This MCQ module is based on: Integer Exercises and Summary
TOPIC 41 OF 41
Integer Exercises and Summary
🎓 Class 6
Mathematics
CBSE
Theory
Ch 10 — The Other Side of Zero
⏱ ~30 min
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This mathematics assessment will be based on: Integer Exercises and Summary
Targeting Class 6 level in Integers, with Basic difficulty.
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10.9 Exercises — End of Chapter
Q1. Write the opposite of each integer: +23, −45, 0, +1, −100.
−23, +45, 0, −1, +100.
Q2. Arrange in ascending order: −7, +2, 0, −1, +10, −3, +5.
−7 < −3 < −1 < 0 < +2 < +5 < +10.
Q3. Write all integers between: (a) −4 and +3 (b) −10 and −5 (c) +1 and +6.
(a) −3, −2, −1, 0, +1, +2 (b) −9, −8, −7, −6 (c) +2, +3, +4, +5.
Q4. Compute:
(a) (−6) + (+9) (b) (−12) + (−7) (c) (+15) − (−8) (d) (−5) − (+3) (e) 0 − (−14) (f) (+4) + (−4).
(a) (−6) + (+9) (b) (−12) + (−7) (c) (+15) − (−8) (d) (−5) − (+3) (e) 0 − (−14) (f) (+4) + (−4).
(a) +3 (b) −19 (c) +23 (d) −8 (e) +14 (f) 0.
Q5. Write using integers:
(a) Gained 200 rupees, then lost 350 rupees. Net? (b) Started at floor +2, went up 3 floors, down 7 floors. Final floor? (c) Temperature −8°C rises by 15°C. New temperature?
(a) Gained 200 rupees, then lost 350 rupees. Net? (b) Started at floor +2, went up 3 floors, down 7 floors. Final floor? (c) Temperature −8°C rises by 15°C. New temperature?
(a) +200 − 350 = −150 (net loss of ₹150). (b) 2 + 3 − 7 = −2 (2nd basement). (c) −8 + 15 = +7°C.
Q6. Find the value of \((-3) + (+7) + (-5) + (+4) + (-2) + 0\).
Positives: 7 + 4 = 11. Negatives: −3 − 5 − 2 = −10. Sum = 11 − 10 = +1.
Q7. In a quiz, +4 is given for each correct answer and −2 for each wrong answer. Soumya answered 7 correctly and 3 wrongly. What was her score?
From correct: 7 × 4 = +28. From wrong: 3 × (−2) = −6. Score = 28 − 6 = +22.
Q8. The temperature at 2 a.m. was −3°C. By noon it had risen by 9°C. By evening it fell by 6°C. What was the evening temperature?
−3 + 9 − 6 = 0°C.
Q9. Fill in with <, >, =:
(a) |−6| ___ |+4| (b) (−3) + (−4) ___ (−3) − (−4) (c) (−2) + (+5) ___ 0 (d) (−8) − (−8) ___ 0.
(a) |−6| ___ |+4| (b) (−3) + (−4) ___ (−3) − (−4) (c) (−2) + (+5) ___ 0 (d) (−8) − (−8) ___ 0.
(a) 6 > 4 → > (b) LHS = −7, RHS = +1 → < (c) +3 > 0 → > (d) 0 = 0 → =.
Q10. Continue each pattern for the next three terms:
(a) 12, 8, 4, 0, ___, ___, ___ (b) −15, −12, −9, ___, ___, ___ (c) 5, 3, 1, −1, ___, ___, ___.
(a) 12, 8, 4, 0, ___, ___, ___ (b) −15, −12, −9, ___, ___, ___ (c) 5, 3, 1, −1, ___, ___, ___.
(a) subtract 4: −4, −8, −12. (b) add 3: −6, −3, 0. (c) subtract 2: −3, −5, −7.
Q11. A diver starts at the surface (0 m). She descends 18 m, rises 5 m, descends 7 m, rises 10 m. What is her depth at the end?
0 − 18 + 5 − 7 + 10 = −10 m (10 m below surface).
Q12. A book-keeper's ledger shows: credit ₹1200, debit ₹500, credit ₹300, debit ₹700, debit ₹200. Using + for credit and − for debit, find the net balance.
+1200 − 500 + 300 − 700 − 200 = +100 (net credit ₹100).
Chapter Summary
Integers
Whole numbers together with their negatives: …, −3, −2, −1, 0, +1, +2, +3, …. Written as Z.
Number Line
Negatives lie to the left of 0, positives to the right. Extends infinitely both ways.
Opposites
+a and −a are opposite numbers (additive inverses). Their sum is 0.
Order
Right of a number on the number line = bigger. Any positive > 0 > any negative.
Absolute Value
|a| is the distance of a from 0. Always ≥ 0.
Addition
Same signs → add magnitudes, keep sign. Opposite signs → subtract, keep sign of larger magnitude.
