CBSE Class 6 Mathematics The Other Side of Zero Practice Paper Assignment Set 02 with Answers

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Practice Paper 23 for CBSE Class 6 Mathematics (Ganita Prakash) Chapter 10 The Other Side of Zero is a complete 40-mark test with 20 questions spread over Sections A to E, solved here step by step. The questions cover single moves on the number line, integers lying strictly between two numbers, zero as the additive identity, rewriting subtraction as addition of the inverse, and real-life cases on a research drone, land rising and sinking after an earthquake, and the depth of a metro tunnel boring machine.

Section A: Multiple Choice Questions (1 Mark Each)

Question 1: Starting from −8, which single move will place you at +3?
(a) +9
(b) +10
(c) +11
(d) +12
Show Answer & Explanation

Answer: (c) +11

Explanation:
1. Move = final − start = (+3) − (−8).
2. (+3) − (−8) = 3 + 8 = 11.
3. Check: −8 + 11 = +3. The move is +11.

Teacher's Note:
1. 8 steps take you from −8 to 0, and 3 more steps reach +3.
2. Going from a smaller to a larger integer is always a positive move.

Question 2: Which integer lies strictly between −6 and +1?
(a) −7
(b) −5
(c) +1
(d) +3
Show Answer & Explanation

Answer: (b) −5

Explanation:
1. Strictly between −6 and +1 means greater than −6 and less than +1, so −5, −4, −3, −2, −1 or 0.
2. −7 is less than −6, +3 is more than +1, and +1 is an end point, which is not allowed.
3. So the answer is −5.

Teacher's Note:
1. 'Strictly between' leaves out both end numbers.
2. Mark −6 and +1 on a number line and look only at the integers in between.

Question 3: Complete the balance: −13 + □ = −4
(a) +7
(b) +8
(c) +9
(d) +10
Show Answer & Explanation

Answer: (c) +9

Explanation:
1. The missing number is −4 − (−13) = −4 + 13.
2. −4 + 13 = +9.
3. Check: −13 + 9 = −4. The answer is +9.

Teacher's Note:
1. To find a missing addend, subtract the known number from the total.
2. From −13, nine steps up reach −4.

Question 4: Why is −6 greater than −15?
(a) −6 is positive
(b) −6 is closer to zero
(c) −15 has no inverse
(d) −15 lies right of −6
Show Answer & Explanation

Answer: (b) −6 is closer to zero

Explanation:
1. On the number line, the integer on the right is the greater one.
2. −6 is 6 steps from zero and −15 is 15 steps from zero, so −6 lies to the right of −15.
3. So −6 is greater because −6 is closer to zero.

Teacher's Note:
1. (a) is wrong because −6 is negative; (d) is wrong because −15 lies to the left of −6.
2. Every integer has an additive inverse, so (c) is wrong too.

Question 5: Start at 0. Apply −11, +18, −9. The final integer is:
(a) −2
(b) +2
(c) −4
(d) +4
Show Answer & Explanation

Answer: (a) −2

Explanation:
1. 0 + (−11) = −11.
2. −11 + 18 = +7.
3. +7 + (−9) = −2.

Teacher's Note:
1. Apply the moves in the given order.
2. Check: total down = 20, total up = 18, so the result is 2 below zero.

Question 6: Which integer has the maximum distance from zero?
(a) −9
(b) +12
(c) −14
(d) +10
Show Answer & Explanation

Answer: (c) −14

Explanation:
1. Distances from zero: −9 → 9, +12 → 12, −14 → 14, +10 → 10.
2. The largest distance is 14.
3. So −14 is farthest from zero.

Teacher's Note:
1. Distance from zero is the number without its sign.
2. Maximum distance does not mean the greatest integer.

Question 7: Which expression gives the value −8?
(a) −3 − 5
(b) +6 − 12
(c) −10 + 4
(d) +6 − 18
Show Answer & Explanation

Answer: (a) −3 − 5

Explanation:
1. −3 − 5: start at −3 and go 5 steps down to −8.
2. +6 − 12 = −6, −10 + 4 = −6 and +6 − 18 = −12.
3. Only −3 − 5 gives −8.

Teacher's Note:
1. Two downward moves add up: 3 down and 5 more down is 8 down.
2. Work out every option before choosing.

Question 8: Which statement is correct?
(a) −19 > −7
(b) −4 < −11
(c) −6 > −13
(d) −9 = −3
Show Answer & Explanation

Answer: (c) −6 > −13

Explanation:
1. −19 lies left of −7, so −19 < −7; (a) is false.
2. −4 lies right of −11, so −4 > −11; (b) is false. −9 and −3 are not equal; (d) is false.
3. −6 is closer to zero than −13, so −6 > −13 is correct.

