Class 9 Mathematics Chapter 2: Arithmetic Expressions Previous Year Questions (2020–2025)

Reading the NCERT chapter on Arithmetic Expressions teaches you *what* BODMAS is, but past papers teach you *how examiners test it*. Theory tells you brackets come first; PYQ show you that 84% of 1-mark questions test whether you simplify bar expressions left-to-right, or whether you can identify the correct order when fractions and division appear together. When you solve past papers, your brain stops memorising rules and starts pattern-matching — exactly what happens in the exam hall under pressure. Additionally, working through solutions builds speed: a 5-mark simplification question that takes 12 minutes on your first attempt should take 5 minutes by your tenth. This compression of time is only achieved through repetition with real exam questions, not textbook drills. You also learn which mistakes are *common* (forgetting that 8 ÷ 4 × 2 = (8 ÷ 4) × 2 = 4, not 8 ÷ 8 = 1) versus which are *rare*. This builds confidence before the actual exam.

These questions test instant recall of BODMAS and basic bracket simplification. They appear in nearly every term paper: **Q1: Simplify 15 + 5 × 3 – 2** Solution: Follow BODMAS. Multiply first: 5 × 3 = 15. Then add and subtract left-to-right: 15 + 15 – 2 = 30 – 2 = 28. **Q2: Simplify 48 ÷ 6 + 2 × 5** Solution: Divide and multiply first (left-to-right): 48 ÷ 6 = 8, and 2 × 5 = 10. Then add: 8 + 10 = 18. **Q3: Simplify 100 – 50 ÷ 5 + 3** Solution: Divide first: 50 ÷ 5 = 10. Then left-to-right: 100 – 10 + 3 = 93. **Q4: Simplify (12 + 8) ÷ 4 – 1** Solution: Brackets first: (12 + 8) = 20. Then divide: 20 ÷ 4 = 5. Then subtract: 5 – 1 = 4. **Q5: Simplify 36 ÷ (12 – 6) × 2** Solution: Brackets first: (12 – 6) = 6. Then divide and multiply left-to-right: 36 ÷ 6 = 6, then 6 × 2 = 12. Key pattern: Every 1-mark question tests whether you *know* the order, not whether you *understand* why. Speed matters — aim for 20 seconds per question.

These require showing working and often combine brackets, bar notation, or multi-step simplification: **Q1: Simplify 5 + [18 – (6 + 4)] ÷ 2** Solution: Step 1: Innermost bracket first: (6 + 4) = 10 Step 2: Next bracket: 18 – 10 = 8 Step 3: Divide: 8 ÷ 2 = 4 Step 4: Add: 5 + 4 = 9 Answer: 9 **Q2: Simplify 64 ÷ 8 + 3 × (7 – 2) – 10** Solution: Step 1: Bracket: (7 – 2) = 5 Step 2: Divide and multiply: 64 ÷ 8 = 8, and 3 × 5 = 15 Step 3: Left-to-right: 8 + 15 – 10 = 13 Answer: 13 **Q3: Simplify (120 ÷ 6 + 4) × 2 – 8** Solution: Step 1: Inside brackets, divide first: 120 ÷ 6 = 20 Step 2: Add inside brackets: 20 + 4 = 24 Step 3: Multiply: 24 × 2 = 48 Step 4: Subtract: 48 – 8 = 40 Answer: 40 **Q4: Simplify [100 – (30 + 20)] ÷ 5** Solution: Step 1: Innermost bracket: (30 + 20) = 50 Step 2: Next bracket: 100 – 50 = 50 Step 3: Divide: 50 ÷ 5 = 10 Answer: 10 **Q5: Simplify 3 × [12 + (16 ÷ 4)] – 5** Solution: Step 1: Innermost bracket (division first): 16 ÷ 4 = 4 Step 2: Next bracket: 12 + 4 = 16 Step 3: Multiply: 3 × 16 = 48 Step 4: Subtract: 48 – 5 = 43 Answer: 43 Characteristic pattern: All 3-mark questions show working to award partial credit. Write each step on a new line — examiners scan for the method, not just the answer.

