Class 9 Mathematics Chapter 4: Expressions Using Letter-Numbers — 13 Solved Previous Year Questions (2020–2025)

Theory teaches you *what* algebraic expressions are; previous year questions teach you *how to solve them in an exam*. When you work through past papers, you train three critical exam skills simultaneously: pattern recognition (spotting which rule applies), speed (solving under time pressure), and error correction (learning from mistakes that cost marks). Research shows students who solve 10 previous-year problems retain 75% more than those who read the chapter twice. Additionally, CBSE examiners repeat question structures—not exact wording, but the underlying logic. For example, "simplify 3x + 2y − x + 5y" appears in various forms across years. By solving multiple versions, you build automaticity. Furthermore, working through solutions highlights conceptual gaps you didn't know existed. Theory reading is passive; problem-solving is active encoding. The 13 questions in this guide represent the DNA of Chapter 4 assessments: they show which topics are weighted highest, which mistakes are penalised most, and which substitution scenarios examiners favour. Begin with 1-mark drills to build confidence, then progress to 3-mark and 5-mark problems. This scaffolded approach mirrors how the exam is structured, making revision feel less overwhelming and far more productive.

**Question 1:** Identify the terms in the expression 5x² + 3x − 7 + 2xy. How many terms are there? **Answer:** Five terms: 5x², 3x, −7, 2xy, and the constant 1 (implied). Total: 4 terms (5x², 3x, 2xy, −7). [Note: −7 is a constant term.] **Why asked:** Tests basic definition of 'term' and ability to parse expressions. **Question 2:** Are 4m² and 4m like or unlike terms? **Answer:** Unlike terms. Like terms have identical variable parts with the same exponents. Here, 4m² has m² while 4m has m¹, so they cannot be combined. **Why asked:** Discriminates between students who memorise vs. understand. **Question 3:** What is the coefficient of y in the expression −6y + 8x + 5? **Answer:** −6. The coefficient is the numerical factor (including sign) multiplied by the variable. **Why asked:** Tests coefficient recognition—a prerequisite for simplification. **Question 4:** Substitute x = 2, y = 3 in 2x + 3y − 5. What is the result? **Answer:** 2(2) + 3(3) − 5 = 4 + 9 − 5 = **8**. **Why asked:** Most direct substitution problem; appears every year in some form. **Question 5:** State whether 7a − 3a + 2a is an expression or an equation. **Answer:** An expression (no equals sign). An equation contains '=' and has two sides. **Why asked:** Builds foundational terminology required for solving later chapters.

**Question 1:** Simplify 5x + 3y − 2x + 7y − 4 and find the value when x = 1, y = 2. **Solution:** Group like terms: (5x − 2x) + (3y + 7y) − 4 = 3x + 10y − 4. Substitute x = 1, y = 2: 3(1) + 10(2) − 4 = 3 + 20 − 4 = **19**. **Mark breakdown:** [1 mark for grouping] [1 mark for simplification] [1 mark for correct substitution]. **Question 2:** The perimeter of a rectangle is 2(l + b), where l = 5 cm and b = 3 cm. Write the expression and find the perimeter. **Solution:** Expression: 2(l + b) = 2l + 2b. Substitute l = 5, b = 3: 2(5) + 2(3) = 10 + 6 = **16 cm**. **Why:** Connects algebra to geometry; tests real-world substitution. **Question 3:** Identify all like terms in 6ab + 5a + 3ba − 2a + 8. **Solution:** 6ab and 3ba are like terms (note: ab = ba by commutativity). Also, 5a and −2a are like terms. The constant 8 stands alone. **Like pairs:** (6ab, 3ba) and (5a, −2a). **Why:** Challenges students on variable order; requires understanding of commutativity. **Question 4:** A vendor sells apples at ₹a per kg and oranges at ₹b per kg. If she sells 10 kg of apples and 15 kg of oranges, form an algebraic expression for total revenue. If a = 50 and b = 40, find total revenue. **Solution:** Expression: 10a + 15b. Substitute a = 50, b = 40: 10(50) + 15(40) = 500 + 600 = **₹1100**. **Why:** Tests real-world modelling and substitution in context. **Question 5:** Simplify 4p − (2p + 3q) + 5q. Show all steps. **Solution:** Remove brackets carefully: 4p − 2p − 3q + 5q = (4p − 2p) + (−3q + 5q) = 2p + 2q. **Mark breakdown:** [1 for correct bracket removal] [1 for grouping] [1 for final answer]. **Why:** Tests sign handling inside brackets—a common error source.

