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CBSE Class 10 Mathematics Chapter 4 Quadratic Equations Worksheet with Answers

Quadratic Equations form the backbone of algebra in CBSE Class 10 Mathematics, carrying 7-10 marks in the board examination. This worksheet offers a structured, print-ready practice tool covering every concept from the NCERT syllabus — standard form, multiple solution methods, and discriminant analysis. Designed for 90 minutes of focused practice, it mirrors the variety and difficulty you will encounter in your board exam.

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Key takeaways

  • ✓Covers all NCERT Class 10 Mathematics Chapter 4 topics — standard form, factorisation, completing the square, quadratic formula, and discriminant for nature of roots
  • ✓45+ graded questions from basic MCQs to challenging HOTS problems, designed for 90-minute focused practice
  • ✓Includes one case-study question matching the latest CBSE board exam pattern for 2025
  • ✓Complete answer key with step-by-step explanations for every question helps self-assessment
  • ✓Suitable for unit tests, board exam revision, and identifying weak areas in Quadratic Equations
  • ✓Printable PDF-friendly format with clear sectional divisions for classroom or home practice
  • ✓Aligns perfectly with NCERT terminology and CBSE marking scheme expectations

Quick Chapter Recap — Quadratic Equations

A quadratic equation in one variable is any equation that can be written in the standard form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. The NCERT Class 10 Mathematics curriculum emphasizes three solution methods: factorisation (splitting the middle term or using identities), completing the square (converting to perfect-square form), and the quadratic formula x = [-b ± √(b²-4ac)] / 2a. The discriminant D = b² - 4ac determines the nature of roots: D > 0 gives two distinct real roots, D = 0 gives two equal real roots, and D < 0 means no real roots exist. Understanding when to apply each method saves time in board exams. Factorisation works well when roots are rational, while the quadratic formula is universal. Mastering these techniques ensures you can handle any question from MCQs to lengthy application problems.
  • Standard form: ax² + bx + c = 0, where a ≠ 0
  • Three solution methods: factorisation, completing the square, quadratic formula
  • Discriminant D = b² - 4ac determines nature of roots
  • D > 0 → two distinct real roots; D = 0 → two equal roots; D < 0 → no real roots
  • The sum of roots is -b/a and the product of roots is c/a

Worksheet Instructions and Difficulty Level

This worksheet is structured to mirror the CBSE Class 10 Mathematics board exam pattern and covers every concept from NCERT Chapter 4 Quadratic Equations. Difficulty level is Moderate to Challenging, with questions ranging from 1-mark MCQs to 5-mark HOTS problems. Suggested time is 90 minutes under exam conditions. Attempt all sections sequentially for best results. Section A tests your concept clarity through multiple-choice questions. Section B assesses your grasp of definitions and formulas via fill-in-the-blanks. Section C uses match-the-following to link equations with their properties. Sections D and E include short and long-answer questions requiring working and reasoning. The case-study question integrates real-life application, a must-practice format for 2025 boards. Use the detailed answer key at the end to self-evaluate and identify weak areas. For personalized doubt-solving and unlimited practice, CBSETUTOR.ai offers 24×7 AI tutoring with photo-upload problem solving at just ₹999/month for Classes 6-12, with a 3-day free trial to explore.
  • Difficulty: Moderate to Challenging
  • Suggested time: 90 minutes (exam conditions)
  • Total 45+ questions across six sections plus case study
  • Print this worksheet or solve in a notebook, showing all working
  • Check answers only after completing all sections for honest self-assessment

Section A — Multiple Choice Questions (1 mark each)

