Standard Form (Copy)

IGCSE Mathematics Core Practice Exam

Topic: Standard Form (Scientific Notation)
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)

Section A: Converting Numbers (No Calculator)

Total Marks: 16

1. Write the following numbers in standard form: (6 marks)
a) 72,000
b) 0.0045
c) 5,300,000

2. Write the following numbers as ordinary numbers: (6 marks)
a) 3.6 × 10³
b) 7.2 × 10⁻²
c) 9.01 × 10⁵

3. State whether the following are correctly written in standard form. If not, rewrite them correctly: (4 marks)
a) 45 × 10²
b) 0.82 × 10⁴
c) 6.3 × 10⁻³
d) 12 × 10⁵

Section B: Calculations with Standard Form (Calculator Allowed – Paper 3 Style)

Total Marks: 24

4. Multiply the following and give your answer in standard form: (4 marks)
a) (3 × 10²) × (4 × 10³)
b) (5.5 × 10⁴) × (2 × 10²)

5. Divide the following and give your answer in standard form: (4 marks)
a) (6 × 10⁵) ÷ (2 × 10²)
b) (9.6 × 10⁷) ÷ (3.2 × 10³)

6. Add or subtract the following. Give your answer in standard form: (6 marks)
a) (4.5 × 10³) + (3 × 10³)
b) (6.2 × 10⁴) − (4.1 × 10³)
c) (5.8 × 10²) + (7.2 × 10¹)

7. A light-year is approximately 9.46 × 10¹² km. The distance to a star is 4.2 light-years. Calculate the distance in km. Give your answer in standard form. (3 marks)

8. A bacteria measures 2.5 × 10⁻⁶ meters in length. If 1000 bacteria are placed end to end, what is the total length? Give your answer in standard form. (3 marks)

Marking Scheme with Detailed Explanations

Section A

1.
a) 7.2 × 10⁴ (2 marks)
b) 4.5 × 10⁻³ (2 marks)
c) 5.3 × 10⁶ (2 marks)

2.
a) 3600 (2 marks)
b) 0.072 (2 marks)
c) 901000 (2 marks)

3.
a) 45 × 10² → 4.5 × 10³ (1 mark)
b) Correct: 0.82 × 10⁴ (1 mark)
c) Correct: 6.3 × 10⁻³ (1 mark)
d) 12 × 10⁵ → 1.2 × 10⁶ (1 mark)

Section B

4.
a) (3 × 10²) × (4 × 10³) = 12 × 10⁵ = 1.2 × 10⁶ (2 marks)
b) (5.5 × 10⁴) × (2 × 10²) = 11 × 10⁶ = 1.1 × 10⁷ (2 marks)

5.
a) (6 × 10⁵) ÷ (2 × 10²) = 3 × 10³ = 3 × 10³ (2 marks)
b) (9.6 × 10⁷) ÷ (3.2 × 10³) = 3 × 10⁴ = 3 × 10⁴ (2 marks)

6.
a) (4.5 + 3) × 10³ = 7.5 × 10³ (2 marks)
b) Convert:
6.2 × 10⁴ = 62 × 10³
62 × 10³ − 4.1 × 10³ = 57.9 × 10³ = 5.79 × 10⁴ (2 marks)
c) Convert:
5.8 × 10² + 0.72 × 10² = 6.52 × 10² = 6.52 × 10² (2 marks)

7.
9.46 × 10¹² × 4.2 = (9.46 × 4.2) × 10¹² = 39.732 × 10¹² = 3.9732 × 10¹³ km (3 marks)

8.
2.5 × 10⁻⁶ × 1000 = 2.5 × 10³ × 10⁻⁶ = 2.5 × 10⁻³ meters (3 marks)