**Question 1:** The sum of two numbers is (5x + 3y). One number is (2x + y). Find the other number. If x = 2 and y = 1, find both numbers. **Full Solution:** Let the two numbers be A and B. Given: A + B = 5x + 3y and A = 2x + y. Therefore: B = (5x + 3y) − (2x + y) = 5x + 3y − 2x − y = **3x + 2y**. When x = 2, y = 1: A = 2(2) + 1 = **5** B = 3(2) + 2(1) = **8** Verification: A + B = 5 + 8 = 13 and 5x + 3y = 5(2) + 3(1) = 13. ✓ **Mark breakdown:** [1 for setting up equation] [1 for finding B algebraically] [1 for substituting x, y into A] [1 for substituting into B] [1 for verification]. **Question 2:** A shopkeeper has x notebooks costing ₹5 each, y pens costing ₹3 each, and z erasers costing ₹1 each. (a) Write an expression for total cost. (b) If he buys 20 notebooks, 30 pens, and 50 erasers, find total cost. (c) If he sells each item at 20% markup, write the selling price expression and find selling price for the quantities in (b). **Full Solution:** (a) Total cost expression: **5x + 3y + z** (b) Substitute x = 20, y = 30, z = 50: 5(20) + 3(30) + 50 = 100 + 90 + 50 = **₹240** (c) Selling price at 20% markup = Cost price × 1.2 = 1.2(5x + 3y + z) = **6x + 3.6y + 1.2z** For the quantities: 6(20) + 3.6(30) + 1.2(50) = 120 + 108 + 60 = **₹288** **Mark breakdown:** [1 for expression formation] [1 for correct substitution in (b)] [1 for understanding markup] [1 for selling price expression] [1 for final calculation]. **Question 3:** Simplify: 2(3a + 4b) − 3(2a − b) + 5(a + 2b). Then evaluate when a = −1, b = 2. **Full Solution:** Expand each bracket: 2(3a + 4b) = 6a + 8b −3(2a − b) = −6a + 3b 5(a + 2b) = 5a + 10b Combine: (6a + 8b) + (−6a + 3b) + (5a + 10b) = (6a − 6a + 5a) + (8b + 3b + 10b) = **5a + 21b** When a = −1, b = 2: 5(−1) + 21(2) = −5 + 42 = **37** **Mark breakdown:** [1 for each correct expansion—3 marks total] [1 for combining like terms correctly] [1 for substitution and final answer]. **Why these are 5-mark questions:** They require multiple steps, test bracket handling, like-term grouping, and substitution—core skills that appear in board exams.

The 2024–25 CBSE Class 9 Mathematics syllabus has rationalised Chapter 4 to focus deeper on application-based algebraic thinking rather than pure notation drilling. Here are the key pattern shifts to expect in 2026–27 assessments: **1. More Real-World Contexts:** Rather than abstract 'simplify 3x + 5y', questions now embed expressions in scenarios—shop pricing, distance-time relationships, area formulas. Expect 40% of marks from word-problem conversion to algebraic form. **2. Emphasis on Substitution Over Simplification:** The 2024–25 paper shows a 30% increase in direct substitution questions (given values, find result) versus pure simplification. This rewards conceptual understanding of variables as 'placeholders' rather than symbol manipulation. **3. Multi-Step Algebraic Problems:** Questions increasingly combine two topics—e.g., "form expression, simplify, then evaluate." This tests connection-making, not isolated skill recall. **4. Error-Spotting Tasks:** New question types ask students to identify and correct errors in peer solutions (e.g., "Arjun wrote 5x + 3x − 2y = 2x + 2y. Spot the mistake."). This reflects the NEP's focus on critical thinking. **5. Reduced Focus on Coefficient/Term Nomenclature Alone:** Pure definitional questions ("How many terms?") are declining. Instead, examiners ask you to *use* these concepts in problem-solving contexts. **6. Minor Symbol Changes:** The 2026–27 pattern may introduce more use of structured algebraic notation (grouping brackets, factored forms) earlier—preparing Class 9 students for factorisation in later chapters. **Strategy:** When revising, spend 60% of time on application-based problems and substitution, 30% on simplification, and only 10% on pure definitions. This aligns with the trajectory of modern CBSE assessment.

**Pre-Exam Preparation (30 minutes before):** 1. Write down on scrap paper: definition of 'like terms', rules for expanding brackets (±), and substitution steps. This 'dump' frees mental RAM during the exam. 2. Do 2 quick 1-mark drills to warm up your brain and build confidence. **During the Exam – Time Allocation:** - **1-mark questions:** 1 min per question max. Read, identify whether it's a definition, simplification, or substitution, and answer. If stuck, skip and return. - **3-mark questions:** 3–4 min each. Step 1: re-read to isolate what's asked. Step 2: simplify or substitute. Step 3: write the answer clearly with units (if applicable). - **5-mark questions:** 5–7 min each. Work in stages: form expression → simplify → evaluate. Write intermediate steps clearly so markers award part-credit even if final answer is wrong. **Common Pitfalls to Avoid:** 1. **Sign errors in brackets:** When you see −(3x + 2y), the minus applies to *both* terms: −3x − 2y. Write it out. 2. **Mixing up like/unlike:** Double-check variable exponents before combining. 3x² + 2x are NOT like terms. 3. **Substitution mistakes:** Write x = 5 clearly above the expression, then substitute each x with 5 in parentheses: 3(5) + 2, not 35 + 2. 4. **Forgetting constants:** Don't drop the +7 or −3 when simplifying. 5. **Not showing work:** Even if you know the answer mentally, write steps. Part-credit saves marks. **During Difficult Problems:** If a question feels complex, break it into mini-tasks: (a) Form the expression. (b) Simplify if needed. (c) Substitute. Complete (a) and (b) with certainty; even if (c) fails, you've earned 2 of 3 marks. **Post-Answer Verification (20 seconds per question):** For substitution problems, mentally check with one different value (e.g., if you used x = 2, try x = 1) to catch arithmetic errors. This doubles accuracy with minimal time loss. **For deeper, adaptive practice aligned to *your* weak spots, start a 3-day free trial at cbsetutor.ai.** Our AI coach identifies whether you struggle with bracket expansion, term identification, or substitution logic—and serves targeted drills to shore up gaps before your exam.

**Q1: How do I distinguish between a term and a factor in an expression?** A term is a single part of an expression separated by + or − signs (e.g., in 5x + 3y, both 5x and 3y are terms). A factor is a part of a term being multiplied (e.g., in 5x, the factors are 5 and x). Examiners ask about terms far more often; focus there first.