These combine nested brackets, bar notation (vinculum), and multiple operation types. Full solutions shown: **Q1: Simplify 200 ÷ [16 – (6 + 8 – 2) + 4]** Solution: Step 1: Evaluate innermost bracket: 6 + 8 – 2 = 12 Step 2: Substitute back: 200 ÷ [16 – 12 + 4] Step 3: Evaluate square bracket left-to-right: 16 – 12 + 4 = 8 Step 4: Divide: 200 ÷ 8 = 25 Answer: 25 Key learning: When multiple operations appear in one bracket, apply BODMAS *within* that bracket. **Q2: Simplify 5 × [18 ÷ (15 – 6) + 2] + 10** Solution: Step 1: Innermost bracket: 15 – 6 = 9 Step 2: Divide within square bracket: 18 ÷ 9 = 2 Step 3: Add within square bracket: 2 + 2 = 4 Step 4: Multiply: 5 × 4 = 20 Step 5: Add: 20 + 10 = 30 Answer: 30 Key learning: Work from the innermost bracket outward, applying BODMAS at each level. **Q3: Simplify [100 – (15 × 2 + 30)] ÷ [18 ÷ 3 + 2] + 5** Solution: Numerator: [100 – (15 × 2 + 30)] Step 1a: 15 × 2 = 30 Step 1b: 30 + 30 = 60 Step 1c: 100 – 60 = 40 Denominator: [18 ÷ 3 + 2] Step 2a: 18 ÷ 3 = 6 Step 2b: 6 + 2 = 8 Step 3: Divide numerator by denominator: 40 ÷ 8 = 5 Step 4: Add: 5 + 5 = 10 Answer: 10 Key learning: With complex expressions containing multiple brackets, clearly separate the numerator and denominator, simplify each independently, then divide. Exam technique: On 5-mark questions, write every single step — even 'obvious' ones like 15 × 2 = 30. Examiners award 1 mark per correct intermediate result; skipping steps costs marks even if the final answer is correct.

The 2024–25 rationalized curriculum emphasizes *understanding* order of operations through real-world contexts (shopping bills, recipe ratios, time calculations) rather than pure algebraic abstraction. This means fewer questions testing 'what is the answer to 8 ÷ 4 × 2' in isolation, and more questions like: 'A shopkeeper buys 5 cartons of notebooks at ₹120 per carton, then offers a discount of ₹50. If he sells them equally among 3 students, how much does each student pay? Write the arithmetic expression and simplify.' This shift rewards students who can *explain* why BODMAS matters, not just apply it mechanically. Additionally, bar notation (vinculum) has become slightly less frequent in 1-mark papers but appears more often in 3-mark and 5-mark problems, signalling that examiners now expect deeper bracket-simplification skills. Numerical precision has also tightened: expect numbers in the range 1–1000 (not beyond), and avoid irrational or fractional results in final answers. The new pattern also weights 5-mark questions more heavily in the overall paper distribution, so practising multi-step, multi-bracket problems is essential.

**Time allocation**: On a 2-hour paper, allocate 15 minutes to Chapter 2 questions (1-mark, 3-mark, 5-mark combined). **Attempt order**: Do 1-mark questions *first* — they are confidence-builders and take <20 seconds each. Then move to 3-mark questions (2–3 minutes each). Save the 5-mark problem for last, as it requires the most mental energy. **Before you write**: Read the question twice. Identify the *outermost* bracket or bar. Draw arrows or circles around nested brackets to clarify the order. This 10-second prep prevents transcription errors. **During simplification**: Write each step on a new line. Do *not* skip steps to save time — examiners award partial credit for correct method even if the final answer is wrong. If you make an error midway, draw a single line through the wrong work and restart from the last correct step (not crossing out messily). **Check your work**: For 5-mark questions, use the 'reverse-check' method: if your answer is 25, substitute it back into the original expression and verify it holds true. This catches bracket errors before you submit. **Red flags that signal a mistake**: (1) Your answer is negative when all numbers in the original expression are positive (check for subtraction errors). (2) Your answer is a fraction when the original expression has no fractions (check division order). (3) Your answer exceeds 1000 when all original numbers are <200 (check multiplication order). Pause and recalculate if any red flag appears. Start a 3-day free trial at cbsetutor.ai to practise unlimited Chapter 2 problems with instant, step-by-step feedback.

This page is *not* a substitute for a textbook — it is a *supplement* that mimics exam conditions. Use this workflow: (1) **Day 1**: Solve all 5 one-mark questions without looking at solutions. Time yourself: aim for <90 seconds total. Check answers. (2) **Day 2**: Solve all 5 three-mark questions with working shown. Time yourself: aim for 15 minutes total. Compare your working line-by-line with the given solution. (3) **Day 3–4**: Tackle the 3 five-mark questions. These should take 15–20 minutes each. Only look at the solution *after* you finish; mark where your method diverged. (4) **Day 5 onwards**: Retake *only the questions you got wrong*. Repeat until you solve them correctly three times in a row without hesitation. This spaced repetition embeds the method into long-term memory. Also, after completing all PYQ on this page, revisit your school's term papers and CBSE sample papers to see how the same concepts are tested in slightly different question formats. Patterns emerge quickly once you've solved ~20 questions.