Class 10 WBBSE Math Solution offers detailed step-by-step explanations, practice problems, and tips to help you master the subject for better exam performance.
Class 10 WBBSE Math. These questions and answers will help you prepare well for your exams by offering easy-to-understand explanations without any complex formulas.
1. What is the value of x if 3x + 7 = 16?
To solve this, subtract 7 from both sides:
3x = 16 - 7
3x = 9
Now divide by 3:
x = 9 / 3
x = 3.
2. Find the value of x in the equation 5(x - 4) = 20.
Distribute the 5:
5x - 20 = 20
Now, add 20 to both sides:
5x = 40
Now, divide by 5:
x = 40 / 5
x = 8.
3. A rectangle has a length of 12 cm and width of 5 cm. What is its area?
Area of a rectangle = length × width
Area = 12 cm × 5 cm
Area = 60 cm².
4. A triangle has a base of 8 cm and height of 6 cm. Find the area.
Area of a triangle = 1/2 × base × height
Area = 1/2 × 8 cm × 6 cm
Area = 24 cm².
5. Find the perimeter of a square with a side length of 7 cm.
Perimeter of a square = 4 × side
Perimeter = 4 × 7 cm
Perimeter = 28 cm.
6. What is the volume of a cube with a side length of 4 cm?
Volume of a cube = side³
Volume = 4³
Volume = 64 cm³.
7. Simplify the expression: 4x + 7x.
Combine like terms:
4x + 7x = 11x.
8. Solve for y: 2y - 5 = 9.
Add 5 to both sides:
2y = 9 + 5
2y = 14
Now divide by 2:
y = 14 / 2
y = 7.
9. A circle has a radius of 10 cm. What is its circumference?
Circumference of a circle = 2πr
Circumference = 2 × π × 10 cm
Circumference ≈ 62.83 cm.
10. Find the surface area of a sphere with a radius of 6 cm.
Surface area of a sphere = 4πr²
Surface area = 4 × π × 6²
Surface area ≈ 452.39 cm².
11. If the ratio of two numbers is 3:5, and one number is 15, what is the other number?
Let the other number be x.
3/5 = 15/x
Now, cross-multiply:
3x = 5 × 15
3x = 75
Now divide by 3:
x = 75 / 3
x = 25.
12. Solve the equation: 2x - 3 = 13.
Add 3 to both sides:
2x = 13 + 3
2x = 16
Now divide by 2:
x = 16 / 2
x = 8.
13. What is the area of a circle with a radius of 7 cm?
Area of a circle = πr²
Area = π × 7²
Area ≈ 153.94 cm².
14. Find the roots of the quadratic equation x² - 5x + 6 = 0.
Factor the quadratic equation:
(x - 2)(x - 3) = 0
Set each factor equal to zero:
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3.
15. Solve for a: 4a + 5 = 21.
Subtract 5 from both sides:
4a = 21 - 5
4a = 16
Now divide by 4:
a = 16 / 4
a = 4.
16. A cylinder has a radius of 5 cm and height of 10 cm. What is its volume?
Volume of a cylinder = πr²h
Volume = π × 5² × 10
Volume ≈ 785.40 cm³.
17. What is the simple interest for a principal of Rs. 2000 at a rate of 5% for 3 years?
Simple Interest = (P × R × T) / 100
Interest = (2000 × 5 × 3) / 100
Interest = 300.
18. A train travels at a speed of 60 km/h. How far will it travel in 4 hours?
Distance = Speed × Time
Distance = 60 km/h × 4 hours
Distance = 240 km.
19. Find the average of 10, 15, and 20.
Average = (10 + 15 + 20) / 3
Average = 45 / 3
Average = 15.
20. Simplify the expression: 5x - 3x + 7.
Combine like terms:
5x - 3x = 2x
So, the expression becomes:
2x + 7.
21. Solve for z: 3z + 2 = 11.
Subtract 2 from both sides:
3z = 11 - 2
3z = 9
Now divide by 3:
z = 9 / 3
z = 3.
22. Find the perimeter of a triangle with sides 5 cm, 7 cm, and 9 cm.
Perimeter = sum of the sides
Perimeter = 5 cm + 7 cm + 9 cm
Perimeter = 21 cm.
23. A box has a length of 10 cm, width of 6 cm, and height of 4 cm. What is its volume?
Volume = length × width × height
Volume = 10 cm × 6 cm × 4 cm
Volume = 240 cm³.
24. What is the area of a parallelogram with a base of 10 cm and height of 5 cm?
Area = base × height
Area = 10 cm × 5 cm
Area = 50 cm².
25. Find the hypotenuse of a right triangle with legs 3 cm and 4 cm.
Using Pythagoras' Theorem:
Hypotenuse² = 3² + 4²
Hypotenuse² = 9 + 16
Hypotenuse² = 25
Hypotenuse = √25
Hypotenuse = 5 cm.
26. A bag contains 7 red balls and 3 blue balls. What is the probability of drawing a red ball?
Probability = favorable outcomes / total outcomes
Probability = 7 / (7 + 3)
Probability = 7 / 10
Probability = 0.7.
27. If 4 is added to a number and the result is multiplied by 3, the answer is 24. What is the number?
Let the number be x.
3(x + 4) = 24
Now, divide by 3:
x + 4 = 8
Now subtract 4:
x = 8 - 4
x = 4.
