Important Questions: CBSE Class 10 Mathematics Chapter 4 Quadratic Equations

Chapter 4 Quadratic Equations appears in Unit 2 (Algebra) of the CBSE Class 10 Mathematics syllabus. Historically, this chapter commands 10-12 marks in the 80-mark theory paper. Expect 1-2 MCQs (1 mark each), one 2-mark question testing solution methods, one 3-mark word problem involving formation and solving of quadratic equations, and a 5-mark case-based or application question that integrates quadratic concepts with real-life scenarios. The NCERT textbook defines the standard form as ax² + bx + c = 0 where a ≠ 0, and covers three primary solution techniques: factorisation, completing the square, and the quadratic formula. Additionally, the discriminant D = b² - 4ac is pivotal for determining the nature of roots. Given the consistent weightage and variety of question types, this chapter is non-negotiable for students targeting above 90 percent in Mathematics.

One-mark questions from Quadratic Equations usually test concept clarity—recognising the standard form, identifying coefficients a, b, c, or determining the nature of roots via the discriminant. CBSE frequently presents an equation and asks if it is quadratic, or gives values of a, b, c and asks for D. Speed and accuracy matter here; practise 20-25 MCQs to cover all permutations. Always verify that a ≠ 0 when deciding if an equation is quadratic. Below are six representative MCQs with concise answer keys. These mirror the difficulty and phrasing seen in recent board papers, including 2023 and 2024 sets. A single mark can make a grade difference, so avoid careless errors in sign or substitution.

Two-mark questions typically ask you to solve a quadratic by factorisation or to find the discriminant and state the nature of roots. CBSE awards 1 mark for correct method setup and 1 mark for the final answer. Always write the standard form first, then proceed step-by-step. Incomplete working risks losing a mark. Below are six worked 2-mark questions with full solutions written as a student would present on the answer sheet. Practise writing these in under 2 minutes each to build exam speed. Remember to verify your factors by expanding back, and always simplify surds or fractions in final answers.

Three-mark questions almost always involve forming a quadratic equation from a real-life situation, then solving it. Common contexts include area problems (length and breadth with given constraints), consecutive integers, and time-speed-distance scenarios. CBSE allocates 1 mark for correct formation, 1 mark for solving, and 1 mark for verifying/rejecting inadmissible roots (e.g. negative dimensions). Write your let-statement clearly, form the equation step-by-step, solve, and conclude with a sentence stating the answer in context. Below are six representative 3-mark word problems with model solutions. Practise translating English statements into algebraic equations; this skill is where most students lose marks.

Five-mark questions introduced from 2021 are typically case-based: a short paragraph describes a real-world scenario (construction, sports, business), followed by 3-4 sub-questions of varying difficulty. Expect one sub-part to form and solve a quadratic, one to find the discriminant or verify roots, and one to interpret the result contextually. Full marks require neat presentation, correct algebra, and a concluding statement. CBSE values the ability to apply mathematics beyond textbook drills. Below are three full case-based questions (5 marks each) with all sub-parts and model answers. Practise these under timed conditions to build confidence for the board exam.

CBSE question-setters draw from a fixed pool of concepts but vary contexts and numerical values each year. Understanding their blueprint helps you anticipate question types. MCQs often test definition recall (standard form, discriminant conditions). Two-mark questions lean on straightforward factorisation or discriminant calculation without word problems. Three-mark questions almost always embed the quadratic in a real-life scenario—look for keywords like 'consecutive', 'area', 'product', 'sum and product of roots' (though roots formula is more common). Five-mark case-studies blend multiple steps: reading data from a table or graph, forming an equation, solving, and interpreting. Since 2021, CBSE has included one case-based question per chapter in the blueprint. Examiners reward clear let-statements, step-by-step algebra, and verification of inadmissible solutions. Negative dimensions, negative time, or non-integer answers where integers are expected must be explicitly rejected in your working to earn full marks.

Even well-prepared students drop 3-4 marks in Quadratic Equations due to recurring errors. Sign mistakes in the quadratic formula are the most frequent: writing -b ± √D all under 2a but forgetting parentheses, leading to wrong order of operations. Another pitfall is incorrect splitting of the middle term during factorisation—students pick factors of c that do not sum to b. Forgetting to check a ≠ 0 when deciding if an equation is quadratic costs MCQ marks. In word problems, neglecting to reject negative or non-integer solutions (when context demands positive integers) loses the interpretation mark. Discriminant errors include computing b² - 4ac with wrong signs or misreading the nature-of-roots table. Writing the final answer without units or context statement in application problems also forfeits marks. Below is a checklist: review it before every mock test and the board exam.

Time management and method selection are critical. In the board exam, you have roughly 1 minute per mark, so a 5-mark question gets 5 minutes. Scan the question: if coefficients are small integers, factorise; if large or with parameters, use the quadratic formula. Write every step: CBSE marking schemes award step marks generously. For MCQs, eliminate obviously wrong options first, then verify by back-substitution if time permits. In word problems, underline the let-statement so the examiner sees your variable clearly. Draw a small diagram for geometry-based questions—it clarifies your own thinking and earns goodwill. Practise 50+ assorted questions under timed conditions; aim to finish the chapter portion in 12-15 minutes during the 3-hour paper. Revision should focus on the discriminant table (memorise the three cases), the quadratic formula (write it ten times until muscle memory sets in), and five standard word-problem templates (area, consecutive numbers, reciprocal sum, Pythagoras, time-speed). Finally, use CBSETUTOR.ai for instant doubt-clearing: upload a photo of any tricky question and get step-by-step solutions in seconds, available 24×7 at ₹999/month for all classes 6-12 with a 3-day free trial.

One week before the board exam, use this checklist to gauge readiness. Can you write the quadratic formula from memory in under 5 seconds? Can you state the three discriminant cases (D > 0, D = 0, D < 0) and their corresponding root natures? Can you factorise x² + 7x + 12, x² - 5x + 6, 2x² - 7x + 3 in under 1 minute each? Can you set up and solve a consecutive-integer product problem in 3 minutes? If any answer is no, revisit that skill with focused practice. Solve at least two full 5-mark case-studies under timed conditions and compare your presentation with the NCERT exemplar or previous years' topper answers. Check your answer sheet for neatness: are let-statements underlined, are steps numbered, is the final answer boxed or highlighted? These cosmetic details signal exam maturity to the evaluator and can tip half-marks in your favour. Finally, simulate a mini-test: pick 1 MCQ, 1 two-mark, 1 three-mark, and 1 five-mark question from this chapter; set a 12-minute timer and solve. If you finish with time to spare and all answers match the key, you are board-ready for Quadratic Equations.

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