Chapter 4: Exponents and Powers - Mock Test
Instructions
- •This test covers all topics from Chapter 4: Exponents and Powers
- •Questions are arranged as per CBSE paper pattern
- •Section A: 8 questions × 1 mark = 8 marks
- •Section B: 8 questions × 2 marks = 16 marks
- •Section C: 2 questions × 3 marks = 6 marks
- •No negative marking. Show all steps.
Mock Test Questions
Section A: 1 Mark Questions (8 × 1 = 8 marks)
1. Write 3⁴ in expanded form.
Show Answer
Answer: 3⁴ = 3 × 3 × 3 × 3
2. Identify the base in 7⁵.
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Answer: 7
3. What is 10⁰?
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Answer: 1
4. Simplify: 2² × 2³
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Answer: 2⁵ = 32
5. Evaluate: 5⁻¹
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Answer: 1/5 = 0.2
6. Express 8000 in scientific notation.
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Answer: 8 × 10³
7. Simplify: 6⁴ ÷ 6²
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Answer: 6² = 36
8. Is (-2)³ positive or negative?
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Answer: Negative (-8)
Section B: 2 Mark Questions (8 × 2 = 16 marks)
9. Simplify using laws of exponents: 2³ × 2⁴ ÷ 2⁵
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Answer: 2³ × 2⁴ ÷ 2⁵ = 2⁷⁻⁵ = 2² = 4
10. Evaluate: (2²)³
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Answer: (2²)³ = 2⁶ = 64. Using power rule: (aᵐ)ⁿ = aᵐˣⁿ
11. Simplify: (3 × 4)²
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Answer: (3 × 4)² = 3² × 4² = 9 × 16 = 144
12. Find: 2⁻² + 2⁻¹
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Answer: 1/4 + 1/2 = 1/4 + 2/4 = 3/4
13. Compare: (-3)³ and 3³
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Answer: (-3)³ = -27, 3³ = 27. Odd power reverses sign with negative base.
14. Express 0.00056 in scientific notation.
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Answer: 0.00056 = 5.6 × 10⁻⁴
15. Simplify: (5² × 3²) / (5 × 3)
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Answer: 5¹ × 3¹ = 15
16. Prove that 5⁻² = 1/25 by converting to fraction.
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Answer: 5⁻² = 1/5² = 1/25
Section C: 3 Mark Questions (2 × 3 = 6 marks)
17. Simplify and show steps: (2⁴ × 3²) / (2² × 3) and verify using actual values.
Show Answer
Answer: Using laws: (2⁴ × 3²) / (2² × 3) = 2² × 3¹ = 4 × 3 = 12 Verification: (16 × 9)/(4 × 3) = 144/12 = 12 ✓
18. A bacteria population doubles every hour. If initial count is 100, find the population after 5 hours using exponents.
Show Answer
Answer: Initial population = 100 After 5 hours = 100 × 2⁵ = 100 × 32 = 3200 bacteria
Marking Scheme & Evaluation
Section A (1 Mark)
1 mark for correct answer. No partial marking.
Section B (2 Marks)
- • Correct answer with steps: 2 marks
- • Correct method, minor error: 1 mark
- • Wrong or no working: 0 marks
Section C (3 Marks)
- • Correct with all steps: 3 marks
- • Correct approach with minor errors: 2 marks
- • Partial working (≥50%): 1 mark
- • No attempt: 0 marks
Performance Analysis
27-30 marks: Excellent! Strong grasp of exponents and powers.
22-26 marks: Very Good! Solid understanding of laws and applications.
17-21 marks: Good! Practice more on negative exponents and scientific notation.
12-16 marks: Average. Review laws of exponents and zero/negative exponents.
Below 12 marks: Need improvement. Focus on basics and laws of exponents.
Exam Preparation Tips
- ✓Memorize the four laws of exponents - they are the foundation
- ✓Remember: a⁰ = 1 and a⁻ⁿ = 1/aⁿ are special cases
- ✓In scientific notation, the first number must be between 1 and 10
- ✓Practice converting between scientific and standard notation
- ✓Always show working - partial credit is given for correct method