Case Study WITH SOLUTION VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 10: The Other Side of Zero (Integers)

 

Case Study 1 – Temperature (Daily Weather Report)

The following table shows the recorded temperatures of a city on a particular day:

Time of Day	Temperature (°C)
Morning	–5°C
Noon	0°C
Evening	4°C
Night	–3°C

Answer the questions based on the given data.

Q1. Which time is warmest?
a) Morning b) Noon c) Evening d) Night
✅ Answer: (c) Evening – Highest temperature = 4°C.

Q2. Which time is coldest?
a) Morning b) Night c) Noon d) Evening
✅ Answer: (b) Night – Lowest temperature = –3°C vs –5°C. Correction: Morning is –5°C, which is lower than –3°C. So Answer: (a) Morning.

Q3. Rise in temperature from morning to evening = ?
a) 7°C b) 8°C c) 9°C d) 10°C
✅ Answer: (c) 9°C → 4 – (–5) = 9.

Q4. Fall in temperature from evening to night = ?
a) 6°C b) 7°C c) 8°C d) 9°C
✅ Answer: (a) 7°C → 4 – (–3) = 7.

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Case Study 2 – Bank Transactions (Savings Account)

Ravi has a savings account in a bank. His balance at the beginning of the week was ₹500. During the week, he made the following transactions:

• He withdrew ₹800 on Monday.

• He deposited ₹600 on Wednesday.

• He withdrew ₹400 on Friday.

Answer the following questions based on Ravi’s account transactions.

Q1. Balance after first withdrawal?
a) –300 b) 300 c) –500 d) 200
✅ Answer: (a) –300 → 500 – 800.

Q2. Balance after deposit?
a) 300 b) –200 c) 200 d) –100
✅ Answer: (b) –200 → –300 + 600.

Q3. Balance after last withdrawal?
a) –200 b) –300 c) –400 d) –500
✅ Answer: (b) –300 → –200 – 400.

Q4. Final balance represents:
a) Profit b) Loss c) Debt d) Saving
✅ Answer: (c) Debt – Negative balance.

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Case Study 3 – Lift Movement (Building Elevator)

A lift in a building starts at the ground floor (0). It then moves as follows:

• Goes down 4 floors.

• Goes up 7 floors.

• Finally, goes down 3 floors.

Q1. Position after first move?
a) –4 b) –3 c) 3 d) 4
✅ Answer: (a) –4

Q2. Position after second move?
a) 7 b) 3 c) –3 d) 4
✅ Answer: (b) 3 → –4 + 7.

Q3. Position after third move?
a) –1 b) –2 c) 1 d) 0
✅ Answer: (a) –1 → 3 – 3 = 0 actually, careful. Correction: 3 – 3 = 0, so Answer: (b) 0.

Q4. Final position = ?
a) –1 b) 0 c) 1 d) –2
✅ Answer: (b) 0

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Case Study 4 – Cricket Scores (Performance Analysis)

In four cricket matches, Virat scored the following runs:

• Match 1 = +50

• Match 2 = –10 (runs deducted as penalty)

• Match 3 = +70

• Match 4 = –20 (runs deducted as penalty)

Q1. Highest score = ?
a) 50 b) 70 c) –10 d) –20
✅ Answer: (b) 70

Q2. Lowest score = ?
a) –20 b) –10 c) 50 d) 70
✅ Answer: (a) –20

Q3. Total runs in 4 matches = ?
a) 80 b) 90 c) 100 d) 110
✅ Answer: (b) 90 → 50 –10 +70 –20 = 90.

Q4. Negative score represents:
a) Runs scored b) Bonus c) Penalty d) Extras
✅ Answer: (c) Penalty

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Case Study 5 – Sea Level (Submarine Journey)

A submarine starts at a depth of –200 m below sea level. It then:

• Descends further by 300 m.

• Later ascends by 600 m.

Q1. Position after descent = ?
a) –100 b) –300 c) –400 d) –500
✅ Answer: (c) –500 → –200 – 300.

Q2. Position after ascent = ?
a) 200 b) 300 c) 400 d) –200
✅ Answer: (a) 100 → –500 + 600. Correction: –500 + 600 = +100, so Answer: (a) 100.

Q3. Final position above/below sea level = ?
a) 100 above b) 200 above c) 300 above d) 400 above
✅ Answer: (a) 100 above

Q4. Which operation used to combine descent and ascent?
a) Addition b) Subtraction c) Multiplication d) Division
✅ Answer: (a) Addition – Adding integers.

ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 10: The Other Side of Zero (Integers)

ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 10: The Other Side of Zero (Integers)

 

Answer Key – Chapter 10: The Other Side of Zero (Integers)

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1. Multiple Choice Questions (20)

1. (b) –3 → integers are whole numbers + negatives.

2. (a) 7 → opposite of –7 is +7.

3. (b) –3 → lies between –4 and –2.

4. (a) –5 → closer to 0 is greater.

5. (a) –5 → 5 steps left = –5.

6. (a) –9 → –3 + –6.

7. (b) –3 → –7 + 4 = –3.

8. (c) 0 → 0 is its own opposite.

9. (b) –7 → 5 – 12.

10. (b) –3 > –4.

11. (b) 0 → neutral integer.

12. (a) –3 → –10 + 7.

13. (b) –5 → negative means loss.

14. (a) –12 → farthest left.

15. (c) 3 → –3 – (–6) = –3+6=3.

16. (a) –12 → opposite of 12.

17. (a) –8 → smaller is farther left.

18. (a) –20 → –15 + –5.

19. (a) 2 → –5 + 7.

20. (c) 0 → additive inverse property.

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2. Assertion–Reasoning (20)

1. (c) A true, R false.

2. (a) Both true, R explains A.

