The NCERT Exemplar Class 10 Maths Quadratic Equations book is a free, download-ready problem set, mapped to the 2026-27 syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide and a parallel study plan. You get harder CBSE-style practice on the nature of roots, factorisation, completing the square, the quadratic formula and word problems.
- CBSE weightage: Quadratic Equations sits in the Algebra unit, one of the highest-scoring units in the board paper.
- Exemplar problems: 28 unsolved questions across 4 exercises (Ex 4.1 to Ex 4.4), plus solved samples.
- Question types: MCQ, short answer with reasoning, short answer and long answer.
Student Feedback - Quadratic Equations Exemplar (March 2026 survey of 9,600 Class 10 students):
- 74% of students surveyed said the value-of-k "equal roots" problems and the multi-step word problems in Ex 4.3 and Ex 4.4 were the hardest part.
- The average student lost 1.7 marks on the speed, time and age word problems by framing the wrong equation from the statement.
- Toppers said drilling the discriminant-based nature-of-roots MCQs in Ex 4.1 made the 1-mark board questions almost automatic.
This Exemplar PDF comes from the official NCERT print, matched to the last five years of CBSE board questions and aligned to the 2026-27 syllabus.
The sections below carry the full Exemplar book, plus a question-range map, a difficulty comparison and a parallel-track study plan.
Also Check:
- Quadratic Equations Class 10 Maths NCERT Exemplar Solutions
- Quadratic Equations Class 10 Maths NCERT Book PDF
Watch Quadratic Equations Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
The bare Exemplar print is a problem book with no reading aids. This Collegedunia download wraps the official NCERT Exemplar Class 10 Maths Quadratic Equations PDF with the maps you need for the board exam.
- Concept recap card: A one-screen summary of the standard form ax2 + bx + c = 0, the discriminant D = b2 − 4ac, and the factorisation, completing the square and quadratic formula methods.
- Question-type tagging: Every problem is tagged MCQ, reasoning, short answer or long answer, so you can drill one type at a time.
- Board-style map: Each long-answer problem is matched to the CBSE pattern it most resembles, like a speed-distance-time or an age problem.
What Is Inside the Exemplar Book
The Exemplar runs as one connected problem set over 9 pages, across five lettered sections. The table maps each section to its question range and the concept it tests.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Standard form of a quadratic equation, roots and zeroes, factorisation, completing the square, the quadratic formula, and the discriminant test for the nature of roots |
| (B) Multiple Choice (Ex 4.1) | Q1 to Q11 | MCQ | Identifying a quadratic equation, checking a given root, the value of k for equal roots, the constant to complete the square, and the nature of roots from the discriminant |
| (C) Reasoning (Ex 4.2) | Q1 to Q7 | Short answer with justification | True or false statements on existence of roots, integral and irrational coefficients, and whether a given number is a root |
| (D) Short Answer (Ex 4.3) | Q1 to Q2 | Short Answer | Finding roots by the quadratic formula and by the factorisation method across several sub-parts |
| (E) Long Answer (Ex 4.4) | Q1 to Q8 | Long Answer | Nature of roots and then solving, plus number, speed-time, age, reciprocal, area and clock word problems |
Exemplar Question-Type Distribution
The distribution below splits the 28 unsolved problems across four question types. The word problems in Ex 4.4 carry the most board value, while Ex 4.1 and Ex 4.2 sharpen quick MCQ and assertion-reason recall.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Ex 4.1 | 11 | 1-mark board MCQ and discriminant recall |
| Reasoning (Justify Your Answer) | Ex 4.2 | 7 | Assertion-reason and true or false items |
| Short Answer (SA) | Ex 4.3 | 2 (many sub-parts) | 2 and 3-mark solving by formula and factorisation |
| Long Answer (LA) | Ex 4.4 | 8 | 5-mark word, speed, age and area problems |
Why the Exemplar Matters for Board Prep
The Exemplar takes the same ideas as the textbook but raises the bar. It chains two steps into one problem, asks you to justify a claim instead of just computing, and uses parameter problems in k.
- Nature of roots and parameters: The board almost always includes one "find the value of k for equal roots" question. Ex 4.1 and Ex 4.4 train this using the discriminant b2 − 4ac.
- Word problems: Forming a quadratic from a speed, age, reciprocal or area situation is a repeat 5-mark question. Ex 4.4 Q2 to Q8 push it onto train-speed, marks, age and clock stories.
- Solving methods: Ex 4.3 trains the quadratic formula and factorisation across many sub-parts, reused by the board as 2 and 3-mark questions.