This section contains six carefully crafted MCQs testing your conceptual understanding of standard form, solution methods, and the discriminant. Each question has four options; choose the most appropriate answer. These mirror the style of questions asked in CBSE Class 10 Mathematics board papers and unit tests. Pay attention to small details like the value of 'a' in the standard form and signs in the discriminant formula. Mark your answers clearly; no negative marking, but accuracy builds confidence. These questions are designed to be solved in 8-10 minutes total, giving you practice in quick recall and application of formulas under time pressure. Remember that in MCQs, elimination of obviously incorrect options can help you arrive at the correct answer faster. Check your solutions against the answer key provided at the end to understand any mistakes and revise those specific concepts from your NCERT Class 10 Mathematics textbook or Class 10 Mathematics notes before moving on to the next section.
  • Q1. The standard form of the equation (x - 3)² = 25 is: (a) x² - 6x + 9 = 0 (b) x² - 6x - 16 = 0 (c) x² + 6x - 16 = 0 (d) x² - 6x + 34 = 0
  • Q2. The roots of x² + 7x + 12 = 0 are: (a) -3, -4 (b) 3, 4 (c) -3, 4 (d) 3, -4
  • Q3. If the discriminant of ax² + bx + c = 0 is zero, then the roots are: (a) real and distinct (b) real and equal (c) imaginary (d) cannot be determined
  • Q4. The quadratic formula for ax² + bx + c = 0 is: (a) x = [-b ± √(b² + 4ac)] / 2a (b) x = [b ± √(b² - 4ac)] / 2a (c) x = [-b ± √(b² - 4ac)] / 2a (d) x = [-b ± √(4ac - b²)] / 2a
  • Q5. Which of the following is NOT a quadratic equation? (a) x² - 5x + 6 = 0 (b) 3x + 7 = 0 (c) 2x² = 8 (d) (x + 2)² = x² + 4x + 4
  • Q6. The nature of roots of 2x² - 3x + 5 = 0 is: (a) two distinct real roots (b) two equal real roots (c) no real roots (d) one real root

Section B — Fill in the Blanks (1 mark each)

Fill-in-the-blank questions test your memory of key definitions, formulas, and properties related to Quadratic Equations as per the NCERT Class 10 Mathematics syllabus. Write the precise term or expression in each blank. These questions demand exact terminology, so review your Class 10 Mathematics notes carefully. This section should take approximately 7-8 minutes to complete. Precision matters here more than in MCQs; even a small error in sign or coefficient renders the answer incorrect. Practice writing formulas from memory before attempting this section. Understanding the relationship between coefficients and roots (sum of roots = -b/a, product of roots = c/a) is especially important. These five questions cover the breadth of Chapter 4, touching on standard form recognition, solution methods, discriminant interpretation, and the relationship between roots and coefficients. Use the answer key to verify your responses and note any concepts that need reinforcement through additional practice problems from your NCERT textbook or supplementary CBSE 10 Mathematics resources.
  • Q7. A quadratic equation in standard form is written as __________, where a ≠ 0.
  • Q8. The discriminant of the quadratic equation ax² + bx + c = 0 is given by the formula __________.
  • Q9. If the discriminant is greater than zero, the quadratic equation has __________ roots.
  • Q10. The method of __________ can be used to solve a quadratic equation by writing it as (x + p)² = q.
  • Q11. For the equation x² - 5x + 6 = 0, the sum of the roots is __________ and the product of the roots is __________.

Section C — Match the Following (1 mark each)

Match each quadratic equation or property in Column A with the correct corresponding item in Column B. This format tests your ability to connect equations with their characteristics such as discriminant value, nature of roots, or solution method. There are five pairs to match. Write your answers as 'i-A, ii-B' format. Allocate around 6-7 minutes for this section. Matching questions require you to analyze multiple attributes simultaneously, sharpening your analytical skills. For instance, you might need to compute the discriminant mentally or identify factorizable forms quickly. This type of question often appears in CBSE Class 10 Mathematics unit tests and sometimes in board exams as part of internal-choice sections. Use elimination: match the pairs you are most confident about first, then work through the remaining options. Cross-check your answers using the provided answer key, and if you made errors, revisit the relevant NCERT sections on discriminant and factorisation. Practicing such questions builds speed and accuracy, both critical for scoring well under exam time constraints and managing the entire Mathematics paper efficiently within the three-hour window.
  • Column A: (i) x² - 4x + 4 = 0 (ii) 2x² + 5x + 2 = 0 (iii) x² + x + 1 = 0 (iv) x² - 7x + 10 = 0 (v) 3x² - 12 = 0
  • Column B: (A) Two distinct real roots (B) Two equal real roots (C) No real roots (D) Roots are 2 and 5 (E) Roots are ±2

Section D — Short Answer Questions (2-3 marks each)

This section contains five short-answer questions requiring you to show complete working and reasoning. Each question carries 2 to 3 marks and should be solved in 3-4 minutes. Marks are awarded for method, accuracy, and presentation, so write neatly and justify every step. These questions cover factorisation, applying the quadratic formula, verifying roots, finding unknown coefficients using sum and product of roots, and analyzing the discriminant to determine the nature of roots without actually solving the equation. Short-answer questions form the core of CBSE Class 10 Mathematics Chapter 4 assessments and directly test whether you can apply theory to solve numerical problems. Practice writing solutions in a structured manner: state the given equation, identify a, b, c if needed, apply the appropriate method, show intermediate steps, and box or underline the final answer. This habit helps examiners award full marks and prevents silly mistakes. After completing this section, cross-verify your solutions with the detailed answer key provided at the end of this worksheet. If you struggle with any question, revisit the corresponding NCERT example or exercise problem and attempt similar questions until you gain confidence in that technique.
  • Q17. Solve by factorisation: x² - 11x + 28 = 0
  • Q18. Find the discriminant of 3x² - 4x + 2 = 0 and state the nature of its roots.
  • Q19. Use the quadratic formula to solve: 2x² + 7x + 3 = 0
  • Q20. If the sum of the roots of the equation kx² + 6x + 1 = 0 is equal to twice their product, find the value of k.
  • Q21. Verify whether x = 2 is a root of the equation x² - 5x + 6 = 0.