3. (a) Both true, R explains A.

4. (a) Both true, R explains A.

5. (a) Both true, R explains A.

6. (c) A false, R true.

7. (c) A true, R false.

8. (a) Both true, R explains A.

9. (a) Both true, R explains A.

10. (c) A true, R false.

11. (a) Both true, R explains A.

12. (b) Both true, R doesn’t explain A.

13. (a) Both true, R explains A.

14. (a) Both true, R explains A.

15. (a) Both true, R explains A.

16. (a) Both true, R explains A.

17. (a) Both true, R explains A.

18. (c) A true, R false.

19. (a) Both true, R explains A.

20. (a) Both true, R explains A.

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3. True or False (10)

1. False (–3 < –2).

2. True.

3. False (–10 < –15 is wrong; actually –10 > –15).

4. True.

5. False (–7+7=0).

6. False (right = increase).

7. True.

8. True.

9. False (no smallest integer).

10. True.

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4. Short Answer I (15)

1. Integers = {..., –3, –2, –1, 0, 1, 2...}.

2. Opposites: +8 → –8, –15 → 15, 0 → 0.

3. On number line: –5 left, +7 right of 0.

4. –7 > –12.

5. –6 + 10 = 4.

6. 7 – 15 = –8.

7. –10 – (–4) = –10 + 4 = –6.

8. –3 + –8 = –11.

9. Additive inverse of –25 = 25.

10. –4+6 = 2°C.

11. –800+200 = –600 m.

12. –100 > –150.

13. –8, –2, –1, 0, 5.

14. Examples: temperatures below 0, debts.

15. –20+15 = –5.

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5. Short Answer II (10)

1. –3, –1 left of 0; 2, 4 right.

2. –12+–8+15 = –20+15 = –5.

3. 25–(–10)=35.

4. –5–12=–17.

5. –20–10=–30, then –30+15=–15.

6. –10, –5, 0, 7, 12.

7. –8+–7=–15, –15–(–4)=–15+4=–11.

8. –15–(–5)=–10, then –10+–10=–20.

9. 10–15=–5.

10. Subtracting negative = adding positive. Eg: 3–(–2)=5.

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6. Long Answer (10)

1. (–3)+(–4)=–7 on number line.

2. 6–(–3)=9.

3. –500–300=–800, then –800+700=–100.

4. –8→6, rise = 14°C.

5. –2000+1500=–500 balance.

6. –10+–15=–25, +20=–5, –(–5)=+5, total=0.

7. –25–(–15)=–10, +–10=–20.

8. –20, –15, –5, 0, 8, 10.

9. Rules: same sign → add mags, keep sign; different → subtract mags, take bigger sign.

10. Eg: temperature –5°C, money debts.

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7. Case-Based (5 sets × 4 MCQs)

Case 1 (Temp)
1(c) Evening, 2(b) Night, 3(c) 9°C, 4(a) 7°C.

Case 2 (Bank)
1(a) –300, 2(b) –200, 3(b) –300, 4(c) Debt.

Case 3 (Lift)
1(a) –4, 2(b) 3, 3(a) –1, 4(a) –1.

Case 4 (Cricket)
1(b) 70, 2(a) –20, 3(a) 90, 4(c) Penalty.

Case 5 (Sea Level)
1(c) –500, 2(b) 100, 3(a) 100 above, 4(a) Addition.

Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 10: The Other Side of Zero (Integers)

 

Class 6 – Mathematics (Ganita Prakash)

Chapter 10: The Other Side of Zero (Integers)

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Chapter Subsections Covered

• Understanding Negative Numbers

• Introduction to Integers (positive & negative)

• Representation of Integers on Number Line

• Ordering & Comparison of Integers

• Addition and Subtraction of Integers on Number Line

• Word Problems with Integers

• Real-life Applications (temperature, debts, gains, heights, etc.)

[Insert Image: Number Line with integers – Page 212]
[Insert Image: Integer representation examples – Page 215]
[Insert Image: Addition of integers on number line – Page 220]
[Insert Image: Subtraction of integers on number line – Page 223]

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1. Multiple Choice Questions (20)

Q1. Which of the following is an integer?
a) 2.5 b) –3 c) ½ d) √2
(Competency: Identifying integers)

Q2. The opposite of –7 is:
a) 7 b) –7 c) 0 d) –1
(Competency: Understanding opposites)

Q3. Which integer lies between –4 and –2?
a) –5 b) –3 c) –1 d) 0
(Competency: Ordering integers)

Q4. Which of these is greater?
a) –5 b) –8 c) –10 d) –12
(Competency: Comparing integers)

Q5. On a number line, moving 5 steps left from 0 gives:
a) –5 b) 5 c) –10 d) 10
(Competency: Number line movement)

Q6. The sum of (–3) and (–6) is:
a) –9 b) –3 c) 3 d) 9
(Competency: Addition of integers)

Q7. The sum of (–7) + 4 = ?
a) –11 b) –3 c) 3 d) 11
(Competency: Addition using number line)

Q8. Which integer has no opposite?
a) 1 b) –1 c) 0 d) 2
(Competency: Properties of integers)

Q9. The difference (5 – 12) = ?
a) 7 b) –7 c) 17 d) –17
(Competency: Subtraction of integers)

Q10. Which of the following is true?
a) –4 > –3 b) –3 > –4 c) –3 = –4 d) –4 = –2
(Competency: Comparing integers)

Q11. Which integer is neither positive nor negative?
a) –1 b) 0 c) 1 d) 2
(Competency: Zero as neutral integer)

Q12. Add: –10 + 7 = ?
a) –3 b) 3 c) –17 d) 17
(Competency: Integer addition)

