Important Questions: CBSE Class 8 Mathematics Chapter 2 Linear Equations in One Variable

Linear Equations in One Variable is a core algebra chapter in CBSE Class 8 Mathematics, introduced in NCERT textbook Chapter 2. The chapter builds on the equation-solving skills from Class 7, advancing to equations where variables appear on both sides and multi-step word problems. In the annual CBSE exam, this chapter typically contributes 8-10 marks out of the 80-mark Mathematics paper. Questions appear as 1-mark MCQs in Section A, 2-3 mark short-answer problems in Section B, and 5-mark case-based or word problems in Section C. The 2024 and 2025 sample papers from CBSE show increased emphasis on application-based questions, where students must form equations from real-world scenarios (discounts, geometry, age puzzles) and solve them systematically. Mastery of transposition rules, sign conventions, and verification is essential.

One-mark questions test quick recall and conceptual clarity. CBSE Class 8 Mathematics papers usually include 2-3 MCQs from this chapter in Section A. These questions assess basic equation-solving steps, identification of linear equations, and simple transposition. Students must answer in under 30 seconds per question. The key is to eliminate obviously wrong options and verify the answer mentally by substitution. Practise these daily to build speed and confidence, as every mark counts in competitive school rankings and scholarship exams.

Two-mark questions require one or two clear steps of working. CBSE examiners award 1 mark for the correct method and 1 mark for the final answer. Common formats include solving simple equations, transposing terms, and verifying solutions. Students should write each step on a new line to demonstrate logical progression. Partial marks are awarded if the method is correct but a calculation error occurs, so always show your working even under time pressure. These questions typically take 2-3 minutes each in an exam setting.

Three-mark questions examine equations where the variable appears on both sides of the equal sign, requiring careful transposition and simplification. CBSE mark schemes allocate 1 mark for correctly bringing variables to one side, 1 mark for simplifying constants, and 1 mark for the final answer with verification if asked. Students must remember that transposing a term changes its sign: a positive term becomes negative when moved across the equals sign, and vice versa. These questions appear in Section B of the paper and test systematic algebraic manipulation. Always collect like terms methodically to avoid errors.

Five-mark questions are application-driven, testing the ability to translate real-world scenarios into linear equations. CBSE now includes case-based questions where a short passage describes a situation — pricing, measurements, journeys, age relationships — followed by sub-questions. Marks are distributed as: 1 mark for identifying the variable and forming the equation, 2 marks for solving, 1 mark for interpreting the solution in context, and 1 mark for verification or a follow-up calculation. Students should define the variable clearly (e.g. 'Let the present age be x years'), write the equation from the problem statement, solve step-by-step, and state the answer in words. These questions distinguish A+ students from the rest, so daily practice of 2-3 word problems is essential.

CBSE question-setters follow specific patterns when designing questions for Linear Equations in One Variable. In Section A, MCQs test direct formula recall and one-step solutions. Section B short-answer questions (2-3 marks) mix procedural solving with verification, often asking students to 'solve and check'. Section C long-answer questions (5 marks) are always contextual: age problems, number puzzles, geometry (perimeter, area), commerce (profit, discount), or motion (distance, time). From 2023 onwards, CBSE introduced competency-based questions where a single real-life scenario spawns 3-4 sub-questions of varying difficulty. Examiners also favour questions requiring students to 'form the equation' separately before solving, testing conceptual understanding, not just mechanical calculation. To score full marks, students must write clear statements defining the variable, show all transposition steps, and interpret the numerical answer back into the problem's language (e.g. 'Hence, the son's present age is 10 years').

Even bright students lose 2-3 marks per exam on avoidable errors in linear equations. The most frequent mistake is incorrect sign change during transposition: when moving +7 from the left side to the right, students forget it becomes -7, writing +7 instead. Another common pitfall is mishandling brackets, especially in equations like 3(2x - 1) = 9; students expand to 6x - 1 instead of 6x - 3. Calculation errors in fractional equations (forgetting to find the LCM before clearing denominators) are rampant. In word problems, students often assign the variable to the wrong quantity or misread 'more than' as addition when subtraction is needed. Verification is skipped due to time pressure, costing the final mark. To avoid these errors, practise writing each transposition step explicitly, double-check sign changes, use brackets carefully, and always substitute the solution back into the original equation. Spending 20 seconds on verification can secure that crucial last mark.

Beyond the questions above, students aiming for 95+ percent should solve these additional problems, which mirror CBSE's trickier formats and higher-order thinking requirements. These questions integrate multiple concepts — combining like terms, nested brackets, and multi-step word problems. They are designed to take 4-6 minutes each, simulating exam pressure. After solving, check your answer by substitution and compare your method with the model solution. Regular timed practice of such questions builds the speed and accuracy needed to finish the 80-mark paper in 3 hours with time to review. CBSETUTOR.ai offers a 24×7 AI tutor where students can upload a photo of any question from this chapter and receive instant step-by-step solutions, explanations of common mistakes, and similar practice problems. At just ₹999 per month for all subjects and classes 6-12, it is an affordable alternative to expensive tuition centres, accessible on any smartphone. A 3-day free trial lets students experience the platform before committing.

Success in CBSE Class 8 Mathematics exams demands not only conceptual clarity but also exam strategy. For linear equations, always start by reading the question twice to identify what is given and what is asked. In word problems, underline key phrases ('more than', 'less than', 'ratio', 'times') and translate them into algebraic symbols before forming the equation. Allocate time wisely: spend 1 minute per MCQ, 2-3 minutes per 2-3 mark question, and 5-7 minutes per 5-mark question. If stuck, move on and return later; never leave a question unattempted — even partial working earns marks. Write neatly and box the final answer so the examiner spots it immediately. In equations with fractions, always clear denominators first by multiplying through by the LCM to avoid messy arithmetic. For verification, use a pencil to substitute the solution in the margin; if LHS ≠ RHS, recheck your steps before finalising. Finally, revise this chapter by solving previous years' CBSE question papers and NCERT exemplar problems, which expose you to the full range of question styles and difficulty levels.