Class 6 Maths Chapter 10 The Other Side of Zero Practice Paper 2

Class: VI Subject: Mathematics Session: 2025-26 Chapter: 10 - The Other Side of Zero (Integers) Time: 1½ Hours Max. Marks: 40

General Instructions:

1. All questions are compulsory.

2. This question paper contains 20 questions divided into five sections A, B, C, D and E.

3. Section A contains 10 MCQs of 1 mark each.

4. Section B contains 4 questions of 2 marks each.

5. Section C contains 3 questions of 3 marks each.

6. Section D contains 1 question of 5 marks.

7. Section E contains 2 Case Study Based questions of 4 marks each.

SECTION A - Multiple Choice Questions (1 mark each)

Q.1 The value of (–12) + (+5) is:
(a) –17
(b) –7
(c) +7
(d) +17

Q.2 Which integer lies between –3 and +2?
(a) –5
(b) +3
(c) 0
(d) –4

Q.3 What is (–9) – (+4)?
(a) –13
(b) –5
(c) +5
(d) +13

Q.4 The successor of –1 is:
(a) –2
(b) 0
(c) +1
(d) –0

Q.5 Which of the following is true?
(a) –10 > –5
(b) 0 > –1
(c) –7 > 0
(d) –2 > +3

Q.6 What is (+6) + (–6)?
(a) +12
(b) –12
(c) 0
(d) +6

Q.7 The predecessor of 0 is:
(a) +1
(b) –1
(c) 0
(d) Does not exist

Q.8 If the temperature drops from +3°C to –5°C, the change in temperature is:
(a) –8°C
(b) +8°C
(c) –2°C
(d) +2°C

Q.9 On a number line, which number is to the left of –4?
(a) –3
(b) 0
(c) –6
(d) +2

Q.10 What is (–5) – (–8)?
(a) –13
(b) +3
(c) –3
(d) +13

SECTION B - Short Answer Questions (2 marks each)

Q.11 Write all integers between –5 and +3.

Q.12 Find the sum of all integers from –4 to +4.

Q.13 A shopkeeper gains ₹150 on Monday, loses ₹200 on Tuesday, and gains ₹300 on Wednesday. What is his net profit or loss? Use integers.

Q.14 Simplify: (–7) + (+12) – (–5)

SECTION C - Short Answer Questions (3 marks each)

Q.15 In Bela's Building of Fun, you are on Floor –3. You press the lift buttons in the following sequence: +5, – 2, +4, –6. On which floor will you finally be? Show all steps.

Q.16 A diver is at 45 m below sea level. He ascends 20 m and then descends 15 m. At what depth is he now? Represent using integers.

Q.17 Arrange the following integers in descending order and mark them on a number line: +4, –6, 0, –2, +7, –1, +3

SECTION D - Long Answer Question (5 marks)

Q.18 Using the token model (positive and negative tokens):
(a) Show how to add (–4) + (+6) using tokens. Draw the tokens and show zero pairs.
(b) Show how to subtract (+3) – (+7) using tokens. Explain why you need to add zero pairs.
(c) Verify both answers using a number line.

SECTION E - Case Study Based Questions (4 marks each)

Q.19 Case Study 1: Lift Movement in a Building A building has 8 floors above ground (numbered +1 to +8) and 3 floors below ground (numbered –1 to –3). The ground floor is numbered 0. Meera enters the lift at Floor +2 and makes the following movements: First: Goes down 5 floors Second: Goes up 3 floors Third: Goes down 2 floors Fourth: Goes up 6 floors (i) On which floor is Meera after the first movement? (1 mark) (ii) On which floor is Meera after all four movements? (1 mark) (iii) Write the complete expression using integers for all movements. (1 mark) (iv) If she wants to reach Floor +6 from her current position, should she go up or down? By how many floors?

(1 mark)

Q.20 Case Study 2: Temperature Variation The table shows temperature readings of a city for 5 days: Day Monday Tuesday Wednesday Thursday Friday Temperature –3°C +2°C –5°C +1°C –4°C (i) On which day was the temperature highest and on which day was it lowest? (1 mark) (ii) What is the difference between the highest and lowest temperatures? (1 mark) (iii) What was the temperature change from Tuesday to Wednesday? (1 mark) (iv) If Friday's temperature rises by 7°C on Saturday, what will be Saturday's temperature? (1 mark) DETAILED ANSWER KEY - PAPER 02

SECTION A - Answers to MCQs

1.
(b) –7 (–12) + (+5) = –7 (Subtract 5 from 12 and keep the sign of the larger number)

2.
(c) 0 Integers between –3 and +2 are: –2, –1, 0, +1. Among options, only 0 is present.