Q13. Which of the following represents a loss of ₹5?
a) +5 b) –5 c) 0 d) 10
(Competency: Integers in daily life)

Q14. Which point is farthest to the left on a number line?
a) –12 b) –5 c) 0 d) 6
(Competency: Position on number line)

Q15. Subtract: (–3) – (–6) = ?
a) –9 b) 9 c) 3 d) –3
(Competency: Integer subtraction)

Q16. The opposite of +12 is:
a) –12 b) 0 c) 12 d) –1
(Competency: Opposite numbers)

Q17. Which integer is smaller? –8 or –2?
a) –8 b) –2 c) Both equal d) 0
(Competency: Comparing negative integers)

Q18. Add: (–15) + (–5) = ?
a) –20 b) –10 c) 20 d) 10
(Competency: Addition of negatives)

Q19. Which integer is 7 units to the right of –5?
a) 2 b) –2 c) –12 d) 12
(Competency: Using number line shifts)

Q20. The result of (–25) + (25) = ?
a) –50 b) 50 c) 0 d) 1
(Competency: Additive inverse property)

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2. Assertion–Reasoning (20)

Q1. A: Every whole number is an integer.
R: Every integer is a whole number.
(a) Both true, R explains A (b) Both true, R doesn’t explain A
(c) A true, R false (d) A false, R true
(Competency: Difference between integers & whole numbers)

Q2. A: Negative numbers are less than zero.
R: On a number line, negative numbers lie to the left of 0.
(Competency: Understanding negative integers)

Q3. A: Zero is an integer.
R: Zero has no opposite.
(Competency: Properties of zero)

Q4. A: –5 is greater than –8.
R: On a number line, greater numbers lie to the right.
(Competency: Ordering integers)

Q5. A: The opposite of (–a) is a.
R: Every integer has a unique opposite.
(Competency: Opposites of integers)

Q6. A: Addition of two negative integers gives a positive integer.
R: (–3) + (–5) = –8.
(Competency: Misconceptions in integer addition)

Q7. A: (–6) – (–2) = –4.
R: Subtraction of integers can be done by adding the opposite.
(Competency: Subtraction rule)

Q8. A: (–7) + 7 = 0.
R: Integers have additive inverses.
(Competency: Additive inverse property)

Q9. A: (–10) is smaller than (–8).
R: The farther left on the number line, the smaller the integer.
(Competency: Number line comparison)

Q10. A: Integers extend infinitely on both sides of zero.
R: There is a largest positive integer.
(Competency: Infinity concept with integers)

Q11. A: Subtracting a negative number increases the value.
R: –5 – (–3) = –2.
(Competency: Integer subtraction rule)

Q12. A: Zero is neither positive nor negative.
R: Zero is the smallest integer.
(Competency: Properties of zero)

Q13. A: (–3) + (–7) = –10.
R: When signs are the same, add magnitudes and keep sign.
(Competency: Addition rule)

Q14. A: (–15) – (+10) = –25.
R: Subtracting positive is same as moving left.
(Competency: Subtraction with positives)

Q15. A: The integer opposite to +1 is –1.
R: Opposites are equidistant from zero.
(Competency: Symmetry on number line)

Q16. A: The opposite of 0 is 0.
R: 0 is its own opposite.
(Competency: Unique property of zero)

Q17. A: Adding (–3) to a positive integer decreases its value.
R: –3 is smaller than 0.
(Competency: Effect of negatives)

Q18. A: Integers can be represented on a number line.
R: Integers cannot be shown in tabular form.
(Competency: Representations of integers)

Q19. A: 2 – (–4) = 6.
R: Subtracting a negative is equivalent to adding positive.
(Competency: Integer subtraction)

Q20. A: On a cold day, the temperature rose from –5°C to –2°C. It increased.
R: On a number line, moving right means increase.
(Competency: Real-life interpretation of integers)

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3. True or False (10)

1. –3 is greater than –2. (False)

2. Zero has no sign. (True)

3. –10 < –15. (False)

4. Opposite of –12 is 12. (True)

5. Sum of –7 and 7 is –14. (False)

6. On a number line, right movement means decreasing. (False)

7. Integers include positive, negative, and zero. (True)

8. (–8) + (–2) = –10. (True)

9. The smallest integer exists. (False)

10. Subtraction of integers can be replaced with addition of opposite. (True)

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4. Short Answer I – 2 Marks (15)

1. Define integers with examples.

2. Write opposite of: +8, –15, 0.

3. Represent –5 and +7 on a number line.

4. Which is greater: –12 or –7?

5. Add: –6 + 10.

6. Subtract: 7 – 15.

7. Subtract: –10 – (–4).

8. Find: –3 + (–8).

9. What is the additive inverse of –25?

10. Temperature was –4°C in the morning, rose by 6°C. Find new temperature.

11. A submarine is at –800 m, rises 200 m. Find new depth.

12. Compare –100 and –150.

13. Arrange in ascending order: –2, –8, 5, 0, –1.

14. Write two real-life examples where negative numbers are used.

15. Add: (–20) + 15.

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5. Short Answer II – 3 Marks (10)

1. Represent integers –3, –1, 2, 4 on a number line.

2. Add: (–12) + (–8) + 15.

3. Find: 25 – (–10).

4. Subtract: (–5) – 12.

5. A diver is at –20 m depth. He goes down 10 m, then rises 15 m. Find final position.

6. Arrange: –5, 7, –10, 12, 0 in ascending order.

7. Evaluate: (–8) + (–7) – (–4).

8. Simplify: [–15 – (–5)] + (–10).

9. A temperature was 10°C at noon. At night it fell by 15°C. Find new temperature.

10. Explain with example the rule: Subtracting a negative integer means adding a positive.

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6. Long Answer – 5 Marks (10)

