Class 9 Mathematics Chapter 6 Number Play Previous Year Questions (2020–2025)

Reading Chapter 6 notes once teaches you *what* integers are; solving past papers teaches you *how examiners test* them. PYQs reveal patterns: which properties appear most (closure, commutativity under addition vs. subtraction), which mistakes are common (sign errors in division, order of operations), and what depth of explanation scores full marks. When you solve a 5-mark question on negative number applications in real life, you strengthen pattern recognition far more than re-reading a worked example. CBSE examiners set papers to test both conceptual grip and procedural fluency—PYQs are the direct window into that intent. You'll notice that 1-mark questions often ask 'identify the property' rather than 'compute the answer,' while 3-mark questions demand both computation *and* justification. By solving these 13 questions, you'll train yourself to spot these nuances in exam hall, manage time better, and build confidence. This approach is especially valuable for Number Play, where a single misplaced negative sign or forgotten property can collapse a multi-step solution.

One-mark questions in this chapter test quick recall of properties and basic operations. These five represent the most common patterns: **Q1: Which property is illustrated by (–5) + 7 = 7 + (–5)?** Answer: Commutative property of addition. Explanation: Addition of integers is commutative; order does not change the sum. **Q2: Simplify: (–12) ÷ (–3).** Answer: 4. Explanation: Division of two negative integers gives a positive result. **Q3: Is the set of integers closed under division? Yes/No.** Answer: No. Explanation: 5 ÷ 2 = 2.5, which is not an integer. Division does not satisfy closure for integers. **Q4: What is the additive identity for integers?** Answer: 0. Explanation: For any integer a, a + 0 = a. Zero is the additive identity. **Q5: Evaluate: (–8) × (–6).** Answer: 48. Explanation: Multiplication of two negative integers yields a positive product.

Three-mark questions require both correct computation and clear reasoning. These five types appear regularly: **Q1: Verify that (–4) × (5 + 3) = (–4) × 5 + (–4) × 3 and name the property.** Solution: LHS: (–4) × (5 + 3) = (–4) × 8 = –32 RHS: (–4) × 5 + (–4) × 3 = –20 + (–12) = –32 LHS = RHS. Property: Distributive property of multiplication over addition. **Q2: A submarine is at –200 m below sea level. It ascends 50 m, then descends 30 m. What is its final position?** Solution: Initial position: –200 m After ascending 50 m: –200 + 50 = –150 m After descending 30 m: –150 + (–30) = –180 m Final position: –180 m below sea level. **Q3: Using the commutative and associative properties, simplify: (–7 + 8) + (–8) + 7.** Solution: = (–7 + 8) + (–8) + 7 = (–7 + 7) + (8 + (–8)) [Rearranging using commutativity and associativity] = 0 + 0 = 0 **Q4: Check whether 0 ÷ (–9) = 0. Justify your answer.** Solution: 0 ÷ (–9) means we find a number that, when multiplied by (–9), gives 0. (–9) × 0 = 0. Yes, 0 ÷ (–9) = 0. Division of zero by any non-zero integer is zero. **Q5: Arrange in ascending order: –5, 3, 0, –12, 8, –3.** Solution: –12, –5, –3, 0, 3, 8. Explanation: On the number line, negative integers increase (become less negative) from left to right, then zero, then positive integers increase.

Five-mark questions test deeper understanding and multi-step reasoning. These three are exemplary: **Q1: Temperature Change Problem** The temperature in a freezer was –15°C. During a power failure, it rose by 8°C per hour for 3 hours, then fell by 5°C per hour for 2 hours. What was the final temperature? Solution: Initial temperature: –15°C Temperature rise over 3 hours: 8 × 3 = 24°C Temperature after rise: –15 + 24 = 9°C Temperature fall over 2 hours: 5 × 2 = 10°C Final temperature: 9 + (–10) = 9 – 10 = –1°C Answer: –1°C (1°C below freezing point) **Q2: Verify and Explain Using Number Properties** Prove that [–3 × (–2)] × 4 = –3 × [(–2) × 4] and identify the property. Then explain why this property is important in simplifying integer expressions. Solution: LHS: [–3 × (–2)] × 4 = 6 × 4 = 24 RHS: –3 × [(–2) × 4] = –3 × (–8) = 24 LHS = RHS. Property: Associative property of multiplication. Importance: Allows us to regroup factors for easier computation; order of grouping doesn't affect the product. This reduces calculation errors. **Q3: Number Pattern and Rule Discovery** Consider the sequence: –2, –4, –8, –16, … (i) Write the next two terms. (ii) Find the general rule (nth term). (iii) Is this sequence an arithmetic or geometric progression? Justify. Solution: (i) Observe: each term is multiplied by 2. Next two terms: –32, –64. (ii) General rule: aₙ = –2 × 2ⁿ⁻¹ = –2ⁿ (iii) Geometric progression. Justification: The ratio between consecutive terms is constant (= 2). In an arithmetic progression, the common difference between consecutive terms is constant, which is not the case here.