Teacher's Note:
1. Among negative integers, the one with the smaller number after the minus sign is greater.
2. Use a lift picture: floor −6 is above floor −13.

Question 9:
Assertion (A): Adding zero to an integer does not change its value.
Reason (R): Zero is the additive identity for integers.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. For example −7 + 0 = −7 and 5 + 0 = 5. A is true.
2. 'Additive identity' is exactly the name for the number that leaves every number unchanged when added. R is true.
3. A happens because zero is the additive identity, so R correctly explains A.

Teacher's Note:
1. On the number line, adding 0 means making no move at all.
2. Check A and R separately first; only then ask whether R gives the reason for A.

Question 10:
Assertion (A): (−11) − (+4) = −15
Reason (R): Subtracting a positive integer moves left on the number line.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. (−11) − (+4): start at −11 and move 4 steps left to −15. A is true.
2. Taking away a positive number always means moving to the left, so R is true.
3. The answer −15 is reached exactly by that leftward move, so R explains A.

Teacher's Note:
1. Left on the number line means smaller values.
2. Check A and R separately first; only then ask whether R gives the reason for A.

Section B: Short Answer Questions (2 Marks Each)

Question 11. (a) Write the additive inverse of +96
(b) Find their sum
Answer:
(a) The additive inverse of +96 is the integer with the same size and opposite sign: −96.
(b) (+96) + (−96) = 0.
In simple words: Change the sign to get the inverse; the two always cancel to zero.

Teacher's Note:
1. +96 and −96 are mirror images about 0 on the number line.
2. Every integer has exactly one additive inverse.

 

Question 12. (a) Starting integer = −21, final integer = +5
(b) Find the total movement
Answer:
(a) Movement = final − start = (+5) − (−21).
(b) (+5) − (−21) = 5 + 21 = +26.
So we move 26 steps in the positive direction. Check: −21 + 26 = +5.
In simple words: 21 steps take us from −21 to 0, and 5 more to +5, so 26 steps up.

Teacher's Note:
1. Subtracting a negative number is the same as adding its inverse.
2. A positive movement means up or to the right.

 

Question 13. (a) Which is greater: −68 or −54?
(b) Give one valid reason
Answer:
(a) −54 is greater.
(b) −54 is closer to zero than −68, so it lies to the right of −68 on the number line.
In simple words: −54 is 54 steps below zero and −68 is 68 steps below, so −54 is higher.

Teacher's Note:
1. We can write −68 < −54.
2. Do not be misled by 68 being bigger than 54.

 

Question 14. (a) Final integer = −10, starting integer = +8
(b) Find the operation performed
Answer:
(a) Change = final − start = (−10) − (+8).
(b) (−10) − (+8) = −10 − 8 = −18.
So the operation performed is adding −18 (subtracting 18): +8 + (−18) = −10.
In simple words: From +8, it takes 8 steps down to 0 and 10 more to −10, which is 18 steps down.

Teacher's Note:
1. The change is always final minus start.
2. Check by applying the change to the start: 8 − 18 = −10.

 

Section C: Short Answer Questions (3 Marks Each)

Question 15. (a) Evaluate: −52 + 29
(b) Explain using number-line movement
(c) State the sign of the result
Answer:
(a) The negative part (52) is bigger than the positive part (29), so the answer is negative, with size 52 − 29 = 23. So −52 + 29 = −23.
(b) Start at −52 and move 29 steps to the right (adding a positive number). We stop at −23, which is still to the left of zero.
−60 −50 −40 −30 −20 −10 0 +29 start −52 end −23
(c) The result is negative.
In simple words: Climbing 29 steps from −52 is not enough to reach zero; we stop 23 steps short.

Teacher's Note:
1. With tokens: 52 negative and 29 positive give 29 zero pairs and 23 negatives left over.
2. The answer takes the sign of the number farther from zero.

 

Question 16. (a) Rewrite as addition: +14 − (+37)
(b) Solve
(c) Interpret the result
Answer:
(a) Subtracting +37 means adding its inverse: +14 − (+37) = +14 + (−37).
(b) The negative part is bigger: 37 − 14 = 23, so the answer is −23.
(c) Starting at +14 and moving 37 steps down crosses zero and ends 23 steps below zero. The result is negative, which shows a net downward movement (a net decrease of 23 from zero).
In simple words: Taking 37 away from 14 is more than we have, so we end 23 below zero.

