Chapter 3: Rational Numbers - Mock Test
Instructions
- •This test has 20 questions covering all topics from Chapter 3
- •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: 4 questions × 4 marks = 16 marks
- •No negative marking
- •Show all steps in your calculations
- •Reduce all answers to standard form
Mock Test Questions
Section A: 1 Mark Questions (8 × 1 = 8 marks)
1. Is -3/7 in standard form?
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Answer: Yes. Denominator is positive, GCD(3,7) = 1, so it's in standard form.
2. Reduce 10/15 to standard form.
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Answer: 10/15 = 2/3 (divide by GCD = 5)
3. What is the additive inverse of 3/5?
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Answer: -3/5
4. What is the multiplicative inverse of 2/7?
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Answer: 7/2
5. Compare: 1/2 and 2/5
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Answer: 1/2 > 2/5 (cross-multiply: 1×5=5 > 2×2=4)
6. Which is NOT a rational number: 0, -4, √5, 1/3?
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Answer: √5 (irrational)
7. Simplify: (1/2) + (1/2)
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Answer: 1
8. Simplify: (2/3) × (3/2)
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Answer: 1
Section B: 2 Mark Questions (8 × 2 = 16 marks)
9. Reduce to standard form: -18/24 and 15/-20
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Answer: -18/24 = -3/4 (GCD=6). 15/-20 = -3/4 (GCD=5). Both equal -3/4
10. Simplify: (1/3) + (1/4) - (1/6)
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Answer: LCM(3,4,6)=12. (4/12)+(3/12)-(2/12) = 5/12
11. Find: (5/6) × (3/10)
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Answer: (5/6)×(3/10) = 15/60 = 1/4
12. Evaluate: (2/5) ÷ (1/3)
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Answer: (2/5)÷(1/3) = (2/5)×(3/1) = 6/5
13. Verify: (1/2) × [(1/3)+(1/4)] = (1/2)×(1/3)+(1/2)×(1/4)
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Answer: Left: (1/2)×(7/12)=7/24. Right: (1/6)+(1/8)=7/24 ✓
14. Arrange in ascending order: -1, 0, 1/2, -1/2
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Answer: -1 < -1/2 < 0 < 1/2
15. What is: (3/4) + (-3/4)?
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Answer: 0 (sum of additive inverses)
16. Simplify: (7/8) - (1/4)
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Answer: (7/8)-(2/8) = 5/8
Section C: 4 Mark Questions (4 × 4 = 16 marks)
17. A piece of string is 3/4 meter long. Another piece is 2/5 meter long. What is the total length? Express in standard form.
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Answer: Total = 3/4 + 2/5 LCM(4,5) = 20 = 15/20 + 8/20 = 23/20 meters In standard form: 23/20 (GCD(23,20)=1)
18. Simplify: (3/5) × (5/6) ÷ (1/2). Show all steps.
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Answer: Step 1: (3/5) × (5/6) = 15/30 = 1/2 Step 2: (1/2) ÷ (1/2) = (1/2) × (2/1) = 1
19. A pizza is divided into 8 equal slices. Ravi eats 3/8 and Priya eats 2/8. How much remains? What fraction did they eat together?
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Answer: Ravi ate: 3/8 Priya ate: 2/8 Together: 3/8 + 2/8 = 5/8 Remaining: 1 - 5/8 = 8/8 - 5/8 = 3/8
20. Verify the distributive property: (2/3)×[(1/2)+(1/3)] = (2/3)×(1/2) + (2/3)×(1/3)
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Answer: Left side: (2/3)×[(1/2)+(1/3)] = (2/3)×(3/6+2/6) = (2/3)×(5/6) = 10/18 = 5/9 Right side: (2/3)×(1/2) + (2/3)×(1/3) = 2/6 + 2/9 = 6/18 + 4/18 = 10/18 = 5/9 ✓
Marking Scheme & Evaluation
Section A (1 Mark)
1 mark for correct answer. No partial marking.
Section B (2 Marks)
- • Correct answer in standard form: 2 marks
- • Correct working with calculation error: 1 mark
- • Wrong answer without working: 0 marks
Section C (4 Marks)
- • Correct answer with all steps: 4 marks
- • Correct approach with minor error: 3 marks
- • Partially correct (≥50% work): 2 marks
- • Some relevant working: 1 mark
- • No attempt or completely wrong: 0 marks
Performance Analysis
36-40 marks: Excellent! You have mastered the chapter.
30-35 marks: Very Good! Strong understanding of rational numbers.
24-29 marks: Good! Review operations and comparison methods.
18-23 marks: Average. Focus on standard form and operations.
Below 18 marks: Need improvement. Review fundamentals and practice more.
Exam Preparation Tips
- ✓Always express final answer in standard form (lowest terms)
- ✓For comparison, use cross-multiplication for speed
- ✓In division, multiply by reciprocal (flip divisor)
- ✓Show all working steps for partial credit
- ✓Time management: ~3 min for 1-mark, ~5 min for 2-mark, ~8 min for 4-mark