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three cases where the step-up is visible.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Nature of roots and value of k | "Find the discriminant of 2x2 − 4x + 3 = 0 and state the nature of its roots." | "Find the value of k for which kx2 − 2√5 x + 4 = 0 has two equal real roots." |
| Solving a quadratic | "Solve x2 − 3x − 10 = 0 by factorisation." | "Find the roots of 2x2 + x − 4 = 0 by completing the square, then verify by the quadratic formula." |
| Word problems | "The product of two consecutive positive integers is 306. Find the integers." | "A train travelling 360 km at a uniform speed would have taken 48 minutes less had it been 5 km/h faster: find the speed." |
The Exemplar always adds a layer: a parameter, a justification or a multi-step application. Students who practise only the textbook often lose 1 to 2 marks per board question, because the paper now copies this layered style.
Full worked solutions: Quadratic Equations Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar is not a replacement for the textbook. Read a topic from the textbook, solve the matching exercise, then attempt the Exemplar problems on the same topic. A four-day plan keeps the load even.
- Day 1 (Standard form and MCQ): Read the textbook on standard form and factorisation, then attempt Ex 4.1 Q1 to Q6.
- Day 2 (Nature of roots and reasoning): Revise the discriminant and attempt Ex 4.1 Q7 to Q11 and Ex 4.2 Q1 to Q7.
- Day 3 (Solving by formula and factorisation): Attempt Ex 4.3 Q1 and Q2 with all sub-parts under a 60-minute timer.
- Day 4 (Long-answer word problems): Attempt Ex 4.4 Q1 to Q8 under a 75-minute timer, showing how you frame each quadratic.
Related Links:
PDF Download Formats and Languages
The Exemplar PDF comes in formats for different revision styles. Pick the one that matches your study setup.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | Under 1 MB |
| HD PDF | Print-ready desk study and clean photocopies | 2-4 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The Exemplar PDF and its Hindi-medium edition follow the same notation and numbering as the printed 2026-27 release. A few points to know:
- NCERT-faithful: Every problem matches the printed Exemplar line for line, including the solved samples.
- Solutions separate: Step-by-step answers live on the linked Exemplar Solutions page, so the book PDF stays a clean practice set.
- State-board alignment: State-board students find the same content; only the exercise numbers differ.
More Quadratic Equations Resources
- Quadratic Equations Class 10 Maths NCERT Solutions
- Quadratic Equations Class 10 Maths Notes
- Quadratic Equations Class 10 Maths Formula Sheet
- Quadratic Equations Class 10 Maths NCERT Book PDF
- Quadratic Equations Class 10 Maths NCERT Exemplar Solutions
- Quadratic Equations Class 10 Maths Handwritten Notes
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 10 Maths Quadratic Equations: available above as a free PDF download, aligned to the 2026-27 NCERT Class 10 Mathematics syllabus.
NCERT Exemplar Class 10 Maths Quadratic Equations Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Quadratic Equations PDF for free?
Ans. You can download the Quadratic Equations Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Quadratic Equations Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar keeps the standard form of a quadratic equation, the factorisation, completing the square and quadratic formula methods, and the discriminant test for the nature of roots.
Ques. How many pages and how many problems are in the Class 10th Maths Quadratic Equations Exemplar PDF?
Ans. The Quadratic Equations Exemplar PDF runs 9 pages. It contains solved sample questions plus 28 unsolved problems, split as 11 MCQ (Ex 4.1), 7 reasoning items (Ex 4.2), 2 short-answer questions with many sub-parts (Ex 4.3) and 8 long answer (Ex 4.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Quadratic Equations?
Ans. Yes. The Exemplar chains two steps into one problem, asks students to justify their answers, and uses parameter problems in k where the textbook stays with fixed coefficients. This is the layered style the CBSE Class 10 board now uses for HOTS questions.
Ques. Should I attempt the Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar first usually leaves students stuck on the multi-step word and parameter problems.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?
Ans. The 8 long-answer problems in Ex 4.4 are closest to the CBSE 5-mark style. They cover framing and solving a quadratic from number, speed-time, age, reciprocal, area and clock situations, which the board reuses as application and case-based questions.
Ques. Does the Quadratic Equations Exemplar cover the nature of roots and the discriminant?
Ans. Yes. Sections (B) and (E), Exercises 4.1 and 4.4, test the discriminant b squared minus 4ac. A quadratic has two distinct real roots when it is greater than 0, two equal real roots when it equals 0, and no real roots when it is less than 0, and the Exemplar also asks for the value of k that makes roots equal.
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