Teacher's Note:
1. a − b = a + (inverse of b).
2. Check: −23 + 37 = 14.

 

Question 17. (a) Arrange: −17, +34, −61 in increasing order
(b) Find the integer nearest to zero
(c) Find the integer farthest from zero
Answer:
(a) −61 is furthest left, then −17, then +34. Increasing order: −61 < −17 < +34.
(b) Distances from zero: 17, 34 and 61. The nearest to zero is −17.
(c) The farthest from zero is −61.
In simple words: Smallest first means leftmost first; nearest to zero has the smallest distance.

Teacher's Note:
1. Every negative integer is less than every positive integer.
2. Distance from zero ignores the sign.

 

Section D: Long Answer Question (5 Marks)

Question 18. A research drone is initially 10 units above reference level. It descends 24 units, rises 15 units, descends 7 units, and rises 4 units.
(a) Write the integer expression
(b) Simplify stepwise
(c) Find the final position
(d) Find the net vertical movement
(e) Find the position relative to reference level
Answer:
Reference level = 0; up is positive, down is negative.
(a) (+10) + (−24) + (+15) + (−7) + (+4), that is, 10 − 24 + 15 − 7 + 4.
(b) 10 − 24 = −14; −14 + 15 = +1; +1 − 7 = −6; −6 + 4 = −2.
(Grouping: (10 + 15 + 4) − (24 + 7) = 29 − 31 = −2.)
−16 −12 −8 −4 0 +4 +8 +12 reference level 0 −24 +15 −7 +4 +10 start −14 move 1 +1 move 2 −6 move 3 −2 move 4
(c) Final position = −2.
(d) Net vertical movement = (−24) + 15 + (−7) + 4 = −12, i.e. 12 units down overall (check: 10 + (−12) = −2).
(e) The drone is 2 units below the reference level.
In simple words: The drone fell 31 units and rose 19 units, a net drop of 12 units, ending 2 units below the reference level.

Teacher's Note:
1. Do not include the starting height in the net movement.
2. Grouping all ups and all downs is a quick way to check.

 

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: During an earthquake study, scientists measure changes in land elevation using integers, where zero represents the original ground level. After the first tremor, the land subsides by 16 units. Later, tectonic adjustment raises the land by 23 units. A minor aftershock then causes the land to sink by 4 units. Positive integers represent upward movement, while negative integers represent downward movement. Using integer operations, answer the following questions.
(a) Write the integer that represents the land subsiding by 16 units after the first tremor.
(b) Find the land elevation after it rises by 23 units from the subsided level.
(c) Calculate the final land elevation after it sinks by 4 units again.
(d) State whether the final elevation is above, below, or at the original ground level.
Answer:
(a) Subsiding means going down, so it is −16.
(b) (−16) + (+23) = +7, i.e. 7 units above the original level.
(c) (+7) + (−4) = +3.
(d) +3 is positive, so the final elevation is above the original ground level (by 3 units).
In simple words: The land went down 16, up 23 and down 4, ending 3 units higher than it started.

Teacher's Note:
1. Read the sign from the words: subside and sink are negative, raise is positive.
2. Check: −16 + 23 − 4 = +3.

 

Question 20. Case Study 2: During metro construction, engineers track tunnel depth using integers. Ground level is zero. The tunnel boring machine first moves down 12 units, then comes up 18 units for inspection, and finally moves down 5 units to resume work. Using integer operations, answer the following questions.
(a) Write the integer that represents the first downward movement of the tunnel boring machine.
(b) Find the position of the machine after it moves up 18 units for inspection.
(c) Calculate the final depth of the tunnel after the machine moves down 5 units again.
(d) State whether the final position is above, below, or at the ground level.
Answer:
(a) A downward movement of 12 units is −12.
(b) (−12) + (+18) = +6, i.e. 6 units above ground level.
(c) (+6) + (−5) = +1. So the final position is +1.
−14 −12 −10 −8 −6 −4 −2 0 +2 +4 +6 +8 ground level 0 −12 +18 −5 0 start −12 down 12 +6 up 18 +1 down 5
(d) +1 is positive, so the machine ends above the ground level (by 1 unit).
In simple words: Down 12 and up 18 puts the machine 6 above ground; down 5 leaves it 1 unit above ground.

Teacher's Note:
1. The numbers here make the machine finish above the ground, so the 'depth' in (c) is really a height of 1 unit.
2. Check: −12 + 18 − 5 = +1.

 

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Chapter Assignment & Practice Material for Class 6 Mathematics Chapter 10 The Other Side of Zero

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