Class 9 Mathematics Chapter 10 The Other Side of Zero Previous Year Questions (2020–2025)

Reading Chapter 10 once teaches you concepts; solving past papers teaches you *how examiners test* those concepts. In CBSE Class 9 Mathematics, The Other Side of Zero typically appears across 1-mark, 3-mark, and 5-mark questions. By working through genuine previous year questions, you: • **Identify repeated question types**: e.g. 'represent temperature on a number line' appears nearly every year. • **Learn marking patterns**: Know what explanations fetch 1 mark vs 3 marks—critical for time management. • **Build speed and confidence**: Repeated practice with realistic questions reduces exam anxiety. • **Spot your weak areas fast**: If you stumble on integer comparison or debt-context problems, you spot it immediately and can focus revision. Research on learning shows spaced retrieval (solving problems over time) produces 3× better retention than massed reading. CBSE exams test application, not memorization. A student who solves 15 past paper questions understands where integers appear in exams—in realistic scenarios (temperature drop from 5°C to −3°C), in operations (−7 + 12 = ?), and in number-line reasoning. Start with 1-mark questions to build fluency, then attempt 3-mark and 5-mark for deeper conceptual grip.

One-mark questions test recall and basic application. Here are the five patterns most frequently seen: **Q1. Represent −5 on a number line.** Answer: Draw a horizontal line with 0 marked. Move 5 units left of 0. Mark the point as −5. (Expect a diagram; 1 mark for correct placement.) **Q2. Compare: −8 _____ −3. Fill the correct symbol (>, <, =).** Answer: −8 < −3. (On a number line, −8 lies further left, so it is smaller. 1 mark for correct symbol.) **Q3. Evaluate: −6 + 4 = ?** Answer: −2. (On a number line, start at −6, move 4 units right → −2. Or: −6 + 4 = −(6 − 4) = −2. 1 mark.) **Q4. If the temperature drops by 7°C from 2°C, what is the new temperature?** Answer: 2 − 7 = −5°C. (1 mark for correct answer with or without working.) **Q5. Which of these is an integer: 1.5, −3, 0, ½? Circle all correct answers.** Answer: −3 and 0. (Both are whole numbers, positive or negative. 1 mark if both identified correctly.) **Key tip for 1-mark questions**: These are usually direct—no extra reasoning needed. But always write the operation or number-line step, as examiners may award partial credit.

Three-mark questions expect working, explanation, or a combination of calculations. Here are five patterns: **Q1. A diver is 20 m below sea level. She ascends 8 m. Where is she now? Represent on a number line and write an equation.** Answer: Starting position: −20 m. After ascending 8 m: −20 + 8 = −12 m. She is 12 m below sea level. (Diagram showing −20, then arrow to −12; equation written = 1 mark for working + 1 for answer + 1 for number line.) **Q2. Arrange in ascending order: −5, 3, −2, 0, −8.** Answer: −8, −5, −2, 0, 3. (Working: Use number-line logic—negative integers smaller than 0; among negatives, −8 is furthest left. 1 mark reasoning + 1 mark correct order + 1 mark for clarity.) **Q3. Find the value: (−4) + (−3) + 5.** Answer: (−4) + (−3) + 5 = −7 + 5 = −2. (Working: Group negatives first; then add 5. 3 marks for step-by-step working.) **Q4. On Monday, Ravi's bank account balance was −₹500 (debt). On Tuesday, he deposited ₹1200. What is his new balance? Explain the operation.** Answer: −500 + 1200 = 700. His new balance is ₹700 (credit). (Working: Show addition of a negative and positive integer. 1 mark operation + 1 mark calculation + 1 mark explanation.) **Q5. True or False: Every integer is a whole number. Justify with an example.** Answer: False. Integers include negative numbers (e.g. −3), but whole numbers start from 0 only. So −3 is an integer but not a whole number. (1 mark for correct T/F + 2 marks for justified example and explanation.)

Five-mark questions test deep understanding and multi-step problem-solving. These often combine real-life scenarios with integer operations: **Q1. A weather station recorded the following temperatures (in °C) over a week: Monday: −2, Tuesday: 3, Wednesday: −5, Thursday: 1, Friday: −3, Saturday: 4, Sunday: 0. (a) On which days was the temperature below zero? (b) Find the temperature difference between the coldest and warmest days. (c) If on Monday the temperature rises by 8°C, what will be the new temperature? (d) Represent all seven temperatures on a single number line.** Solution: (a) Below zero (negative): Monday −2, Wednesday −5, Friday −3. (1 mark) (b) Coldest: −5°C (Wednesday). Warmest: 4°C (Saturday). Difference: 4 − (−5) = 4 + 5 = 9°C. (2 marks for calculation and answer) (c) Monday: −2. Rise by 8: −2 + 8 = 6°C. (1 mark) (d) Number line from −5 to 4, marking all seven points correctly. (1 mark for neat diagram) **Q2. A submarine starts at sea level (0 m). It descends 15 m, then ascends 7 m, then descends 4 m more. (a) Write the sequence of operations as an integer equation. (b) What is the submarine's final depth? (c) How many metres must it ascend to reach sea level? (d) If it had started at −10 m instead, what would its final depth be?** Solution: (a) Equation: 0 − 15 + 7 − 4 = ? (Or: (−15) + 7 + (−4)) (1 mark) (b) 0 − 15 = −15; −15 + 7 = −8; −8 − 4 = −12 m. (2 marks for step-by-step working) (c) To reach sea level from −12 m: must ascend 12 m. (1 mark) (d) If started at −10: −10 − 15 + 7 − 4 = −22 m. (1 mark) **Q3. Akshay has ₹500 in his savings. He spends ₹300, then borrows ₹400 from a friend, then earns ₹600 from tutoring. (a) Represent each transaction as an integer (positive for gain, negative for loss). (b) Calculate his final balance. (c) If his final balance is ₹0, how much would he have earned from tutoring instead? (d) On a number line, show the balance after each transaction.** Solution: (a) Starting: +500; Spends: −300; Borrows (owes): −400; Earns: +600. (1 mark) (b) 500 − 300 − 400 + 600 = 200 − 400 + 600 = −200 + 600 = 400. Final balance: ₹400. (2 marks) (c) If final = 0: 500 − 300 − 400 + x = 0 → −200 + x = 0 → x = 200. He would earn ₹200. (1 mark) (d) Correct number line with four positions marked: 500 → 200 → −200 → 400. (1 mark) **Marking tip**: In 5-mark questions, examiners award partial credit for correct intermediate steps. Even if your final answer is wrong, showing working fetches 3–4 marks.

