Limits of Accuracy (Copy)

IGCSE Mathematics Core Practice Exam

Topic: Upper and Lower Bounds
Total Marks: 40
Time: 35 minutes
(With Detailed Solutions)

Section A: Finding Upper and Lower Bounds (No Calculator)

Total Marks: 24

1. A length is measured as 84 cm, correct to the nearest cm.
Write down: (4 marks)
a) The lower bound
b) The upper bound

2. A number is written as 3500, correct to the nearest 100.
Find: (4 marks)
a) The lower bound
b) The upper bound

3. A weight is recorded as 5.4 kg, correct to 1 decimal place.
State: (4 marks)
a) The smallest possible value
b) The largest possible value

4. A distance is given as 3.75 km, correct to 2 decimal places.
Write down the upper and lower bounds. (4 marks)

5. A number is 0.067, correct to 2 significant figures.
Find the lower and upper bounds. (4 marks)

6. A value is 600, correct to 1 significant figure.
Find: (4 marks)
a) The lower bound
b) The upper bound

Section B: Contextual Bounds Questions (Calculator Allowed)

Total Marks: 16

7. The length of a room is measured as 4.2 m, correct to the nearest 0.1 m.
The width is measured as 3.6 m, correct to the nearest 0.1 m.
Write down: (4 marks)
a) The upper bound for the length
b) The lower bound for the width

8. A car’s speed is recorded as 90 km/h, correct to the nearest 10 km/h.
What is the range of possible speeds? (3 marks)

9. The weight of a bag of sugar is 1.00 kg, correct to 2 decimal places.
Find the upper and lower bounds. (3 marks)

10. A plank is cut to 2.5 m, correct to the nearest 0.05 m.
Find: (3 marks)
a) The lower bound
b) The upper bound

11. A bottle contains 750 ml, correct to the nearest 10 ml.
Find the maximum possible amount it could contain. (3 marks)

Marking Scheme with Detailed Explanations

Section A

1.
Nearest cm → Unit = 1 → Half = 0.5
a) Lower Bound = 84 − 0.5 = 83.5 cm (2 marks)
b) Upper Bound = 84 + 0.5 = 84.5 cm (2 marks)

2.
Nearest 100 → Half = 50
a) Lower Bound = 3500 − 50 = 3450 (2 marks)
b) Upper Bound = 3500 + 50 = 3550 (2 marks)

3.
1 d.p. → Unit = 0.1 → Half = 0.05
a) 5.35 kg (2 marks)
b) 5.45 kg (2 marks)

4.
2 d.p. → Unit = 0.01 → Half = 0.005
Lower Bound = 3.745 km
Upper Bound = 3.755 km (2 marks each)

5.
2 s.f. in 0.067 → Unit = 0.001 → Half = 0.0005
Lower Bound = 0.0665
Upper Bound = 0.0675 (2 marks each)

6.
1 s.f. in 600 → Unit = 100 → Half = 50
Lower Bound = 550
Upper Bound = 650 (2 marks each)

Section B

7.
Length: Nearest 0.1 → Half = 0.05 → Upper Bound = 4.25 m (2 marks)
Width: Lower Bound = 3.6 − 0.05 = 3.55 m (2 marks)

8.
Nearest 10 → Half = 5
Range = 85 km/h to 95 km/h (3 marks)

9.
2 d.p. → Unit = 0.01 → Half = 0.005
Lower Bound = 0.995 kg
Upper Bound = 1.005 kg (3 marks)

10.
Nearest 0.05 → Half = 0.025
a) Lower Bound = 2.475 m (1.5 marks)
b) Upper Bound = 2.525 m (1.5 marks)

11.
Nearest 10 ml → Half = 5 ml
Upper Bound = 750 + 5 = 755 ml (3 marks)