Estimatin (Copy)

IGCSE Mathematics Core Practice Exam

Topic: Rounding, Estimation & Degrees of Accuracy
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)

Section A: Rounding (No Calculator)

Total Marks: 20

1. Round the following numbers as instructed: (6 marks)
a) 5764 to the nearest 1000
b) 849 to the nearest 10
c) 45,678 to 2 significant figures
d) 0.004376 to 2 significant figures
e) 12.9876 to 3 decimal places
f) 3.14159 to 2 decimal places

2. Write each number correct to 1 significant figure and then estimate the value: (6 marks)
a) (9.79 × 0.765) ÷ 41.3
b) 482 × 19
c) (298 ÷ 51)

3. Round the following to the specified degree of accuracy: (4 marks)
a) 0.07389 to 3 significant figures
b) 67,450 to 1 significant figure
c) 5.6789 to 2 decimal places
d) 999 to the nearest 100

4. State whether the following statements are True or False: (4 marks)
a) 0.0567 rounded to 2 s.f. is 0.057
b) 12345 to 3 s.f. is 12300
c) 7.499 rounded to 1 decimal place is 7.5
d) 14.5 rounded to the nearest 10 is 10

Section B: Contextual Rounding & Estimation (Calculator Allowed)

Total Marks: 20

5. A distance is calculated as 256.789 km. Measurements were given to the nearest km. Round your answer appropriately. (2 marks)

6. The total bill at a restaurant is $87.456. How much should you pay, rounded to the nearest dollar? (2 marks)

7. Estimate the value of the following by rounding each number to 1 significant figure: (6 marks)
a) (123 × 49) ÷ 8.2
b) 3.14 × 19.7
c) (0.045 × 678)

8. A container holds 5.678 litres of water. The measuring equipment is accurate to 1 decimal place. What is the recorded volume? (2 marks)

9. A runner completes a race in 123.456 seconds. Give this time to: (4 marks)
a) 2 decimal places
b) 3 significant figures

10. Estimate the cost of 19 items priced at $48.75 each. (4 marks)

Marking Scheme with Detailed Explanations

Section A

1.
a) 6000 (1 mark)
b) 850 (1 mark)
c) 46000 (1 mark)
d) 0.0044 (1 mark)
e) 12.988 (1 mark)
f) 3.14 (1 mark)

2.
a) (10 × 0.8) ÷ 40 = 0.2 (2 marks)
b) 500 × 20 = 10,000 (2 marks)
c) 300 ÷ 50 = 6 (2 marks)

3.
a) 0.0739 (1 mark)
b) 70,000 (1 mark)
c) 5.68 (1 mark)
d) 1000 (1 mark)

4.
a) True (1 mark)
b) False (should be 12300) (1 mark)
c) True (1 mark)
d) True (1 mark)

Section B

5.
Since measurements were to the nearest km → 257 km (2 marks)

6.
$87.456 rounded to nearest dollar = $87 (2 marks)

7.
a) (100 × 50) ÷ 8 = 625 (2 marks)
b) 3 × 20 = 60 (2 marks)
c) 0.05 × 700 = 35 (2 marks)

8.
5.678 litres to 1 d.p. = 5.7 litres (2 marks)

9.
a) 123.456 → 123.46 seconds (2 marks)
b) 123.456 → 123 seconds (2 marks)

10.
Estimate: 20 items × $50 = $1000 (4 marks)