1. Draw a number line from –10 to +10. Show addition: (–3) + (–4).

2. Draw a number line and show subtraction: 6 – (–3).

3. A submarine is at –500 m. It descends 300 m, then ascends 700 m. Find final position.

4. The temperature at 6 am was –8°C, at 3 pm it was 6°C. Find change in temperature.

5. A bank account has overdraft of ₹2000 (–2000). Deposit of ₹1500 is made. Find balance.

6. Simplify: (–10) + (–15) + 20 – (–5).

7. Solve: [–25 – (–15)] + (–10).

8. Arrange in ascending order: –15, –20, 10, –5, 0, 8.

9. Write rules of addition and subtraction of integers with examples.

10. Explain two real-life situations involving integers (temperature, money, height).

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7. Case-Based Questions (5 × 4 MCQs)

Case Study 1 – Temperature (Daily Weather Report)

The following table shows the recorded temperatures of a city on a particular day:

Time of Day	Temperature (°C)
Morning	–5°C
Noon	0°C
Evening	4°C
Night	–3°C

Answer the questions based on the given data.

(Then Q1–Q4 as you wrote.)

Morning: –5°C, Noon: 0°C, Evening: 4°C, Night: –3°C.
Q1. Which time is warmest?
a) Morning b) Noon c) Evening d) Night
Q2. Which time is coldest?
a) Morning b) Night c) Noon d) Evening
Q3. Rise in temperature from morning to evening = ?
a) 7°C b) 8°C c) 9°C d) 10°C
Q4. Fall in temperature from evening to night = ?
a) 6°C b) 7°C c) 8°C d) 9°C

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Case Study 2 – Bank Transactions (Savings Account)

Ravi has a savings account in a bank. His balance at the beginning of the week was ₹500. During the week, he made the following transactions:

• He withdrew ₹800 on Monday.

• He deposited ₹600 on Wednesday.

• He withdrew ₹400 on Friday.

Answer the following questions based on Ravi’s account transactions.

Balance = ₹500. Withdraw ₹800, Deposit ₹600, Withdraw ₹400.
Q1. Balance after first withdrawal?
a) –300 b) 300 c) –500 d) 200
Q2. Balance after deposit?
a) 300 b) –200 c) 200 d) –100
Q3. Balance after last withdrawal?
a) –200 b) –300 c) –400 d) –500
Q4. Final balance represents:
a) Profit b) Loss c) Debt d) Saving

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Case Study 3 – Lift Movement (Building Elevator)

A lift in a building starts at the ground floor (0). It then moves as follows:

• Goes down 4 floors.

• Goes up 7 floors.

• Finally, goes down 3 floors.

Answer the following questions based on the lift’s movement.

(Then Q1–Q4.)

A lift is at ground floor (0). Goes down 4 floors, up 7 floors, down 3 floors.
Q1. Position after first move?
a) –4 b) –3 c) 3 d) 4
Q2. Position after second move?
a) 7 b) 3 c) –3 d) 4
Q3. Position after third move?
a) –1 b) –2 c) 1 d) 0
Q4. Final position = ?
a) –1 b) 0 c) 1 d) –2

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Case Study 4 – Cricket Scores (Performance Analysis)

In four cricket matches, Virat scored the following runs:

• Match 1 = +50

• Match 2 = –10 (runs deducted as penalty)

• Match 3 = +70

• Match 4 = –20 (runs deducted as penalty)

Answer the following questions based on his performance.

(Then Q1–Q4.)

Virat scored: Match 1 = +50, Match 2 = –10, Match 3 = +70, Match 4 = –20.
Q1. Highest score = ?
a) 50 b) 70 c) –10 d) –20
Q2. Lowest score = ?
a) –20 b) –10 c) 50 d) 70
Q3. Total runs in 4 matches = ?
a) 80 b) 90 c) 100 d) 110
Q4. Negative score represents:
a) Runs scored b) Bonus c) Penalty d) Extras

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Case Study 5 – Sea Level (Submarine Journey)

A submarine starts at a depth of –200 m below sea level. It then:

• Descends further by 300 m.

• Later ascends by 600 m.

Answer the following questions based on the submarine’s movement.

(Then Q1–Q4.)

Submarine at –200 m, descends 300 m, ascends 600 m.
Q1. Position after descent = ?
a) –100 b) –300 c) –400 d) –500
Q2. Position after ascent = ?
a) 200 b) 300 c) 400 d) –200
Q3. Final position above/below sea level = ?
a) 100 above b) 200 above c) 300 above d) 400 above
Q4. Which operation used to combine descent and ascent?
a) Addition b) Subtraction c) Multiplication d) Division

Q & ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 4: Data Handling and Presentation.

 Q&ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics  Chapter 4: Data Handling and Presentation.

Class 6 Mathematics – Ganita Prakash

Chapter 4: Data Handling and Presentation

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Chapter Subsections Covered

• 4.1 Introduction to Data

• 4.2 Collecting and Organizing Data

• 4.3 Pictographs

• 4.4 Bar Graphs

• 4.5 Line Graphs

• 4.6 Circle Graphs (Pie Charts – Introductory)

• 4.7 Central Tendencies – Mean, Median, Mode

• 4.8 Application of Data Handling in Daily Life

[Insert Image: Data table of students absent – Page 75]
[Insert Image: Pictograph of favourite fruits – Page 77]
[Insert Image: Bar graph of favourite games – Page 81]
[Insert Image: Line graph showing daily temperatures – Page 86]
[Insert Image: Pie chart showing daily routine – Page 92]
[Insert Image: Frequency table of marks of students – Page 98]

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1. Multiple Choice Questions (20)

Q1. Which of the following is not a form of data representation?
a) Bar graph b) Line graph c) Pictograph d) Cube root table
(Competency: Understanding types of data representation)

(d) Cube root table – not a data representation.

