Comprehensive Sample Paper for Class 10 Maths 2023-24 with Detailed Solutions

Sample paper class 10 maths 2023-24 with solutions to help students practice and improve their exam preparation for better results in the upcoming board exams.

Sample Paper Class 10 Maths 2023-24 with Solutions: Questions and Answers

Here are sample questions and answers for Class 10 Maths 2023-24 to help students prepare effectively for their exams.

Question 1:

What is the sum of the interior angles of a triangle?

Answer: The sum of the interior angles of a triangle is always 180 degrees.

Question 2:

If the radius of a circle is 7 cm, what is its circumference?

Answer: The circumference of the circle is 2 * π * radius. So, the circumference is approximately 44 cm.

Question 3:

Simplify the expression: 5x - 3x + 7.

Answer: The simplified expression is 2x + 7.

Question 4:

Find the area of a rectangle with length 10 cm and width 5 cm.

Answer: The area of the rectangle is length * width, so the area is 50 square centimeters.

Question 5:

Solve for x: 3x + 5 = 20.

Answer: Subtract 5 from both sides to get 3x = 15. Divide both sides by 3 to get x = 5.

Question 6:

Find the value of y when x = 3 in the equation 2x + y = 10.

Answer: Substitute x = 3 into the equation. 2(3) + y = 10, so 6 + y = 10. Subtract 6 from both sides to get y = 4.

Question 7:

What is the volume of a cube with side length 4 cm?

Answer: The volume of the cube is side³, so the volume is 64 cubic centimeters.

Question 8:

How do you find the median of a set of numbers?

Answer: To find the median, arrange the numbers in ascending order and choose the middle number. If there are two middle numbers, average them.

Question 9:

What is the probability of getting an even number when rolling a fair six-sided die?

Answer: The even numbers on a six-sided die are 2, 4, and 6. The probability is 3 out of 6, or 1/2.

Question 10:

Simplify the expression: (2x + 3) - (x - 5).

Answer: Simplify the terms to get x + 8.

Question 11:

What is the Pythagorean theorem?

Answer: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question 12:

If the base of a parallelogram is 8 cm and the height is 5 cm, what is the area?

Answer: The area of the parallelogram is base * height, so the area is 40 square centimeters.

Question 13:

What is the value of 3 raised to the power of 4?

Answer: The value of 3⁴ is 81.

Question 14:

Find the roots of the quadratic equation x² - 5x + 6 = 0.

Answer: Factor the quadratic to get (x - 2)(x - 3) = 0. Therefore, the roots are x = 2 and x = 3.

Question 15:

Solve for x: 2x - 4 = 10.

Answer: Add 4 to both sides to get 2x = 14. Divide by 2 to get x = 7.

Question 16:

If the radius of a sphere is 6 cm, what is its surface area?

Answer: The surface area of a sphere is 4 * π * radius². So, the surface area is approximately 452.39 cm².

Question 17:

What is the difference between a rational and an irrational number?

Answer: A rational number can be expressed as a fraction of two integers, while an irrational number cannot be written as a simple fraction.

Question 18:

Find the length of the hypotenuse of a right triangle with legs of lengths 6 cm and 8 cm.

Answer: Use the Pythagorean theorem. The hypotenuse is √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Question 19:

If the angle of elevation to the top of a building is 30 degrees and the distance from the observer to the building is 50 meters, how tall is the building?

Answer: The height of the building can be found using trigonometry. The height = tan(30°) * 50 meters ≈ 28.87 meters.

Question 20:

Solve the system of equations: x + y = 10 and x - y = 2.

Answer: Add the two equations to get 2x = 12. So, x = 6. Substitute x = 6 into x + y = 10 to get y = 4.

Question 21:

What is the formula for the area of a triangle?

Answer: The area of a triangle is ½ * base * height.

Question 22:

Simplify: (x² + 2x + 3) - (x² - x + 1).

Answer: The simplified expression is 3x + 2.

Question 23:

What is the formula for the volume of a cylinder?

Answer: The volume of a cylinder is π * radius² * height.

Question 24:

Find the median of the following set of numbers: 3, 5, 8, 2, 9.

Answer: Arrange the numbers in ascending order: 2, 3, 5, 8, 9. The median is 5.

Question 25:

How do you find the slope of a line?

Answer: The slope of a line is the change in y divided by the change in x between two points on the line.

Question 26:

What is the relationship between the sides of a 30-60-90 triangle?

Answer: In a 30-60-90 triangle, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter side.

Question 27:

What is the value of sin(45°)?

Answer: The value of sin(45°) is √2/2 or approximately 0.7071.

Question 28:

What is the area of a sector of a circle with a central angle of 60° and a radius of 10 cm?

Answer: The area of the sector is (θ/360) * π * radius². So, the area is (60/360) * π * 100 = approximately 52.36 square centimeters.

Question 29:

What is the volume of a cone with a radius of 3 cm and a height of 9 cm?

Answer: The volume of a cone is (1/3) * π * radius² * height. So, the volume is approximately 25.13 cubic centimeters.

Question 30:

What is the distance between the points (2, 3) and (6, 7)?

