CBSE Class 10 Maths Standard 2021-22 Sample Paper with Solutions for Exam Prep

Download the CBSE sample paper for Class 10 Maths Standard 2021-22 with detailed solutions. Improve your exam preparation with this comprehensive guide.

---

---

Prepare for your Class 10 Maths exam with the CBSE Sample Paper 2021-22. This paper, along with its solutions, helps you practice important concepts and get familiar with the exam pattern. Use this resource to improve your problem-solving skills and boost your confidence for the upcoming exams.

CBSE Sample Paper 2021-22 Class 10 Maths Standard with Solutions: Questions & Answers

Sample Questions and Answers:

Question 1:
What is the solution to the quadratic equation x² - 5x + 6 = 0?
Answer:
The factors of the equation are (x - 2)(x - 3). So, the solution is x = 2 and x = 3.

Question 2:
Find the value of x if 3x + 7 = 22.
Answer:
Solving for x, we subtract 7 from both sides: 3x = 15. Now, divide by 3, so x = 5.

Question 3:
What is the perimeter of a rectangle with length 12 cm and breadth 5 cm?
Answer:
The perimeter of a rectangle is given by 2(l + b). Substituting the values, the perimeter is 2(12 + 5) = 34 cm.

Question 4:
If a triangle has sides of length 6 cm, 8 cm, and 10 cm, is it a right-angled triangle?
Answer:
Yes, it is a right-angled triangle because 6² + 8² = 10² (36 + 64 = 100), which satisfies the Pythagorean theorem.

Question 5:
What is the area of a circle with a radius of 7 cm?
Answer:
The area of a circle is given by πr². Substituting the value of r, the area is π(7)² = 154 cm² (approximately).

Question 6:
How do you find the surface area of a cube with side 4 cm?
Answer:
The surface area of a cube is 6 times the area of one side. The area of one side is 4² = 16 cm². So, the surface area is 6 × 16 = 96 cm².

Question 7:
If a car travels 60 km in 1 hour, what is its speed?
Answer:
The speed is distance/time. So, the speed is 60 km/h.

Question 8:
What is the value of the expression (3x + 4) when x = 2?
Answer:
Substituting x = 2, the expression becomes (3(2) + 4) = 6 + 4 = 10.

Question 9:
Solve for y in the equation 5y - 4 = 16.
Answer:
Adding 4 to both sides, 5y = 20. Dividing by 5, y = 4.

Question 10:
What is the sum of the angles in a triangle?
Answer:
The sum of the angles in any triangle is always 180°.

Question 11:
Find the value of x in the equation 2x + 5 = 15.
Answer:
Subtracting 5 from both sides, 2x = 10. Dividing by 2, x = 5.

Question 12:
What is the volume of a cube with side length 3 cm?
Answer:
The volume of a cube is given by side³. So, the volume is 3³ = 27 cm³.

Question 13:
If a cylinder has a radius of 5 cm and a height of 10 cm, find its volume.
Answer:
The volume of a cylinder is πr²h. Substituting the values, the volume is π(5)²(10) = 785 cm³ (approximately).

Question 14:
What is the difference between the highest and lowest numbers in the set 12, 15, 7, 20, 8?
Answer:
The highest number is 20, and the lowest number is 7. The difference is 20 - 7 = 13.

Question 15:
How do you find the mean of the numbers 10, 15, 20, 25?
Answer:
The mean is the sum of the numbers divided by the total count. So, (10 + 15 + 20 + 25) / 4 = 70 / 4 = 17.5.

Question 16:
What is the perimeter of a square with side length 6 cm?
Answer:
The perimeter of a square is 4 times the side length. So, the perimeter is 4 × 6 = 24 cm.

Question 17:
Find the area of a right-angled triangle with base 5 cm and height 12 cm.
Answer:
The area of a right-angled triangle is (1/2) × base × height. So, the area is (1/2) × 5 × 12 = 30 cm².