Q2. In a pictograph, 🍎 represents 10 apples. If 5 symbols are shown, how many apples are there?
a) 15 b) 25 c) 50 d) 100
(Competency: Interpreting pictographs)

(c) 5 × 10 = 50.

Q3. A bar graph uses:
a) Circles b) Triangles c) Rectangular bars d) Arrows
(Competency: Basics of bar graphs)

(c) Rectangular bars are used.

Q4. The average of 5 numbers is 20. What is their total?
a) 20 b) 25 c) 50 d) 100
(Competency: Calculating mean) 

(d) 20 × 5 = 100.

Q5. In a line graph, the horizontal axis usually represents:
a) Categories b) Time c) Temperature d) None of these
(Competency: Understanding line graphs)

(b) Time is on the x-axis.

Q6. The total angle of a pie chart is:
a) 90° b) 180° c) 270° d) 360°
(Competency: Basics of pie chart)

(d) 360°.

Q7. The mode of data is:
a) Middle value b) Average value c) Most frequent value d) Largest value
(Competency: Concept of mode)

(c) Most frequent value.

Q8. The range of the data 5, 10, 15, 20 is:
a) 5 b) 10 c) 15 d) 20
(Competency: Understanding range)

(c) 20 – 5 = 15.
Q9. In a pictograph, if 🍊 = 2 oranges, and 8 symbols are drawn, how many oranges are there?

a) 8 b) 10 c) 12 d) 16
(Competency: Pictograph calculations)

(d) 2 × 8 = 16.

Q10. A survey shows 10 students like cricket, 5 football, 15 hockey. Which graph best represents this?
a) Bar graph b) Line graph c) Pie chart d) All of these
(Competency: Choosing correct data representation)

(a) Bar graph best shows categories.

Q11. The median of 7, 8, 9, 10, 11 is:
a) 7 b) 9 c) 10 d) 11
(Competency: Finding median)

(b) 9 is the middle value.

Q12. The mean of first 5 natural numbers is:
a) 2 b) 3 c) 4 d) 5
(Competency: Mean calculation)

(b) (1+2+3+4+5)/5 = 3.

Q13. Which of these is qualitative data?
a) Height b) Weight c) Colour of eyes d) Marks
(Competency: Types of data)

(c) Colour of eyes is qualitative.

Q14. Which central tendency is most affected by extreme values?
a) Mean b) Median c) Mode d) None
(Competency: Understanding mean, median, mode)

(a) Mean is affected by extremes.

Q15. If 40% of a circle graph is shaded, what angle is it?
a) 72° b) 120° c) 144° d) 160°
(Competency: Converting percentage to angle in pie chart)

(c) 40% of 360° = 144°.

Q16. A frequency table shows maximum marks of 40 students. The highest frequency means:
a) Most common score b) Highest score c) Lowest score d) Average score
(Competency: Reading frequency table)

(a) Highest frequency = most common score.

Q17. Which graph is most suitable for time vs temperature data?
a) Bar graph b) Line graph c) Pie chart d) Pictograph
(Competency: Choosing suitable graph)

(b) Line graph shows continuous change.

Q18. A pie chart shows 90° for books. What fraction of total money is for books?
a) ¼ b) ⅓ c) ½ d) ⅙
(Competency: Fractions in pie charts)

(a) 90°/360° = ¼.

Q19. Which measure of central tendency is obtained by dividing sum of observations by number of observations?
a) Mean b) Median c) Mode d) Range
(Competency: Definition of mean)

(a) Mean = sum ÷ number.

Q20. In a survey, 30 liked tea, 20 coffee, 10 milk. What is the mode?
a) Tea b) Coffee c) Milk d) None
(Competency: Mode identification) 

(a) Tea (highest frequency)

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2. Assertion and Reasoning (20 Qs)

Each question has two statements:

• Assertion (A)

• Reason (R)
  Choose the correct option:
  a) A and R both true, R explains A
  b) A and R both true, but R does not explain A
  c) A true, R false
  d) A false, R true

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Q1.
A: Data is a collection of facts.
R: Data cannot be represented using tables.
(Competency: Basic understanding of data)

Q2.
A: Pictographs use pictures or symbols to represent data.
R: Pictographs are never used in primary classes.
(Competency: Understanding pictographs)

Q3.
A: A bar graph can be either horizontal or vertical.
R: Bars must always be equal in width.
(Competency: Features of bar graph)

Q4.
A: A line graph is useful to show change over time.
R: A line graph uses pictures instead of lines.
(Competency: Features of line graphs)

Q5.
A: In a pie chart, the sum of all angles is 360°.
R: A circle has 360°.
(Competency: Geometry connection with pie chart)

Q6.
A: Mean is the middle value of a dataset.
R: Median is calculated as sum ÷ number of items.
(Competency: Differentiating mean and median)

Q7.
A: The mode of data is the most frequent observation.
R: Mode is always greater than median.
(Competency: Understanding mode)

Q8.
A: The range of a dataset is the difference between highest and lowest values.
R: Range measures how spread out the data is.
(Competency: Concept of range)

Q9.
A: Bar graphs are better than pictographs for larger data.
R: Bar graphs can represent bigger numbers more clearly.
(Competency: Choosing data representation)

Q10.
A: A survey is a method of collecting information.
R: Asking students about their favourite colour is a survey.
(Competency: Data collection methods)

Q11.
A: Pie charts are always drawn using compasses and protractors.
R: Each slice represents a fraction of the whole.
(Competency: Understanding circle graphs)

Q12.
A: The mean is affected by extreme values.
R: Adding a very high number increases the mean.
(Competency: Mean sensitivity to data)

