Class 6 Maths Chapter 10 The Other Side of Zero Practice Paper 3

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 additive inverse of +15 is:
(a) +15
(b) –15
(c) 0
(d) +1/15

Q.2 Which of the following is the smallest integer?
(a) 0
(b) –1
(c) –100
(d) Does not exist

Q.3 What is (+8) – (+15)?
(a) +7
(b) –7
(c) +23
(d) –23

Q.4 If you start from Floor 0 and go down 7 floors, you will be on Floor:
(a) +7
(b) –7
(c) 0
(d) +1

Q.5 Which statement is correct?
(a) Every integer has a successor
(b) –20 is greater than –15
(c) The sum of two negative integers is always positive
(d) Zero is a positive integer

Q.6 The value of (–11) + (–9) is:
(a) +20
(b) –20
(c) +2
(d) –2

Q.7 Which integer comes exactly between –8 and –6?
(a) –7
(b) 0
(c) –14
(d) +1

Q.8 A submarine was at –80 m. It rose 30 m. Its new position is:
(a) –110 m
(b) –50 m
(c) +50 m
(d) +110 m

Q.9 According to Brahmagupta's rules, what is (negative) × (negative)?
(a) Positive
(b) Negative
(c) Zero
(d) Cannot be determined

Q.10 What is (–14) + (+14) – (+5)?
(a) +5
(b) –5
(c) 0
(d) +33

SECTION B - Short Answer Questions (2 marks each)

Q.11 Find two integers whose sum is –8 and difference is 4.

Q.12 A plane is flying at an altitude of 3000 m above sea level. A submarine is 500 m below sea level. What is the vertical distance between them? Use integers.

Q.13 Verify that: (–6) + (+10) = (+10) + (–6). State the property used.

Q.14 Using the number line, find the value of: (+5) – (+9)

SECTION C - Short Answer Questions (3 marks each)

Q.15 A businessman has the following transactions in a week (using integers to represent profit and loss): Day 1: Loss of ₹500 Day 2: Profit of ₹800 Day 3: Loss of ₹300 Day 4: Profit of ₹600 Day 5: Loss of ₹200 What is his net profit or loss for the week? Show all calculations.

Q.16 On an unmarked number line, point A represents –3 and point B represents +5. If point C is exactly halfway between A and B, what integer does point C represent? Explain your method.

Q.17 The temperature at midnight was –7°C. It rose by 3°C every hour for 4 hours. What was the temperature after 4 hours? Show the calculation step by step.

SECTION D - Long Answer Question (5 marks)

Q.18 Answer the following based on the concept of zero pairs and the token model:
(a) Explain what a zero pair is with an example.
(b) Show using tokens how to calculate: (–5) + (+2)
(c) Show using tokens how to calculate: (+4) – (+9). Explain why you need to add zero pairs.
(d) If you have 7 positive tokens and 3 negative tokens, what integer do they represent together? (e) How many zero pairs can you make from 5 positive and 8 negative tokens? What will be left over?

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

Q.19 Case Study 1: Ocean Depths and Heights The table shows the positions of different objects relative to sea level (0 m): Object Position (in meters) Helicopter +400 Boat 0 Scuba diver –25 Submarine –120 (i) What is the distance between the helicopter and the submarine? (1 mark) (ii) If the scuba diver descends 15 m more, at what position will they be? (1 mark) (iii) The submarine rises 50 m. What is its new position? (1 mark) (iv) Arrange all four objects in ascending order of their positions. (1 mark)

Q.20 Case Study 2: Bank Account Transactions Rahul's bank account transactions for one week are shown below (deposits are positive, withdrawals are negative): Day Transaction (₹) Monday +2000 (deposit) Tuesday –800 (withdrawal) Wednesday +1500 (deposit) Thursday –1200 (withdrawal) Friday –300 (withdrawal) His opening balance on Monday morning was ₹5000. (i) What is the total amount deposited during the week? (1 mark) (ii) What is the total amount withdrawn during the week? (1 mark) (iii) What is the net change in his account (using integers)? (1 mark) (iv) What is his closing balance on Friday evening? (1 mark) DETAILED ANSWER KEY - PAPER 03

SECTION A - Answers to MCQs

1.
(b) –15 The additive inverse of a number is the number that when added to it gives zero. (+15) + (–15) = 0

2.
(d) Does not exist Integers extend infinitely in the negative direction. There is no smallest integer. We can always find a smaller one.

3.
(b) –7 (+8) – (+15) = (+8) + (–15) = –7

4.
(b) –7 Starting from 0, going down 7 floors: 0 + (–7) = –7

5.
(a) Every integer has a successor Every integer n has a successor n+1. Options
(b) ,
(c) , and
(d) are false.

6.
(b) –20 When adding two negative integers, add their absolute values and keep the negative sign: (–11) + (–9) = – 20

7.
(a) –7 Between –8 and –6, the integer in the middle is –7 (it's equidistant from both).