Question 18:
What is the solution for x in the equation x + 9 = 16?
Answer:
Subtracting 9 from both sides, x = 16 - 9 = 7.

Question 19:
If the base of a parallelogram is 8 cm and the height is 4 cm, find its area.
Answer:
The area of a parallelogram is base × height. So, the area is 8 × 4 = 32 cm².

Question 20:
What is the product of 7 and 9?
Answer:
The product is 7 × 9 = 63.

Top Indian Books for CBSE Sample Paper 2021-22 Class 10 Maths Standard with Solutions

1. RD Sharma Class 10 Mathematics
   Author: RD Sharma
   Publisher: Dhanpat Rai Publications
   This book contains a variety of sample papers with detailed solutions, which are perfect for exam preparation. It covers all the important topics in Class 10 Maths and offers a well-rounded collection of problems to strengthen understanding.

2. Mathematics Class 10 (CBSE) - X
   Author: RS Aggarwal
   Publisher: S Chand & Company
   It provides a large number of practice questions, including sample papers and solutions. The book is ideal for learning various types of questions and strategies, including problem-solving techniques for complex topics like algebra and geometry.

3. Together with Mathematics Sample Papers Class 10
   Author: Together with Team
   Publisher: Together with Publications
   This book offers solved sample papers and question banks designed according to the CBSE syllabus. It includes problems from all chapters, providing a thorough practice experience, especially for revision before exams.

4. Arihant CBSE Mathematics Sample Papers
   Author: Arihant Experts
   Publisher: Arihant Publications
   The book features a collection of sample papers with detailed solutions to guide students. The questions are based on the latest exam pattern, helping students practice different question formats for better exam readiness.

5. Self-Help to CBSE Sample Papers Class 10
   Author: Sandeep Garg
   Publisher: Self-Help Publications
   This book contains various sample papers with solutions, specifically for students seeking focused practice for the final exam. The solutions are explained in an easy-to-understand manner, which helps in reinforcing core concepts.

6. CBSE Most Likely Question Bank Class 10 Maths
   Author: Pradeep Publications
   Publisher: Pradeep Publications
   The question bank features model test papers and the most likely questions for the CBSE exams. It helps students predict the kind of questions that may appear, providing an edge in the final preparation.

7. Mathematics for Class 10 (10th Edition)
   Author: R S Aggarwal
   Publisher: S Chand
   The book includes several solved sample papers and practice tests. It covers a wide range of problems with an emphasis on critical thinking and time management, both essential for performing well in exams.

8. All in One CBSE Sample Papers Class 10
   Author: Vikas Gupta
   Publisher: Oswal Publishers
   This book offers solved sample papers along with additional practice exercises to boost performance. It also includes chapter-wise questions and solutions to address each topic in detail.

9. Xam Idea CBSE Mathematics Class 10 Sample Papers
   Author: Xam Idea Team
   Publisher: Xam Idea Publications
   Featuring sample papers designed to mimic real exam questions, this book provides a strategic approach to preparing for board exams. The solutions help clarify concepts and improve problem-solving abilities.

10. CBSE Mathematics Class 10 Sample Papers with Solutions
    Author: Laxmi Publications
    Publisher: Laxmi Publications
    It offers a wide range of sample questions and provides solutions for all problems, helping students get an in-depth understanding of mathematical concepts. It also includes sample tests for timed practice.

11. MTG CBSE Mathematics Class 10 Sample Papers
    Author: MTG Editorial Board
    Publisher: MTG Learning Media
    This book has a collection of CBSE-style sample papers with an emphasis on conceptual clarity. The solutions are detailed and cover each step involved in solving the questions.

12. Kiran’s CBSE Class 10 Mathematics Sample Papers
    Author: Kiran Prakashan
    Publisher: Kiran Prakashan
    With solved sample papers and model test papers, this book offers a good variety of problems for practice. It is highly recommended for students looking to build their confidence for the exams.