Q13.
A: The median divides the data into two equal halves.
R: Median is always the largest value.
(Competency: Median concept)

Q14.
A: In a frequency table, the highest frequency tells us the mode.
R: Mode is the observation with highest frequency.
(Competency: Using frequency tables)

Q15.
A: A line graph always shows continuous data.
R: Temperature change is best shown by a line graph.
(Competency: Application of line graphs)

Q16.
A: Pie charts cannot be used to show percentages.
R: A pie chart can only show fractions.
(Competency: Misconceptions about pie charts)

Q17.
A: Primary data is collected first-hand.
R: Secondary data is collected by someone else.
(Competency: Types of data)

Q18.
A: Bar graphs are unsuitable for showing monthly rainfall.
R: Line graphs better represent rainfall over time.
(Competency: Choosing suitable graphs)

Q19.
A: Data handling is useful in real life.
R: We can use it to analyze cricket scores, rainfall, population, etc.
(Competency: Application of data handling)

Q20.
A: All three measures of central tendency (mean, median, mode) are always equal.
R: In every dataset, mean = median = mode.

(Competency: Misconceptions in statistics)

2. Assertion–Reasoning (20)

1. (c) A true, R false.

2. (c) A true, R false.

3. (a) Both true, R explains A.

4. (c) A true, R false.

5. (a) Both true, R explains A.

6. (c) A true, R false (definitions mixed up).

7. (c) A true, R false.

8. (a) Both true, R explains A.

9. (a) Both true, R explains A.

10. (a) Both true, R explains A.

11. (b) Both true, but R doesn’t explain A.

12. (a) Both true, R explains A.

13. (c) A true, R false.

14. (a) Both true, R explains A.

15. (a) Both true, R explains A.

16. (d) A false, R true.

17. (a) Both true, R explains A.

18. (a) Both true, R explains A.

19. (a) Both true, R explains A.

20. (c) A true, R false.

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3. True or False (10 Qs)

Q1. A pictograph uses symbols to represent data.
(True)
(Competency: Basics of pictographs)

Q2. In a bar graph, the width of bars may be different.
(False – all bars must have equal width)
(Competency: Features of bar graphs)

Q3. A line graph is used to show changes over time.
(True)
(Competency: Application of line graph)

Q4. The total angle at the centre of a pie chart is 180°.
(False – it is 360°)
(Competency: Geometry connection with circle graphs)

Q5. The mean of 5 and 15 is 10.
(True)
(Competency: Calculation of mean)

Q6. The median is the most frequently occurring value.
(False – that is mode, median is the middle value)
(Competency: Differentiating measures of central tendency)

Q7. Mode can be found from a frequency table.
(True)
(Competency: Using frequency tables)

Q8. The range of data is maximum value minus minimum value.
(True)
(Competency: Concept of range)

Q9. Surveys are not part of data collection.
(False – surveys are one of the main methods)
(Competency: Data collection methods)

Q10. All three – mean, median, and mode – are always the same for every dataset.
(False – they may differ)

(Competency: Clarifying misconceptions)

3. True or False (10)

1. True

2. False (bars equal width)

3. True

4. False (360° not 180°)

5. True

6. False (median is middle, not frequent)

7. True

8. True

9. False (surveys are data collection)

10. False (mean, median, mode can differ)

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4. Short Answer I – 2 Marks (15 Qs)

Q1. Define data with an example from your daily life.
(Competency: Understanding data concept)

Q2. Write the difference between primary data and secondary data with examples.
(Competency: Types of data)

Q3. A pictograph shows 🍎 = 10 apples. If 4 symbols are shown, how many apples are there?
(Competency: Pictograph interpretation)

Q4. In a survey, 15 students like cricket, 10 football, 5 tennis. Represent this in tabular form.
(Competency: Data organization in tables)

Q5. Define “range” of a dataset. Find the range of 12, 18, 25, 30.
(Competency: Range calculation)

Q6. Find the mean of 6, 7, 8, 9, 10.
(Competency: Mean calculation)

Q7. Write two advantages of bar graphs over pictographs.
(Competency: Data representation comparison)

Q8. Find the median of 5, 8, 12.
(Competency: Median calculation)

Q9. If in a pie chart, “games” = 90°, find the fraction of circle it represents.
(Competency: Pie chart fractions)

Q10. A frequency table shows 5 students scored 10 marks, 10 students scored 20 marks. Which score is more common?
(Competency: Frequency table interpretation)

Q11. A line graph shows temperature on Monday = 25°C, Tuesday = 30°C. Find the increase.
(Competency: Reading line graph)

Q12. Which type of graph is most suitable for showing favourite subjects of students? Why?
(Competency: Choosing data representation)

Q13. In a pictograph, 🍊 = 2 oranges. 12 symbols are shown. How many oranges are there?
(Competency: Pictograph calculations)

Q14. A pie chart shows “food” = 120°. What percentage is spent on food?
(Competency: Pie chart conversion to percentage)

Q15. Explain why surveys are important in data handling.

(Competency: Application of surveys)

4. Short Answer I (15)

1. Data = collection of facts, e.g., daily temperatures.

2. Primary = collected first-hand; Secondary = taken from books/newspapers.

3. 4 × 10 = 40 apples.

4. Table form with Cricket =15, Football=10, Tennis=5.

5. Range = 30 – 12 = 18.

6. (6+7+8+9+10)/5 = 40/5 = 8.

7. Bar graphs handle large data; pictographs less precise.

8. Middle = 8.

9. 90°/360° = ¼.

10. More common = 20 marks (10 students).

11. 30 – 25 = 5°C.

12. Bar graph (categorical data).

13. 12 × 2 = 24 oranges.

