Get the Latest Sample Paper for Class 10 Maths with Solutions in PDF Format

Sample paper class 10 maths with solution PDF for board exam preparation. Download the latest CBSE sample papers with detailed solutions and improve your score.

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Question: What is the value of x if 2x + 5 = 15? Answer: x = (15 - 5) / 2 = 5

Question: If a number is doubled and increased by 7, it becomes 25. What is the number? Answer: Let the number be x. 2x + 7 = 25. Solving, x = 9.

Question: Find the value of x in the equation 3x - 4 = 2x + 1. Answer: x = 5.

Question: The sum of two consecutive numbers is 29. What are the numbers? Answer: The numbers are 14 and 15.

Question: A number when subtracted from twice itself gives 12. Find the number. Answer: The number is 12.

Geometry

Question: A triangle has sides 3 cm, 4 cm, and 5 cm. Is it a right-angled triangle? Answer: Yes, it follows the Pythagorean theorem.

Question: The perimeter of a square is 40 cm. Find its side length. Answer: Side length = 40 / 4 = 10 cm.

Question: A circle has a radius of 7 cm. Find its diameter. Answer: Diameter = 2 × 7 = 14 cm.

Question: If two angles of a triangle are 50° and 60°, find the third angle. Answer: Third angle = 180° - (50° + 60°) = 70°.

Question: Find the area of a rectangle with length 12 cm and width 5 cm. Answer: Area = 12 × 5 = 60 cm².

Mensuration

Question: A cube has a side length of 4 cm. Find its volume. Answer: Volume = 4 × 4 × 4 = 64 cm³.

Question: The radius of a cylinder is 3 cm and height is 7 cm. Find its volume. Answer: Volume = π × 3 × 3 × 7 = 63π cm³.

Question: A rectangular box has dimensions 10 cm, 8 cm, and 5 cm. Find its volume. Answer: Volume = 10 × 8 × 5 = 400 cm³.

Question: Find the perimeter of a circle with a radius of 14 cm. Answer: Perimeter = 2π × 14 = 28π cm.

Question: The base of a triangle is 8 cm, and its height is 6 cm. Find its area. Answer: Area = 1/2 × 8 × 6 = 24 cm².

Trigonometry

Question: If sin A = 1/2, find the value of angle A. Answer: A = 30°.

Question: If cos A = 0, what is the value of A? Answer: A = 90°.

Question: If tan A = 1, find the angle A. Answer: A = 45°.

Question: If sin 30° = 1/2, find cos 30°. Answer: cos 30° = √3/2.

Question: If the hypotenuse of a right-angled triangle is 10 cm and one side is 6 cm, find the other side. Answer: The other side is 8 cm.

Statistics & Probability

Question: What is the median of the numbers 4, 8, 10, 12, 14? Answer: The median is 10.

Question: Find the mean of 3, 6, 9, 12, 15. Answer: Mean = (3+6+9+12+15) / 5 = 9.

Question: A coin is tossed. What is the probability of getting heads? Answer: 1/2.

Question: A die is rolled. What is the probability of getting a number greater than 4? Answer: 2/6 or 1/3.

Question: The numbers 2, 4, 6, 8, and 10 have a mode of? Answer: No mode, as no number repeats.

Coordinate Geometry

Question: Find the distance between (3, 4) and (6, 8). Answer: Distance = 5 units.

Question: Find the midpoint of the line segment joining (2, 3) and (6, 7). Answer: Midpoint = (4, 5).

Question: What is the equation of a line passing through (2, 3) with slope 2? Answer: y - 3 = 2(x - 2).

Question: Find the slope of the line passing through (1, 2) and (3, 6). Answer: Slope = 2.

Question: The x-axis is also called? Answer: The horizontal axis.

Quadratic Equations

Question: Solve x² - 5x + 6 = 0. Answer: x = 2 or x = 3.

Question: Solve x² - 9 = 0. Answer: x = ±3.

Question: The roots of x² - 4x + 4 = 0 are? Answer: x = 2, 2.

Question: If a quadratic equation has a discriminant of 0, how many roots does it have? Answer: One root.

Question: Solve x² - 2x - 8 = 0. Answer: x = 4 or x = -2.

Linear Equations

Question: Solve 2x + 3 = 7. Answer: x = 2.

Question: Find x if 3x - 9 = 0. Answer: x = 3.

Question: The solution of x - 5 = 10 is? Answer: x = 15.

Question: If 4x + 8 = 16, find x. Answer: x = 2.

Question: Solve 5x - 10 = 15. Answer: x = 5.

These questions cover major topics in Class 10 Maths and provide a good foundation for practice. Hope this helps!

Best Indian Books for Class 10 Maths Sample Papers with Solutions

Here is a list of some of the best Indian books for Class 10 Maths sample papers with solutions. These books are highly recommended for students preparing for their board exams as they provide quality questions, detailed solutions, and exam-oriented practice.