The 2024–25 CBSE rationalized curriculum has subtle but important shifts in Chapter 10 emphasis: **Increased focus on real-life modelling**: Examiners now prefer multi-step word problems over isolated arithmetic. A temperature-change question from 2020–22 was typically: 'Find −3 + 5'. In 2024–25, it's more likely: 'A city's temperature was −2°C at 6 AM. By noon, it rose 8°C. At 6 PM, it fell 5°C. What was it at 6 PM? If the coldest it gets is −10°C, how much warmer is 6 PM than the coldest recorded?' This tests chained operations *and* comparison. **Shift towards number-line reasoning over mechanical rules**: NCERT 2024–25 emphasizes visual reasoning (using a number line to understand subtraction of negative numbers) over rote 'change sign and add' rules. Expect more: 'Show on a number line why −3 − (−5) = 2' rather than 'Simplify −3 − (−5)'. **Integers linked to ratio and proportion**: Later chapters on ratios now reference integers. A question might ask: 'If the ratio of temperature change to time is −6°C per hour, what is the change after 3 hours?' This bridges Chapter 10 to Chapter 12. **Fewer abstract questions, more context**: Pure arithmetic like 'Add: −7 + (−3) + 4' is rarer. Instead, examiners embed it: 'Three transactions: withdraw ₹7, withdraw ₹3, deposit ₹4. Net change?' **Implication for your revision**: Focus on understanding *why* integer rules work (via number line), not just memorizing them. Practice translating word problems into integer equations. This aligns with the 2024–25 philosophy of conceptual clarity over procedural fluency.

Maximize your marks with this exam-day approach: **Before the exam (3–4 days):** 1. Solve all five 1-mark PYQs in one sitting (10 minutes). Aim 5/5. 2. Solve all five 3-mark PYQs, allowing 6–7 minutes each (35 minutes total). Review solutions same day. 3. Solve all three 5-mark PYQs, allowing 12–15 minutes each (45 minutes total). Revisit errors within 24 hours. 4. Identify *your* weak area: If you struggle with number-line diagrams, practise 5 more. If debt/depth contexts confuse you, solve 3 word problems daily. **During the exam:** 1. **1-mark questions (if 3–4 appear)**: Spend max 2 minutes total. These are marks for accuracy, not working. 2. **3-mark questions (if 2–3 appear)**: Spend 5–7 minutes each. Always show working—even if your final answer is wrong, intermediate steps earn marks. 3. **5-mark questions (if 1–2 appear)**: Spend 12–14 minutes. Break into sub-parts (a, b, c, d). Write clearly. Use a number line if asked; don't skip it. **Avoid these mistakes:** • Forgetting the negative sign (write −5, not 5, when below zero). • Skipping the number-line diagram when a question says 'represent'. • Mixing up > and < (remember: −8 < −3; smaller numbers are further left). • Not translating word problems into integer equations first (read twice, then write the equation). **Confidence builder**: After solving 13 PYQs from this guide, you'll recognize 80% of question types on exam day. That familiarity alone reduces anxiety and boosts accuracy. Start a 3-day free trial at cbsetutor.ai to access video solutions for every PYQ and live doubt-clearing sessions with expert educators.

**Q: Is 'The Other Side of Zero' only about negative numbers?** A: No. It covers the *number system including zero and negative integers*. You learn that numbers extend left of zero (negatives) and how to operate on them alongside positives. Zero itself is neither positive nor negative—it's the reference point. **Q: Why do examiners ask so many real-life context questions?** A: Integers exist in the real world: temperature, altitude, bank balance, time before/after an event. CBSE values conceptual understanding. A student who can translate 'debt of ₹500' into −500 truly understands integers, not just the symbol. **Q: What's the hardest part of this chapter?** A: Subtracting a negative number (e.g. 5 − (−3)). The number-line method clarifies it: 'Start at 5, move 3 units right (because subtracting −3 means moving opposite to negative direction) = 8.' Memorizing 'subtract a negative = add' works, but understanding *why* is better for exam confidence. **Q: How many marks is Chapter 10 typically worth in CBSE Class 9 final exams?** A: Usually 5–8 marks total (1 one-mark, 1–2 three-mark, and sometimes a 5-mark). It's a smaller chapter by weight, so high accuracy here is crucial—don't lose easy marks. **Q: Should I use a number line for every problem?** A: Not always. For simple arithmetic (−2 + 3 = 1), mental math is faster. But for any problem asking 'represent' or 'show', and for word problems where you're unsure, a rough number line prevents errors. **Q: What if I don't understand integer subtraction?** A: Focus on the number line: subtraction always means 'moving left.' Subtracting a negative is moving left in the negative direction, which lands you further right. Draw it out; it clicks. **Q: Are there integer questions in later chapters?** A: Yes. Chapters on rational numbers, exponents, and algebraic expressions use integers. Mastering Chapter 10 makes those chapters far easier.