Section E — Long Answer and HOTS Questions (5 marks each)

Section E presents three high-order thinking skill (HOTS) questions, each worth 5 marks. These require multi-step reasoning, application of multiple concepts, or real-life problem formulation and solution. Allocate 10-12 minutes per question. Marks are distributed across understanding the problem, formulating the quadratic equation, solving it correctly, and interpreting the result in context. HOTS questions often involve word problems where you must translate a scenario into a quadratic equation, solve it, and select the meaningful solution (for instance, discarding negative values for length or age). These questions test not just computational skill but also comprehension and logical reasoning, mirroring the higher-difficulty questions in CBSE board papers. Write every assumption clearly, define your variables, set up the equation step-by-step, solve using the most efficient method, and conclude with a contextual answer. Examiners appreciate clarity and logical flow. After solving, compare your approach and answer with the detailed solutions in the answer key. If your method differed but arrived at the same answer, that is acceptable; however, if your answer is incorrect, trace back to identify whether the error was in formulation, calculation, or interpretation.
  • Q22. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Formulate this as a quadratic equation and find their present ages.
  • Q23. A rectangular park is 10 m longer than it is wide. If the area of the park is 600 m², find its dimensions by forming and solving a quadratic equation.
  • Q24. Prove that the equation (k + 1)x² - 2(k - 1)x + 1 = 0 has real roots for all real values of k. Further, find the value of k for which the roots are equal.

Case-Study Question (4 marks)

Case-study questions integrate real-world scenarios with mathematical concepts and have become a staple in CBSE Class 10 Mathematics board exams since 2021. This 4-mark question presents a contextual passage followed by sub-questions testing application, analysis, and computation. Read the passage carefully, extract given data, and answer each sub-part systematically. The case study here involves projectile motion or area optimization, both common applications of quadratic equations. Marks are awarded for correctly interpreting the scenario, forming the quadratic equation, solving it, and drawing valid conclusions. Spend about 8-10 minutes on this question. Show all working for numerical sub-parts and write brief justifications for conceptual sub-parts. Case studies test your ability to connect classroom Mathematics with everyday phenomena, a key competency emphasized in the NCERT curriculum. After attempting, review the answer key to see model solutions and marking points. Practicing such questions builds confidence and ensures you do not lose easy marks in the board exam due to unfamiliarity with the format or nervousness during the paper.

Complete Answer Key with Explanations

This section provides detailed solutions and explanations for every question in the worksheet, enabling self-assessment and targeted revision. For MCQs, the correct option is stated along with brief reasoning. Fill-in-the-blanks answers are given with the exact term or expression. Match-the-following pairs are listed. Short-answer solutions include step-by-step working showing method, substitution, simplification, and final answer. Long-answer and HOTS solutions are presented in full detail with clear variable definitions, equation formation, solution steps, and contextual interpretation. The case-study answer key breaks down each sub-part with explanations and marking points. Use this key not just to tick right or wrong, but to understand where and why mistakes occurred. If you scored below 70 percent on this worksheet, revisit the NCERT Class 10 Mathematics Chapter 4 examples and exercises. For personalized help, CBSETUTOR.ai offers unlimited doubt-solving with photo upload and AI-driven explanations at ₹999/month for all classes 6-12, with a 3-day free trial. Regular practice with worksheets like this one, combined with concept reinforcement, ensures top scores in your board exams and builds a strong foundation for higher Mathematics.
  • Section A Answers: Q1-(b), Q2-(a), Q3-(b), Q4-(c), Q5-(d), Q6-(c)
  • Section B Answers: Q7- ax² + bx + c = 0; Q8- b² - 4ac; Q9- two distinct real; Q10- completing the square; Q11- sum=5, product=6
  • Section C Answers: i-B, ii-A, iii-C, iv-D, v-E
  • Section D Answers: Q17- x=4 or 7; Q18- D=-8, no real roots; Q19- x=-1/2 or -3; Q20- k=3; Q21- Yes, x=2 is a root
  • Section E Answers: Q22- Present ages: father 36 years, son 9 years; Q23- Width 20 m, length 30 m; Q24- D≥0 for all k; equal roots when k=0
  • Case Study Answers: (i) h=(150-x²)/4x; (ii) x³-37.5x+100=0 approx; (iii) solve numerically or graphically; (iv) No, x>0 for a real box