Answer: The distance is √[(x₂ - x₁)² + (y₂ - y₁)²] = √[(6 - 2)² + (7 - 3)²] = √16 + 16 = √32 ≈ 5.66 units.

Question 31:

What is the surface area of a cone with radius 4 cm and slant height 6 cm?

Answer: The surface area of a cone is π * radius * slant height + π * radius². So, the surface area is approximately 125.66 cm².

Question 32:

Find the value of x in the equation 2x + 3 = 15.

Answer: Subtract 3 from both sides to get 2x = 12. Then divide by 2 to get x = 6.

Question 33:

What is the perimeter of a square with side length 5 cm?

Answer: The perimeter of a square is 4 * side length. So, the perimeter is 20 cm.

Question 34:

What is the cosine of 60°?

Answer: The cosine of 60° is 1/2 or 0.5.

Question 35:

Solve the equation: 4x - 7 = 9.

Answer: Add 7 to both sides to get 4x = 16. Divide by 4 to get x = 4.

Question 36:

Find the area of a trapezoid with bases of 8 cm and 12 cm, and a height of 6 cm.

Answer: The area of the trapezoid is ½ * (base₁ + base₂) * height = ½ * (8 + 12) * 6 = 60 square centimeters.

Question 37:

What is the difference between a permutation and a combination?

Answer: A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects without considering the order.

Question 38:

What is the formula for the area of a circle?

Answer: The area of a circle is π * radius².

Question 39:

What is the volume of a sphere with a radius of 5 cm?

Answer: The volume of a sphere is (4/3) * π * radius³. So, the volume is approximately 523.6 cubic centimeters.

Question 40:

If the angles of a quadrilateral are 90°, 80°, 100°, and 90°, what is the fourth angle?

Answer: The sum of the angles of a quadrilateral is 360°. So, the fourth angle is 360° - (90° + 80° + 100° + 90°) = 360° - 360° = 0°. Hence, the fourth angle is 0°.

Question 41:

What is the value of cos(30°)?

Answer: The value of cos(30°) is √3/2 or approximately 0.866.

Question 42:

What is the area of a rhombus with diagonals of lengths 10 cm and 12 cm?

Answer: The area of a rhombus is ½ * diagonal₁ * diagonal₂. So, the area is 60 square centimeters.

Question 43:

Find the length of the diagonal of a square with side length 7 cm.

Answer: The length of the diagonal is √(side² + side²) = √(7² + 7²) = √98 ≈ 9.90 cm.

Question 44:

What is the formula for the surface area of a cylinder?

Answer: The surface area of a cylinder is 2 * π * radius * height + 2 * π * radius².

Question 45:

Solve for x: 5x - 2 = 13.

Answer: Add 2 to both sides to get 5x = 15. Divide by 5 to get x = 3.

Question 46:

What is the relationship between the sides of a 45-45-90 triangle?

Answer: In a 45-45-90 triangle, both legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Question 47:

What is the tangent of 45°?

Answer: The tangent of 45° is 1.

Question 48:

Find the area of a square with a diagonal of 8 cm.

Answer: The area of the square is (diagonal²)/2. So, the area is (8²)/2 = 64/2 = 32 square centimeters.

Question 49:

Solve for y: 3y + 6 = 18.

Answer: Subtract 6 from both sides to get 3y = 12. Divide by 3 to get y = 4.

Question 50:

What is the surface area of a sphere with a radius of 3 cm?

Answer: The surface area of a sphere is 4 * π * radius². So, the surface area is approximately 113.1 cm².

This sample paper includes 50 questions and answers designed to cover a wide range of topics, making it an excellent tool for preparing for your Class 10 Maths exams in 2023-24.

Top Indian Books for Class 10 Maths 2023-24 with Solutions

Mathematics for Class 10 by R.D. Sharma (Dhanpat Rai Publications)
This book provides a comprehensive set of sample papers with solutions, covering every important concept needed for the Class 10 Maths exam. It includes detailed explanations and numerous practice questions, making it perfect for revision and practice.

Xam Idea Mathematics Class 10 by Xam Idea (Xam Idea Publications)
Known for its systematic approach, this book offers a wide range of sample papers and model test papers that align with the current curriculum. It covers all chapters and provides step-by-step solutions to enhance problem-solving skills.

Oswal Publishers - Sample Papers Class 10 Maths by Oswal Publishers (Oswal Publishers)
This book offers a variety of sample papers that match the latest CBSE guidelines. With a special emphasis on previous year questions and a wide array of questions with answers, it allows students to practice effectively.

Together with Mathematics Class 10 by Rachna Sagar (Rachna Sagar Publications)
This book includes well-structured sample papers and model tests along with detailed solutions. The book focuses on increasing the student’s understanding of fundamental concepts with practical applications.

Arihant All in One Class 10 Maths by Arihant Experts (Arihant Publications)
Arihant’s "All in One" series provides a rich collection of sample papers with detailed solutions. This book ensures that students have ample opportunities to practice various types of questions, including MCQs, short-answer, and long-answer questions.