3.
(a) –13 (–9) – (+4) = (–9) + (–4) = –13

4.
(b) 0 Successor means the next number. The number after –1 is 0.

5.
(b) 0 > –1 Zero is greater than all negative numbers. On the number line, 0 is to the right of –1.

6.
(c) 0 (+6) + (–6) = 0 (A number added to its additive inverse equals zero)

7.
(b) –1 Predecessor means the previous number. The number before 0 is –1.

8.
(a) –8°C Change = Final – Initial = (–5) – (+3) = –8°C (negative means drop)

9.
(c) –6 On the number line, numbers to the left are smaller. –6 < –4, so –6 is to the left of –4.

10.
(b) +3 (–5) – (–8) = (–5) + (+8) = +3

SECTION B - Answers to Short Answer Questions

11. Answer: Integers between –5 and +3 are: –4, –3, –2, –1, 0, +1, +2

12. Answer: 0 Integers from –4 to +4: –4, –3, –2, –1, 0, +1, +2, +3, +4 Sum = (–4) + (–3) + (–2) + (–1) + 0 + (+1) + (+2) + (+3) + (+4) = (–4 + 4) + (–3 + 3) + (–2 + 2) + (–1 + 1) + 0 = 0 Each number cancels with its opposite, so the sum is 0.

13. Answer: Net profit of ₹250 Monday: +150 Tuesday: –200 Wednesday: +300 Total: (+150) + (–200) + (+300) = +250 Net profit is ₹250

14. Answer: +10 (–7) + (+12) – (–5) = (–7) + (+12) + (+5) = (+5) + (+5) = +10

SECTION C - Answers to Short Answer Questions

15. Answer: Floor –2 Starting Floor: –3 Step 1: (–3) + (+5) = +2 Step 2: (+2) + (–2) = 0 Step 3: (0) + (+4) = +4 Step 4: (+4) + (–6) = –2 Final Answer: You will be on Floor –2

16. Answer: –40 m (40 m below sea level) Initial position: –45 m Step 1: Ascends 20 m: (–45) + (+20) = –25 m Step 2: Descends 15 m: (–25) + (–15) = –40 m The diver is now at –40 m (40 m below sea level)

17. Answer: Descending order (largest to smallest): +7, +4, +3, 0, –1, –2, –6 Number line: –6____–2____–1____0____+3____+4____+7

SECTION D - Answer to Long Answer Question

18. Token Model and Number Line Verification:
(a) Adding (–4) + (+6) using tokens: • Start with 4 negative tokens: – – – – • Add 6 positive tokens: + + + + + + • Make zero pairs: Match 4 negative with 4 positive • Remaining: 2 positive tokens • Result: (–4) + (+6) = +2
(b) Subtracting (+3) – (+7) using tokens: • Start with 3 positive tokens: + + + • Need to remove 7 positive tokens, but we only have 3 • Add 4 zero pairs (4 positive + 4 negative tokens) • Now we have: + + + + + + + – – – – • Remove 7 positive tokens • Remaining: 4 negative tokens • Result: (+3) – (+7) = –4 • We needed zero pairs because we didn't have enough positive tokens to subtract from
(c) Verification using number line:

For (–4) + (+6): Start at –4, move 6 steps right → reach +2 ✓ For (+3) – (+7): Target – Starting = Movement This means: Starting + Movement = Target (+3) + (?) = Result, where we remove 7 (+3) + (–7) = –4 ✓

SECTION E - Answers to Case Study Based Questions

19. Case Study 1: Lift Movement in a Building (i) Floor after first movement: Starting: +2 Goes down 5 floors: (+2) + (–5) = –3 Meera is on Floor –3 (ii) Floor after all four movements: After 1st: –3 After 2nd (up 3): (–3) + (+3) = 0 After 3rd (down 2): (0) + (–2) = –2 After 4th (up 6): (–2) + (+6) = +4 Meera is on Floor +4 (iii) Complete expression: (+2) + (–5) + (+3) + (–2) + (+6) = +4 (iv) Movement to reach Floor +6: Current floor: +4 Target floor: +6 Movement: (+6) – (+4) = +2 She should go UP by 2 floors

20. Case Study 2: Temperature Variation (i) Highest and lowest temperature days: Highest: Tuesday (+2°C) Lowest: Wednesday (–5°C) (ii) Difference between highest and lowest: (+2) – (–5) = +2 + 5 = 7°C (iii) Temperature change from Tuesday to Wednesday: Change = (–5) – (+2) = –7°C Temperature dropped by 7°C (iv) Saturday's temperature: Friday: –4°C Rises by 7°C: (–4) + (+7) = +3°C Saturday's temperature will be +3°C