Indices I (Copy)
IGCSE Mathematics Core Practice Exam
Topic: Indices (Positive, Zero, Negative) & Rules of Indices
Total Marks: 40
Time: 40 minutes
(With Detailed Solutions)
Section A: Short Questions (No Calculator)
Total Marks: 20
1. Evaluate the following: (6 marks)
a) 7⁰
b) 4⁻²
c) 3³
d) 2⁻³ × 2⁴
e) 5² ÷ 5⁴
f) (2³)²
2. Simplify the following expressions using index laws: (6 marks)
a) 6⁵ ÷ 6²
b) (3²)³
c) 10⁻¹ × 10³
d) 8² × 8⁰
e) 9⁴ ÷ 9⁴
f) 2⁻²
3. State whether the following statements are True or False: (4 marks)
a) 5⁰ = 0
b) 4³ × 4² = 4⁵
c) 3⁴ ÷ 3² = 3²
d) 2⁻³ = −8
4. Fill in the blanks: (4 marks)
a) (7²)³ = 7^___
b) 5⁶ ÷ 5³ = 5^___
c) 2⁻³ = 1 / ___
d) Any number to the power of 0 = ___
Section B: Structured Questions (Calculator Allowed)
Total Marks: 20
5. Work out the value of the following: (6 marks)
a) (4²)²
b) 3⁵ ÷ 3²
c) 2⁴ × 2⁻¹
6. Simplify fully: (4 marks)
a) (5³)² ÷ 5⁴
b) 10⁰ + 2³
7. A machine reduces a value by applying a power of −2. If the input is 9², calculate the final value: (3 marks)
8. Given that x = 2³ and y = 2⁻², calculate: (4 marks)
a) x × y
b) x ÷ y
9. Simplify and write your answer as a fraction: (3 marks)
5⁻² × 25
Marking Scheme with Detailed Explanations
Section A
1.
a) 7⁰ = 1 (1 mark)
b) 4⁻² = 1 / 4² = 1/16 (1 mark)
c) 3³ = 27 (1 mark)
d) 2⁻³ × 2⁴ = 2¹ = 2 (1 mark)
e) 5² ÷ 5⁴ = 5⁻² = 1/25 (1 mark)
f) (2³)² = 2⁶ = 64 (1 mark)
2.
a) 6⁵ ÷ 6² = 6³ = 216 (1 mark)
b) (3²)³ = 3⁶ = 729 (1 mark)
c) 10⁻¹ × 10³ = 10² = 100 (1 mark)
d) 8² × 8⁰ = 8² = 64 (1 mark)
e) 9⁴ ÷ 9⁴ = 9⁰ = 1 (1 mark)
f) 2⁻² = 1/4 (1 mark)
3.
a) False (5⁰ = 1) (1 mark)
b) True (1 mark)
c) True (1 mark)
d) False (2⁻³ = 1/8) (1 mark)
4.
a) 7²×³ = 7⁶ (1 mark)
b) 5³ (1 mark)
c) 1 / 8 (1 mark)
d) 1 (1 mark)
Section B
5.
a) (4²)² = 4⁴ = 256 (2 marks)
b) 3⁵ ÷ 3² = 3³ = 27 (2 marks)
c) 2⁴ × 2⁻¹ = 2³ = 8 (2 marks)
6.
a) (5³)² ÷ 5⁴ = 5⁶ ÷ 5⁴ = 5² = 25 (2 marks)
b) 10⁰ + 2³ = 1 + 8 = 9 (2 marks)
7.
(9²)⁻² = 9⁻⁴ = 1 / 9⁴ = 1 / 6561 (3 marks)
8.
x = 2³ = 8
y = 2⁻² = 1/4
a) x × y = 8 × 1/4 = 2 (2 marks)
b) x ÷ y = 8 ÷ (1/4) = 8 × 4 = 32 (2 marks)
9.
5⁻² × 25 = (1/25) × 25 = 1 (3 marks)