RD Sharma Mathematics Class 10 by R.D. Sharma (Dhanpat Rai Publications)
This well-established book is perfect for deep diving into Class 10 Mathematics concepts. It is packed with examples, exercises, and sample papers to help students reinforce their learning.

S. Chand’s Mathematics Class 10 by Dr. R.S. Aggarwal (S. Chand Publishing)
This book is a great guide for practice with its carefully curated sample papers that test students on all important concepts. The book is detailed and covers all CBSE topics, including additional practice tests.

Mathematics for Class 10 by R.S. Aggarwal (S. Chand Publications)
This textbook by R.S. Aggarwal is one of the most recommended books for Class 10. It contains a good number of practice questions and sample papers that are well-suited for both the exam preparation and conceptual clarity.

Target Publications - Mathematics Class 10 by Target Publications (Target Publications)
This book provides comprehensive sample papers and their solutions. The content is presented in a structured manner that helps students in better understanding and preparation for the board exams.

Career Point - Sample Papers Class 10 Maths by Career Point (Career Point Publications)
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Kumon Mathematics Class 10 by Kumon (Kumon Publications)
Kumon’s Mathematics book for Class 10 emphasizes building a strong foundation and includes an extensive set of problems that range from basic to advanced levels. It offers sample papers with solutions to enhance practical understanding.

Sample Papers for Class 10 Mathematics by Lakhmir Singh & Manjit Kaur (S. Chand Publications)
This book provides sample papers along with their answers. It focuses on all the critical areas of Class 10 mathematics and gives detailed explanations of solutions.

Mathematics Sample Papers Class 10 by M.L. Aggarwal (M.L. Aggarwal Publications)
A reliable and extensive collection of sample papers with solutions, this book focuses on various question types, helping students to excel in both theoretical and practical aspects of mathematics.

Mathematics Class 10 by Cengage Learning (Cengage Learning India)
Cengage Learning provides an excellent set of sample papers and solutions. It also covers a wide array of question types and promotes critical thinking, problem-solving, and application-based learning.

C.B.S.E. Sample Papers Class 10 Mathematics by Full Marks (Full Marks Publications)
This book includes a variety of sample papers with detailed explanations and solutions. It also includes some model question papers that adhere to the latest exam patterns.

Mathematics for Class 10 by S.K. Gupta & Anubhuti Gangal (S.K. Gupta Publications)
The book provides ample practice questions, including sample papers. It helps students practice the theoretical concepts and apply them in real-life scenarios with solutions.

Mathematics Class 10 by M. Tyra (MTG Learning Media)
Known for offering complete practice and sample papers, this book provides various types of problems along with solutions. It follows the latest syllabus and examination patterns.

V.K. Mehta’s Class 10 Mathematics by V.K. Mehta (V.K. Mehta Publications)
This book offers multiple practice sets with well-explained solutions, designed for both revision and practice. It helps to improve problem-solving speed and accuracy.

Mathematics Sample Papers Class 10 by S. K. Jaiswal (Bharati Bhawan Publications)
This book includes different types of sample papers with answers that provide a good variety of questions covering all the topics that are essential for the Class 10 exam.

Learnwell Mathematics Class 10 by Learnwell Publishers (Learnwell Publications)
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Sample Paper Class 10 Maths 2023-24 with Solutions: Preparing for Success

Mathematics can often feel like a daunting subject for Class 10 students, especially with the pressure of the board exams. However, practicing sample papers with solutions is one of the most effective ways to enhance exam preparation. Sample papers for Class 10 Maths 2023-24 are designed to simulate the real exam experience and can help students get familiar with the question format, time management, and key areas that need focus.

One of the key advantages of using sample papers is the exposure to a wide variety of problems. From algebra to geometry, and from trigonometry to statistics, sample papers cover a comprehensive range of topics that are essential for the exam. They give students the opportunity to practice both easy and challenging questions, helping them build confidence.

Incorporating sample papers into daily study routines not only boosts students’ problem-solving abilities but also reinforces the concepts learned throughout the academic year. By solving these papers, students can identify their strengths and weaknesses, allowing them to allocate time for additional practice where needed. Solutions provided alongside the papers ensure that students can review their answers, understand their mistakes, and learn the correct approaches to solving problems.

Another benefit of working with sample papers is that they enable students to familiarize themselves with the latest exam patterns. Sample papers are usually designed according to the current CBSE syllabus, ensuring that students practice the type of questions they are likely to encounter on the actual exam. Many sample papers also include questions based on real-life applications, helping students appreciate the practical value of mathematical concepts.

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To further enhance preparation, students should review their mistakes and reattempt the questions they struggled with. By doing this, they can refine their problem-solving techniques and improve their accuracy. Furthermore, practicing with a variety of sample papers ensures that students are not caught off guard by unexpected questions or difficult topics.

In conclusion, sample papers for Class 10 Maths 2023-24 with solutions are invaluable tools for exam preparation. They provide students with ample practice, allow them to identify key areas for improvement, and help them build confidence in their mathematical abilities. When used effectively, sample papers are sure to play a pivotal role in helping students achieve success in their board exams.