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