13. Target Publications Class 10 CBSE Mathematics
    Author: Target Publications
    Publisher: Target Publications
    A thorough book with practice papers and solutions that help students improve their accuracy in solving questions. The book follows the CBSE guidelines strictly and includes detailed stepwise solutions.

14. Pearson Mathematics Sample Papers Class 10
    Author: Pearson Education
    Publisher: Pearson India
    Offering a structured approach to solving problems, this book includes a vast collection of sample questions and practice tests. The solutions are designed to enhance problem-solving skills and exam strategies.

15. Manoj Publications Mathematics Sample Paper for Class 10
    Author: Manoj Publications
    Publisher: Manoj Publications
    This book provides solved sample papers and question banks. It covers every chapter with variety, including tough problems, to ensure that students gain enough exposure to the kinds of questions they will face.

16. The Ultimate Guide for Class 10 Mathematics Sample Papers
    Author: Neeraj Kumar
    Publisher: R.L. Publishing
    This book focuses on solving difficult and varied types of questions in Mathematics. It includes practice questions, solutions, and tips to crack board exams efficiently.

17. Success in Mathematics Class 10 Sample Papers
    Author: Success Publications
    Publisher: Success Publications
    It features practice sample papers and solutions with in-depth explanations. The book covers all chapters in the syllabus, offering extensive practice opportunities.

18. Disha Experts CBSE Class 10 Mathematics Sample Papers
    Author: Disha Experts
    Publisher: Disha Publications
    This book contains various sample papers, complete with solutions to help students prepare for exams. It also offers tips for managing time and strategies for attempting exams.

19. CBSE Mathematics Class 10 Sample Papers and Solutions
    Author: Shivam Prakashan
    Publisher: Shivam Prakashan
    It includes model papers, with solutions that break down the problems step by step. The clear explanations make it easier for students to grasp important concepts.

20. Olympiad Success Mathematics Sample Papers for Class 10
    Author: Olympiad Success Team
    Publisher: Olympiad Success
    This book offers a set of advanced practice papers designed for students who want to excel beyond the standard curriculum. It covers not only basic concepts but also focuses on higher-level problems.

The Class 10 CBSE Maths exam is a crucial step in a student’s academic journey. A well-rounded preparation strategy, including consistent practice of sample papers, can significantly impact performance. The CBSE Sample Paper 2021-22 for Class 10 Maths is designed to provide a detailed overview of the exam pattern, question formats, and essential topics. These sample papers not only help students understand what types of questions are likely to appear but also provide them with solutions to reinforce their learning.

Sample papers come in handy for practice as they simulate the actual exam environment. By solving these papers, students get a realistic idea of the level of difficulty, question distribution, and time management skills required. Moreover, solutions provided in these books help students identify where they went wrong and rectify their mistakes.

The CBSE Maths syllabus is vast, covering chapters such as algebra, geometry, trigonometry, statistics, and probability. Each chapter comes with its own set of problem types that need careful practice. For example, algebraic expressions and equations form a substantial part of the exam, with questions ranging from simple equations to quadratic equations. Geometry problems, especially those based on circles, triangles, and coordinate geometry, are another frequent topic in sample papers.

Additionally, trigonometry problems require a strong understanding of the sine, cosine, and tangent ratios. These sample papers usually include questions based on identities and their application in solving problems. Statistics and probability questions focus on concepts such as mean, median, mode, and the basic understanding of probability.

An important feature of these sample papers is the variety of questions they offer. From multiple-choice questions to long-answer problems, the sample papers prepare students for all possible formats. The inclusion of detailed solutions allows students to see the step-by-step process of solving each problem. This reinforces their problem-solving strategies, ensuring they understand the logic behind every solution.

To make the most of the sample papers, students should solve them under exam-like conditions. This practice helps in improving speed and accuracy, which are crucial for managing time during the actual exam. Additionally, students should focus on weak areas and consistently revise challenging topics, making sure they do not leave any stone unturned.

---