litres of water in 25 minutes.
What is the flow rate in litres per minute? (2 marks)

6. The force on a surface is 500 N and the area is 100 m².
Calculate the pressure. (2 marks)

7. A metal block has a mass of 2.4 kg and a volume of 800 cm³.
Calculate the density in g/cm³. (3 marks)

8. The population of a town is 120,000 and the area is 300 km².
Calculate the population density. (3 marks)

9. A runner completes 10 km in 48 minutes. Calculate the average speed in km/h. (2 marks)

Section B: Applied Problems (Calculator Allowed)

Total Marks: 20

10. A cyclist travels 75 km in 4 hours 30 minutes.
Find the average speed in km/h. (3 marks)

11. Convert $500 to Euros if $1 = €0.85. (2 marks)

12. A tank is filled at a rate of 12 litres per minute. How long will it take to fill 180 litres? (2 marks)

13. The pressure on a surface is 8 N/m². If the area is 20 m², calculate the force applied. (3 marks)

14. A wooden block has a density of 0.6 g/cm³ and a volume of 2500 cm³. Calculate its mass. (3 marks)

15. A person is paid $540 for working 36 hours. How much will they earn for 25 hours at the same rate? (3 marks)

16. A car travels 300 km using 20 litres of fuel. How far can it travel on 35 litres at the same rate? (4 marks)

Marking Scheme with Detailed Explanations

Section A

1.
96 ÷ 8 = $12/hour (2 marks)

2.
250 × 1.28 = $320 (2 marks)

3.
180 ÷ 3 = 60 km/h (2 marks)

4.
720 ÷ 60 = 12 km/litre (2 marks)

5.
150 ÷ 25 = 6 litres/min (2 marks)

6.
500 ÷ 100 = 5 N/m² (2 marks)

7.
2.4 kg = 2400 g
2400 ÷ 800 = 3 g/cm³ (3 marks)

8.
120,000 ÷ 300 = 400 people/km² (3 marks)

9.
48 mins = 0.8 hours
10 ÷ 0.8 = 12.5 km/h (2 marks)

Section B

10.
4 hrs 30 mins = 4.5 hrs
75 ÷ 4.5 = 16.67 km/h (3 marks)

11.
500 × 0.85 = €425 (2 marks)

12.
180 ÷ 12 = 15 minutes (2 marks)

13.
Force = Pressure × Area = 8 × 20 = 160 N (3 marks)

14.
Mass = Density × Volume = 0.6 × 2500 = 1500 g = 1.5 kg (3 marks)

15.
Rate = 540 ÷ 36 = 15/hour
25 × 15 = $375 (3 marks)

16.
300 ÷ 20 = 15 km/litre
15 × 35 = 525 km (4 marks)