Subtraction
a − b = a + (−b). Subtraction is adding the opposite.
Closure
Integers are closed under addition, subtraction, and multiplication (but not division).
Key Terms
Integer • Positive integer • Negative integer • Zero • Number line • Opposite number • Additive inverse • Absolute value • Sign • Closure • Zero pair
Quick-Reference Table
| Operation | a, b same sign | a, b opposite signs |
|---|---|---|
| a + b | Add magnitudes, keep sign | Subtract smaller mag. from larger, take sign of larger |
| a − b | Rewrite as a + (−b), then apply addition rule | Rewrite as a + (−b), then apply addition rule |
Chapter-End Project: Integer Story Board
L6 CreateMaterials: A4 sheet, coloured pens, ruler
Goal: Write and illustrate a short story (8–10 sentences) that uses at least 6 integers — some positive, some negative, some zero — and involves at least 2 operations (addition, subtraction).
- Choose a setting: a mountaineer, a submarine, a bank, an elevator, a temperature diary, a quiz game, etc.
- Write the story with numbers clearly placed (e.g., "She was at +500 m; she descended 200 m to +300 m; it rained and she had to wait…").
- Draw a sketch or a small number line annotating key points.
- Pose 2 questions about your story and compute the answers using integer arithmetic.
- Swap with a friend; try to solve each other's stories.
Assessment: Story is coherent (2), at least 6 integers used correctly (3), at least 2 operations shown (2), diagram clear (2), questions well-posed and answers correct (1). Total 10.
Competency-Based Questions
Scenario: In a school quiz, +5 is awarded for each correct answer, −2 for each wrong answer, and 0 for each unattempted question. There are 30 questions in total. Asha scored +80 with 20 correct answers.
Q1. How many questions did Asha answer wrong, and how many did she leave unattempted?
L3 ApplyMarks from 20 correct = 20 × 5 = +100. So negative contribution = 100 − 80 = 20 → wrong answers × 2 = 20 → 10 wrong. Unattempted = 30 − 20 − 10 = 0.
Q2. Ravi scored −6 in the same quiz with 4 correct answers. How many were wrong and how many unattempted?
L4 AnalyseFrom 4 correct: +20. So negative contribution = 20 − (−6) = 26. Wrong answers × 2 = 26 → 13 wrong. Unattempted = 30 − 4 − 13 = 13.
Q3. Evaluate: can a student get exactly a score of −1 in this quiz? Justify.
L5 EvaluateScore = 5c − 2w, where c = correct, w = wrong. For score = −1: 5c − 2w = −1 → 5c + 1 = 2w → 2w ≡ 1 (mod 5) → w ≡ 3 (mod 5). Try w = 3: 2(3) = 6 → 5c = 5 → c = 1. Valid: 1 correct, 3 wrong, 26 unattempted gives score −1. Yes, achievable.
Q4. Design a new quiz mark-scheme where the maximum possible negative score is exactly −15, assuming 30 questions and no "skip" option. State your penalty per wrong and explain.
L6 CreateIf every question is attempted and all are wrong, penalty × 30 = 15 → penalty per wrong = 0.5 marks. So the scheme: +k correct mark, −0.5 wrong. With k = 2: all right gives +60; all wrong gives −15. Balanced and achievable.
Assertion–Reason Questions
Assertion (A): Integers are closed under subtraction.
Reason (R): For any two integers a and b, a − b is an integer.
Reason (R): For any two integers a and b, a − b is an integer.
(a) Closure under subtraction is exactly the statement in R.
Assertion (A): If \(a + b = 0\) then \(b = -a\).
Reason (R): Every integer has a unique additive inverse.
Reason (R): Every integer has a unique additive inverse.
(a) A has only one inverse, which is −a, so b must equal −a.
Assertion (A): For any integer a, \(|a| \ge 0\).
Reason (R): Absolute value is a distance, and distances are never negative.
Reason (R): Absolute value is a distance, and distances are never negative.
(a) Distance from 0 is at least 0 (equals 0 only when a = 0). R correctly explains A.
Frequently Asked Questions
What is the summary of Chapter 10 The Other Side of Zero?
Chapter 10 introduces integers (positive, negative, zero), places them on the number line, and teaches addition and subtraction using tokens, number-line jumps and sign rules.
How do you solve integer word problems?
Assign positive direction (rise, income, above sea level) and negative to the opposite. Translate the story to an addition or subtraction of integers and apply sign rules.
What is the most common mistake in integer questions?
Forgetting to change the sign when subtracting a negative, comparing negatives wrongly (thinking -7 > -3), and mishandling parentheses like -(-5).
What are properties of integer addition?
Closure, commutativity, associativity, additive identity (0) and additive inverse. Integer addition shares all these with whole-number addition and adds inverses.
How do integers help in later classes?
Class 7 extends to multiplication and division of integers, Class 8 introduces rational numbers and Class 9-10 use integers throughout algebra, coordinate geometry and number theory.
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