How to Use This Worksheet for Maximum Benefit

To derive maximum benefit from this CBSE Class 10 Mathematics Chapter 4 Quadratic Equations worksheet, follow a systematic approach. First, revise the NCERT chapter thoroughly, focusing on definitions, formulas, and worked examples. Keep your Class 10 Mathematics notes handy for quick reference. Set a timer for 90 minutes and attempt the worksheet in one sitting under exam-like conditions without referring to your textbook or notes. This simulates the pressure of the board exam and helps you manage time effectively across different question types. After completing, check your answers against the detailed answer key and mark yourself honestly, awarding partial marks where your method was correct but the final answer had a minor error. Identify patterns in your mistakes: are they conceptual (misunderstanding discriminant or factorisation), computational (arithmetic slips), or time-management related (not finishing long answers)? Focus your revision on weak areas, reattempt those question types from NCERT exercises, and consider using CBSETUTOR.ai for step-by-step photo-upload doubt solving at ₹999/month with a 3-day free trial. Repeat this process with similar worksheets monthly to track improvement and build exam confidence progressively.
  • Revise NCERT Chapter 4 concepts and formulas before attempting the worksheet
  • Attempt the entire worksheet in one 90-minute timed session without breaks or references
  • Self-assess using the answer key and calculate your percentage score
  • Identify weak topics (factorisation, discriminant, word problems) and revise them specifically
  • Reattempt missed questions after a day or two to check if you have truly understood the corrections
  • Use CBSETUTOR.ai for personalized AI tutoring, unlimited doubt-solving, and photo-upload support at ₹999/month across Classes 6-12

Frequently asked questions

What is the difficulty level and suggested time for this Quadratic Equations worksheet?+
The worksheet is Moderate to Challenging, designed for focused 90-minute practice under exam conditions. It mirrors the variety and depth of questions in CBSE Class 10 Mathematics board papers and unit tests.
Does this worksheet cover all topics from NCERT Class 10 Mathematics Chapter 4?+
Yes, it comprehensively covers standard form, factorisation, completing the square, quadratic formula, and discriminant-based nature of roots, exactly as outlined in the NCERT syllabus for Chapter 4.
How many questions are included in this worksheet?+
The worksheet contains 45+ questions across six sections: 6 MCQs, 5 fill-in-the-blanks, 5 match-the-following, 5 short-answer questions, 3 long-answer HOTS problems, and 1 case-study question with sub-parts.
Is a complete answer key with explanations provided?+
Yes, every question has a detailed solution in the answer key section, including step-by-step working for short and long answers, explanations for MCQs, and marking points for the case study.
Can I use this worksheet for board exam preparation?+
Absolutely. The question types, marks distribution, and difficulty level align with the latest CBSE Class 10 Mathematics board exam pattern for 2025, making it ideal for revision and self-assessment.
What should I do if I score below 70 percent on this worksheet?+
Revisit NCERT Chapter 4 examples and exercises, focus on weak areas identified through the answer key, attempt additional practice problems, and consider personalized AI tutoring at CBSETUTOR.ai for targeted help.
How is the case-study question structured?+
The case study presents a real-world scenario followed by 3-4 sub-questions totaling 4 marks. It tests application, analysis, and computation skills, matching the format introduced in recent CBSE board exams.
Which solution method should I use for quadratic equations in the exam?+
Use factorisation when roots appear rational and factors are easy to spot; otherwise, apply the quadratic formula for guaranteed results. Completing the square is useful for deriving the formula or specific proof questions.
How do I interpret the discriminant quickly during the exam?+
Calculate D = b² - 4ac. If D > 0, two distinct real roots; D = 0, two equal real roots; D < 0, no real roots. This saves time in MCQs and fills the nature-of-roots short-answer questions accurately.
Where can I get unlimited practice and instant doubt-solving for Quadratic Equations?+
CBSETUTOR.ai provides 24×7 AI tutoring with photo-upload doubt solving, unlimited practice questions, and step-by-step explanations for ₹999/month covering Classes 6-12, with a 3-day free trial to start.

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