8.
(b) –50 m Initial: –80 m, Rises 30 m: (–80) + (+30) = –50 m

9.
(a) Positive According to Brahmagupta's rules: (negative) × (negative) = positive

10.
(b) –5 (–14) + (+14) – (+5) = 0 – (+5) = –5

SECTION B - Answers to Short Answer Questions

11. Answer: –2 and –6 Let the integers be x and y. x + y = –8 ... (1) x – y = 4 ... (2) Adding equations: 2x = –4, so x = –2 Substituting in (1): –2 + y = –8, so y = –6 Verification: (–2) + (–6) = –8 ✓ and (–2) – (–6) = 4 ✓

12. Answer: 3500 m Plane position: +3000 m Submarine position: –500 m Distance = (+3000) – (–500) = +3000 + 500 = 3500 m The vertical distance is 3500 m

13. Answer: Verified, Commutative Property LHS: (–6) + (+10) = +4 RHS: (+10) + (–6) = +4 LHS = RHS Property used: Commutative Property of Addition (The order of adding integers does not change the sum)

14. Answer: –4 Using number line: Start at +5 To subtract +9, move 9 steps to the left +5 → +4 → +3 → +2 → +1 → 0 → –1 → –2 → –3 → –4 Answer: (+5) – (+9) = –4

SECTION C - Answers to Short Answer Questions

15. Answer: Net profit of ₹400 Day 1: –500 (loss) Day 2: +800 (profit) Day 3: –300 (loss) Day 4: +600 (profit) Day 5: –200 (loss) Total = (–500) + (+800) + (–300) + (+600) + (–200) = (+800 + 600) + (–500 – 300 – 200) = (+1400) + (–1000) = +400 Net profit for the week is ₹400

16. Answer: +1 Point A: –3 Point B: +5 Distance from A to B: (+5) – (–3) = 8 units Halfway point: 8 ÷ 2 = 4 units from A Position of C: (–3) + (+4) = +1 Alternative method: Midpoint = (A + B) ÷ 2 = [(–3) + (+5)] ÷ 2 = 2 ÷ 2 = +1 Point C represents +1

17. Answer: +5°C Initial temperature: –7°C After 1 hour: (–7) + (+3) = –4°C After 2 hours: (–4) + (+3) = –1°C After 3 hours: (–1) + (+3) = +2°C After 4 hours: (+2) + (+3) = +5°C Alternative method: Total rise: 3°C × 4 = 12°C Final temperature: (–7) + (+12) = +5°C The temperature after 4 hours was +5°C

SECTION D - Answer to Long Answer Question

18. Zero Pairs and Token Model:
(a) Zero pair explanation: A zero pair consists of one positive token (+) and one negative token (–) that cancel each other to make zero. Example: (+1) + (–1) = 0 When we have + and – together, they form a zero pair and can be removed.
(b) Calculating (–5) + (+2) using tokens: Start with 5 negative tokens: – – – – – Add 2 positive tokens: + + Combined: – – – – – + + Make zero pairs: Match 2 negative with 2 positive Remaining: 3 negative tokens (– – –) Result: (–5) + (+2) = –3
(c) Calculating (+4) – (+9) using tokens:

Start with 4 positive tokens: + + + + Need to remove 9 positive tokens, but we only have 4 Add 5 zero pairs (5 positive + 5 negative) Now we have: + + + + + + + + + – – – – – Remove 9 positive tokens Remaining: 5 negative tokens (– – – – –) Result: (+4) – (+9) = –5 We needed zero pairs because we didn't have enough positive tokens to subtract
(d) 7 positive and 3 negative tokens: Make 3 zero pairs (matching 3 positive with 3 negative) Remaining: 4 positive tokens They represent +4 (e) Zero pairs from 5 positive and 8 negative:

We can make 5 zero pairs (using all 5 positive with 5 negative) Left over: 3 negative tokens (representing –3)

SECTION E - Answers to Case Study Based Questions

19. Case Study 1: Ocean Depths and Heights (i) Distance between helicopter and submarine: Helicopter: +400 m Submarine: –120 m Distance = (+400) – (–120) = +400 + 120 = 520 m (ii) Scuba diver's new position after descending 15 m: Current position: –25 m Descends 15 m: (–25) + (–15) = –40 m (iii) Submarine's new position after rising 50 m: Current position: –120 m Rises 50 m: (–120) + (+50) = –70 m (iv) Ascending order: Submarine (–120) < Scuba diver (–25) < Boat (0) < Helicopter (+400)

20. Case Study 2: Bank Account Transactions (i) Total amount deposited: Monday: +2000 Wednesday: +1500 Total deposits: +2000 + 1500 = ₹3500 (ii) Total amount withdrawn: Tuesday: –800 Thursday: –1200 Friday: –300 Total withdrawals: 800 + 1200 + 300 = ₹2300 (iii) Net change in account: Net change = (+2000) + (–800) + (+1500) + (–1200) + (–300) = (+3500) + (–2300) = +1200 Net increase of ₹1200 (iv) Closing balance: Opening balance: ₹5000 Net change: +1200 Closing balance: 5000 + 1200 = ₹6200