1. Oswaal CBSE Sample Question Papers Class 10 Mathematics

Author: Oswaal Editorial Board
Publication: Oswaal Books
Content: This book includes previous years’ question papers, CBSE sample papers, and chapter-wise revision notes. It also provides concept clarity and self-assessment tools.

2. Arihant CBSE All in One Mathematics for Class 10

Author: Arihant Experts
Publication: Arihant Publications
Content: Contains detailed explanations, sample papers, and chapter-wise exercises. It follows the latest CBSE syllabus and provides tips for quick problem-solving.

3. Educart CBSE Class 10 Mathematics Sample Papers

Author: Educart Experts
Publication: Agrawal Group of Publications
Content: Includes 10+ sample papers with detailed explanations, concept-based questions, and marking scheme analysis.

4. MTG 10 Sample Papers for CBSE Mathematics

Author: MTG Editorial Board
Publication: MTG Learning Media
Content: Focuses on concept-building with stepwise solutions. Covers all typologies of questions and board exam patterns.

5. Xam Idea Mathematics Class 10

Author: Xam Idea Editorial Board
Publication: VK Global Publications
Content: Features board-style sample papers, competency-based questions, HOTS (Higher Order Thinking Skills) problems, and answer keys.

6. Together With CBSE Sample Papers Mathematics

Author: Rachna Sagar Experts
Publication: Rachna Sagar
Content: Covers blueprint-based sample papers, case study-based questions, and step-by-step solutions.

7. RD Sharma Class 10 Mathematics Sample Papers

Author: RD Sharma
Publication: Dhanpat Rai Publications
Content: Provides a mix of simple and challenging problems with detailed solutions. Helpful for both CBSE and state board students.

8. Super 20 Sample Papers Mathematics for CBSE Class 10

Author: Super 20 Editorial Team
Publication: Super 20 Publications
Content: Covers 20 well-researched sample papers with difficulty-level grading and stepwise solutions.

9. Evergreen CBSE Self-Study Sample Papers Mathematics

Author: Evergreen Publications Experts
Publication: Evergreen Publications
Content: Includes solved and unsolved sample papers, board-based exam questions, and NCERT exemplars.

10. Kundra & Bawa CBSE Sample Papers Class 10 Mathematics

Author: Kundra & Bawa
Publication: MBD Group
Content: Offers structured practice with concept-based solutions, objective-type questions, and reasoning-based problems.

11. S. Chand’s CBSE Sample Papers Mathematics Class 10

Author: S. Chand Experts
Publication: S. Chand Publications
Content: Contains NCERT-based questions, case-study problems, and step-by-step solutions.

12. Disha 10 CBSE Sample Papers Mathematics

Author: Disha Experts
Publication: Disha Publications
Content: Provides exam-oriented practice questions and detailed answer explanations.

Sample Paper Class 10 Maths with Solution PDF

Mathematics is one of the most crucial subjects for Class 10 students. Preparing well for the board exams requires rigorous practice, and one of the best ways to do that is by solving sample papers with solutions. These papers help students understand the exam pattern, marking scheme, and frequently asked questions.

Why Solve Sample Papers?

Understanding Exam Pattern: Sample papers follow the latest CBSE guidelines and give students a real-time experience of the exam.
Time Management: Practicing within a time limit improves speed and accuracy.
Concept Clarity: Solving a variety of questions helps reinforce concepts.
Error Identification: Analyzing mistakes and correcting them boosts confidence.

Types of Questions in Sample Papers

Objective Type Questions (1 Mark Each)

Includes multiple-choice questions (MCQs), assertion-reason type, and fill-in-the-blanks.
Focuses on quick problem-solving and conceptual understanding.

Short Answer Type Questions (2-3 Marks Each)

Requires brief explanations or calculations.
Based on direct concepts from the NCERT textbook.

Long Answer Type Questions (4-5 Marks Each)

Involves stepwise solutions, logical reasoning, and problem-solving skills.
Includes geometry-based, algebraic, and application-based questions.

Case Study & Competency-Based Questions

These are real-life application-based problems.
Tests students’ analytical and decision-making abilities.

Best Books for Sample Paper PDFs

Several publishers provide high-quality sample paper books with solutions in PDF format. Some of the best options include Oswaal Books, Educart, MTG, Arihant, and Xam Idea. These books cover all possible question types with detailed solutions.

How to Use Sample Papers Effectively?

Start with NCERT Problems: Ensure a strong foundation before attempting sample papers.
Solve in Exam-Like Conditions: Set a timer and attempt the paper in one go.
Analyze Mistakes: Review incorrect answers and focus on weak areas.
Revise Key Concepts: Regular revision of formulas and theorems helps in quick recall.

Benefits of Using Solution PDFs

Step-by-Step Solutions: Helps students understand the correct way to solve problems.
Self-Assessment: Allows students to check their answers and improve.
Saves Time: Provides structured explanations, reducing confusion.

For Class 10 students, practicing from sample paper books with solutions is a smart way to prepare for the board exams. These books provide an in-depth understanding of concepts, exam trends, and the best strategies to score well.