14. 120°/360° = ⅓ = 33.3%.

15. Surveys help collect opinions systematically.

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5. Short Answer II – 3 Marks (10 Qs)

Q1. The marks obtained by 10 students are: 5, 7, 8, 9, 10, 6, 7, 8, 9, 10.
(i) Prepare a frequency table.
(ii) Find the mode.
(Competency: Organizing data & finding mode)

Q2. Draw a bar graph to show the number of absentees in a week:
Mon – 2, Tue – 5, Wed – 4, Thu – 3, Fri – 6.
(Competency: Drawing bar graphs)

Q3. In a survey, students like:
Cricket – 20, Football – 15, Hockey – 5.
Represent this by a pictograph (use ⚽ = 5 students).
(Competency: Pictograph representation)

Q4. Calculate the mean of: 8, 12, 10, 6, 14.
(Competency: Mean calculation)

Q5. The daily maximum temperature of a city in a week is given:
Mon – 30°C, Tue – 32°C, Wed – 31°C, Thu – 29°C, Fri – 28°C, Sat – 33°C, Sun – 34°C.
Draw a line graph.
(Competency: Drawing line graph)

Q6. The daily expenses of a family are: Food – ₹200, Rent – ₹300, Education – ₹100, Other – ₹100.
Represent this in a pie chart.
(Competency: Pie chart construction)

Q7. Find the range and median of the following data: 12, 15, 18, 22, 20.
(Competency: Range & median)

Q8. A bar graph shows: Hindi – 40, English – 35, Maths – 45, Science – 50.
Which subject is most popular? Which is least popular?
(Competency: Bar graph interpretation)

Q9. The ages of 7 students are: 12, 13, 11, 12, 14, 12, 13. Find the mode.
(Competency: Mode calculation)

Q10. Explain with an example how data handling is used in weather forecasting.

(Competency: Real-life application of data handling)

5. Short Answer II (10)

1. Frequency table: Mode = 7, 8, 9, 10 (tie); most frequent values.

2. Bar graph plotted with absentees data.

3. Pictograph with ⚽ symbols.

4. Mean = (8+12+10+6+14)/5 = 50/5 = 10.

5. Line graph shows temps day-wise.

6. Pie chart: Total = 700. Food = 200/700×360 = 103°, Rent = 154°, Education = 51°, Other = 51°.

7. Range = 22 – 12 = 10; Median = 18.

8. Most popular = Science (50), least = English (35).

9. Mode = 12 (appears 3 times).

10. Weather data shown via line graphs/bar graphs.

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6. Long Answer Questions – 5 Marks (10 Qs)

Q1. The marks obtained by 20 students in a test are:
15, 18, 20, 15, 10, 12, 18, 20, 25, 30, 18, 20, 22, 25, 28, 30, 20, 25, 22, 30.
(i) Prepare a frequency table.
(ii) Find the mean, median, and mode.
(Competency: Central tendencies & frequency table)

Q2. The number of different coloured cars in a parking lot are:
Red – 30, Blue – 20, White – 25, Black – 15, Others – 10.
Draw a pie chart for this data.
(Competency: Pie chart construction)

Q3. The population of a town in 5 years was recorded:
2015 – 20,000; 2016 – 22,000; 2017 – 24,500; 2018 – 27,000; 2019 – 30,000.
Draw a line graph showing this growth.
(Competency: Interpreting growth with line graphs)

Q4. The daily wages of 50 workers are given below:

| Wages (₹) | 100 | 120 | 140 | 160 | 180 |
|-----------|-----|-----|-----|-----|
| Workers | 5 | 10 | 15 | 12 | 8 |

(i) Draw a bar graph of the data.
(ii) Find the mode wages.
(Competency: Bar graph + mode from frequency table)

Q5. The expenditure of a family in a month is:
Rent – ₹8000, Food – ₹6000, Education – ₹4000, Savings – ₹2000.
Draw a circle graph (pie chart) for this.
(Competency: Pie chart conversion & interpretation)

Q6. A survey of 100 students showed:
Cricket – 40, Football – 25, Basketball – 20, Badminton – 15.
Represent the data by:
(i) A bar graph
(ii) A pie chart
(Competency: Comparative use of bar graph & pie chart)

Q7. The maximum temperatures of a city during a week are:
Mon – 32°C, Tue – 34°C, Wed – 31°C, Thu – 29°C, Fri – 30°C, Sat – 33°C, Sun – 35°C.
(i) Draw a line graph.
(ii) State on which day temperature was highest & lowest.
(Competency: Line graph drawing & interpretation)

Q8. 25 students were asked how many hours they study daily. Their responses are:
2, 3, 2, 4, 5, 3, 2, 4, 2, 3, 5, 4, 3, 2, 4, 5, 3, 2, 3, 4, 5, 3, 2, 4, 3.
(i) Prepare a frequency table.
(ii) Find the mean study hours.
(Competency: Frequency table & mean)

Q9. The marks obtained by 15 students in Mathematics are:
12, 18, 20, 15, 25, 22, 20, 18, 30, 25, 15, 20, 18, 30, 22.
(i) Arrange the data.
(ii) Find the median & mode.
(Competency: Organizing data + central tendencies)

Q10. Explain in detail with examples the difference between:
(i) Primary and secondary data
(ii) Pictograph, bar graph, and line graph

(Competency: Conceptual clarity & comparisons)

6. Long Answer (10)

1. Frequency table; Mean ≈ 21.2, Median = 20, Mode = 20.

2. Pie chart: Total=100 cars, Red=108°, Blue=72°, White=90°, Black=54°, Others=36°.

3. Line graph showing steady population growth.

4. Bar graph; Mode wages = 140 (highest frequency = 15).

5. Pie chart: Total=20000. Rent=144°, Food=108°, Education=72°, Savings=36°.

6. Cricket=144°, Football=90°, Basketball=72°, Badminton=54°.

7. Highest=Sun (35°C), Lowest=Thu (29°C).

8. Frequency table: Mean ≈ 3.2 hrs.

9. Median=20, Mode=18 & 20 (both frequent).

10. Primary=first-hand; Secondary=already collected. Pictograph=symbols, Bar graph=bars, Line graph=trend.

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7. Case-Based Questions (CBQs)

(Each case study followed by 4 MCQs)

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Case Study 1 – Pictograph (Fruits)

The pictograph below shows the number of fruits sold by a shop in one day.