The new CBSE pattern places greater emphasis on *application and reasoning* rather than rote calculation. For Chapter 6: Number Play, this means: **Shift 1: From 'Apply property X' to 'Identify when property X fails.'** Older papers asked: 'Verify the commutative property for 5 + 3.' New papers ask: 'For which operations is commutativity not valid? Give an example and explain.' **Shift 2: Real-world contexts are now mandatory even in 1-mark questions.** You'll see scenarios like 'A business has a loss of ₹5000. If it improves by ₹1200 per month, express its position after 4 months as an integer.' Rather than abstract questions like 'Divide –12 by 3.' **Shift 3: Multi-concept 5-mark questions integrating properties + patterns + applications.** Instead of three separate 5-mark questions, examiners now combine: 'A number pattern involves integers. Write the rule, verify closure under multiplication, and apply it to a real scenario.' **Shift 4: Proof and reasoning gain marks over computation.** Showing 'why' a property holds for all integers (not just one example) is increasingly tested. For instance, proving that (–a) × (–b) = ab using the distributive property, not just computing (–3) × (–5) = 15. Adapting now: Practice writing general proofs, solve context-heavy questions, and always justify your property choices—not just name them.

Time is scarce in exams. Here's a tactical sequence for this chapter: **Step 1: Identify the Operation Type (30 seconds)** Read the question and ask: Is this about addition/subtraction (signs matter most), multiplication/division (product/quotient rule), or properties (commutativity, associativity, distributivity, closure, identity)? Circle the operation. **Step 2: Recall the Relevant Rule (20 seconds)** For addition/subtraction: Keep the sign of the larger number, subtract magnitudes. For multiplication/division: Count negatives (odd = negative, even = positive). For properties: Write the rule you'll verify. **Step 3: Compute Carefully (watch for sign errors) (60–90 seconds)** Use a number line for single-operation questions. For multi-step, work left to right, or use associativity/commutativity to group simpler pairs first. Example: (–5) + 8 + 5 + (–8) → group as [(–5) + 5] + [8 + (–8)] = 0 + 0 = 0 (faster than left-to-right). **Step 4: Justify If Required (60 seconds for 3-mark, 90–120 seconds for 5-mark)** For 1-mark: Answer alone suffices. For 3-mark: State the property and show one verification step. For 5-mark: Prove the property holds, explain why it matters, and apply to the context. **Step 5: Sanity Check (20 seconds)** Does the sign make sense? For (–a) + (positive large number), expect positive. For (–a) × (–b), expect positive. For a ÷ b where |a| < |b|, result magnitude < 1, but still an integer if exactly divisible. **Common Exam Pitfalls to Avoid:** – Forgetting that subtraction is NOT commutative: (–5) – 3 ≠ 3 – (–5). – Mixing up sign rules in division with those in multiplication (same rule, but easy to rush). – Not canceling zeros early in multi-step problems (slows you down). – Writing 'verified' without showing the LHS and RHS computation (loses method marks). Practice these 13 PYQs under 90-minute timed conditions. Aim to attempt all 1-mark questions in 15 minutes, 3-mark in 30 minutes, and 5-mark in 35 minutes. Remaining time: review and fix arithmetic.

Before submitting your answers to these PYQs, tick off this checklist: ☐ **Addition & Subtraction of Integers:** I can add/subtract any two integers, including zero. I correctly apply signs (same sign → add magnitudes and keep sign; different signs → subtract magnitudes and take sign of larger). ☐ **Multiplication & Division Rules:** I recall (negative × negative = positive), (negative × positive = negative), (positive × positive = positive). Division follows the same sign rule. I know 0 ÷ a = 0, but a ÷ 0 is undefined. ☐ **Properties Mastery:** I can identify and verify: Closure, Commutativity (addition, multiplication only), Associativity (addition, multiplication only), Distributive property, Identity elements (0 for addition, 1 for multiplication), and Inverse elements. ☐ **Multi-Step Problems:** I group operations using properties to simplify. I don't panic with negative signs in complex expressions. ☐ **Number Patterns:** I spot arithmetic patterns (constant difference) and geometric patterns (constant ratio). I write the general term (nth term formula) correctly. ☐ **Real-World Context:** I translate loss/debt as negative, profit/gain as positive. I correctly set up and solve word problems with negative integers. ☐ **Presentation:** All my working is shown. I justify my property choices. My final answer is clearly marked and is an integer (or I've stated it's undefined). If you tick fewer than 7, revisit the corresponding NCERT section and re-attempt those PYQs. Confidence in this chapter unlocks success in algebra (Chapter 7–9) because those chapters *assume* mastery of integer operations.