[Insert Image: Pictograph of fruits – Page 77]
🍎 = 10 fruits

• Apples 🍎🍎🍎🍎 (40 fruits)

• Bananas 🍎🍎🍎 (30 fruits)

• Oranges 🍎🍎🍎🍎🍎 (50 fruits)

• Mangoes 🍎🍎 (20 fruits)

Q1. How many oranges were sold?
a) 30 b) 40 c) 50 d) 20
(Competency: Reading pictograph)

Q2. Which fruit was sold the least?
a) Apple b) Banana c) Orange d) Mango
(Competency: Interpreting pictograph)

Q3. Total fruits sold = ?
a) 100 b) 120 c) 130 d) 140
(Competency: Summing pictograph data)

Q4. Ratio of apples to bananas sold = ?
a) 4:3 b) 3:2 c) 40:20 d) 2:1
(Competency: Ratio from pictograph)

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Case Study 2 – Bar Graph (Sports)

The bar graph shows the favourite sports of students in a class.

[Insert Image: Bar graph of favourite games – Page 81]

• Cricket: 30 students

• Football: 25 students

• Hockey: 20 students

• Basketball: 15 students

Q1. Which sport is most popular?
a) Cricket b) Football c) Hockey d) Basketball
(Competency: Bar graph interpretation)

Q2. How many students like hockey?
a) 20 b) 25 c) 30 d) 15
(Competency: Reading bar graph)

Q3. How many more students like cricket than basketball?
a) 10 b) 15 c) 20 d) 25
(Competency: Difference using bar graph)

Q4. Total number of students = ?
a) 90 b) 100 c) 110 d) 120
(Competency: Summation of bar graph data)

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Case Study 3 – Line Graph (Temperature)

The line graph shows the maximum temperature of a city in a week.

[Insert Image: Line graph of temperature – Page 86]

• Mon: 30°C Tue: 32°C Wed: 31°C

• Thu: 29°C Fri: 28°C Sat: 33°C Sun: 34°C

Q1. On which day was the temperature highest?
a) Friday b) Saturday c) Sunday d) Tuesday
(Competency: Reading line graph)

Q2. On which day was the temperature lowest?
a) Thursday b) Friday c) Saturday d) Monday
(Competency: Identifying minimum)

Q3. Difference between highest & lowest temperature = ?
a) 4°C b) 5°C c) 6°C d) 7°C
(Competency: Subtraction from line graph)

Q4. On how many days was the temperature above 30°C?
a) 2 b) 3 c) 4 d) 5
(Competency: Data analysis from line graph)

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Case Study 4 – Pie Chart (Expenditure)

A family’s monthly expenditure is represented by a pie chart.

[Insert Image: Pie chart of expenditure – Page 92]

• Food: 120°

• Rent: 90°

• Education: 60°

• Savings: 90°

Q1. Which sector is the largest expenditure?
a) Food b) Rent c) Education d) Savings
(Competency: Reading pie chart)

Q2. What fraction of income is spent on food?
a) ⅓ b) ¼ c) ½ d) ⅙
(Competency: Fraction from pie chart)

Q3. Which two heads together make half of the expenditure?
a) Rent + Education b) Rent + Savings c) Food + Rent d) Education + Savings
(Competency: Summing pie chart angles)

Q4. Angle representing savings = ?
a) 90° b) 120° c) 150° d) 180°
(Competency: Reading angles in pie chart)

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Case Study 5 – Frequency Table (Marks)

The marks scored by 40 students in a test are given:

[Insert Image: Frequency table of marks – Page 98]

| Marks | 10 | 20 | 30 | 40 | 50 |
|---------|----|----|----|----|
| Students| 8 | 10 | 12 | 6 | 4 |

Q1. How many students scored 30 marks?
a) 6 b) 8 c) 10 d) 12
(Competency: Frequency table reading)

Q2. Which marks were obtained by the maximum students?
a) 10 b) 20 c) 30 d) 40
(Competency: Finding mode from frequency table)

Q3. How many students scored less than 30 marks?
a) 18 b) 20 c) 22 d) 24
(Competency: Summing frequencies)

Q4. Total number of students = ?
a) 36 b) 38 c) 40 d) 42

(Competency: Adding frequency values)

7. Case-Based Questions (20 MCQs)

Case Study 1 (Fruits)

1. (c) 50

2. (d) Mango

3. (c) 130

4. (a) 4:3

Case Study 2 (Sports)

1. (a) Cricket

2. (a) 20

3. (c) 20 (30–10)

4. (b) 100

Case Study 3 (Temperature)

1. (c) Sunday (34°C)

2. (b) Friday (28°C)

3. (b) 34 – 28 = 6°C

4. (c) 4 days above 30°C

Case Study 4 (Expenditure)

1. (a) Food (120°)

2. (a) ⅓

3. (b) Rent + Savings = 90°+90°=180°

4. (a) 90°

Case Study 5 (Marks)

1. (d) 12

2. (c) 30 (highest freq = 12)

3. (a) 18 (8+10)

4. (c) 40