28. Find the area of a rhombus with diagonals of 8 cm and 6 cm.
Area of a rhombus = (diagonal₁ × diagonal₂) / 2
Area = (8 cm × 6 cm) / 2
Area = 48 cm² / 2
Area = 24 cm².
29. Find the mean of the following numbers: 5, 10, 15, 20, 25.
Mean = (5 + 10 + 15 + 20 + 25) / 5
Mean = 75 / 5
Mean = 15.
30. A water tank is in the shape of a cylinder with radius 4 m and height 10 m. What is its capacity?
Volume of a cylinder = πr²h
Volume = π × 4² × 10
Volume ≈ 502.65 m³.
31. What is the square root of 144?
The square root of 144 is 12.
32. If the sum of two numbers is 30 and their difference is 6, what are the numbers?
Let the numbers be x and y.
x + y = 30
x - y = 6
Add the two equations:
2x = 36
x = 18
Now substitute x = 18 into x + y = 30:
18 + y = 30
y = 30 - 18
y = 12.
33. Solve for m: 4m - 2 = 18.
Add 2 to both sides:
4m = 18 + 2
4m = 20
Now divide by 4:
m = 20 / 4
m = 5.
34. What is the circumference of a circle with a diameter of 14 cm?
Circumference = πd
Circumference = π × 14 cm
Circumference ≈ 43.98 cm.
35. A right triangle has legs 8 cm and 15 cm. What is its hypotenuse?
Hypotenuse² = 8² + 15²
Hypotenuse² = 64 + 225
Hypotenuse² = 289
Hypotenuse = √289
Hypotenuse = 17 cm.
36. Find the area of a trapezoid with bases of 10 cm and 8 cm, and a height of 6 cm.
Area = 1/2 × (base₁ + base₂) × height
Area = 1/2 × (10 cm + 8 cm) × 6 cm
Area = 1/2 × 18 cm × 6 cm
Area = 54 cm².
37. What is the value of 2³?
2³ = 2 × 2 × 2 = 8.
38. A man buys an item for Rs. 2000 and sells it for Rs. 2500. What is his profit?
Profit = selling price - cost price
Profit = 2500 - 2000
Profit = Rs. 500.
39. A boat travels 50 km upstream in 5 hours and 50 km downstream in 4 hours. What is the speed of the boat in still water?
Speed of boat in still water = (Speed upstream + Speed downstream) / 2
Speed upstream = 50 km / 5 hours = 10 km/h
Speed downstream = 50 km / 4 hours = 12.5 km/h
Speed of boat in still water = (10 km/h + 12.5 km/h) / 2
Speed of boat in still water = 11.25 km/h.
40. Solve for t: 3t + 4 = 16.
Subtract 4 from both sides:
3t = 16 - 4
3t = 12
Now divide by 3:
t = 12 / 3
t = 4.
41. What is the total surface area of a cube with side length 5 cm?
Surface area of a cube = 6 × side²
Surface area = 6 × 5²
Surface area = 6 × 25
Surface area = 150 cm².
42. If a person travels 30 km in 2 hours, what is his average speed?
Average speed = total distance / total time
Average speed = 30 km / 2 hours
Average speed = 15 km/h.
43. What is the area of a sector of a circle with a radius of 6 cm and an angle of 90°?
Area of a sector = (θ / 360°) × πr²
Area = (90° / 360°) × π × 6²
Area = (1/4) × π × 36
Area ≈ 28.27 cm².
44. What is the square of 20?
The square of 20 is 20 × 20 = 400.
45. A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
Probability = favorable outcomes / total outcomes
Probability = 2 / (3 + 2 + 5)
Probability = 2 / 10
Probability = 0.2.
46. Find the mode of the following set of numbers: 3, 5, 7, 5, 9, 5, 8.
The mode is the number that appears most frequently.
The number 5 appears three times, so the mode is 5.
47. What is the value of 10% of 200?
10% of 200 = 200 × 10 / 100 = 20.
48. Solve for p: 6p + 2 = 14.
Subtract 2 from both sides:
6p = 14 - 2
6p = 12
Now divide by 6:
p = 12 / 6
p = 2.
49. A car travels at a speed of 50 km/h. How long will it take to travel 200 km?
Time = Distance / Speed
Time = 200 km / 50 km/h
Time = 4 hours.
50. What is the area of a square with side length 9 cm?
Area of a square = side²
Area = 9²
Area = 81 cm².
Recommended Indian Books for Class 10 WBBSE Math Solutions
"Mathematics for Class 10" by R.D. Sharma
Publisher: Dhanpat Rai Publications
This book provides a comprehensive understanding of all the topics covered in Class 10 WBBSE Mathematics. It includes a wide range of examples, solved problems, and exercises for practice. The book is perfect for building a strong foundation, especially for students looking for detailed explanations and step-by-step solutions.
"ICSE Mathematics for Class 10" by M.L. Aggarwal
Publisher: Arya Publishing House
M.L. Aggarwal’s books are known for their clarity and systematic approach to problems. This book focuses on honing problem-solving skills, covering various types of problems in algebra, geometry, and statistics, specifically tailored for Class 10 students.
"WBBSE Class 10 Mathematics" by K.K. Gupta
Publisher: Laxmi Publications
Specifically designed for West Bengal Board students, this book aligns with the syllabus and provides ample practice material. It includes a variety of solved examples and practice questions, with a detailed explanation of topics such as quadratic equations, geometry, and trigonometry.
"Comprehensive Mathematics" by S. K. Gupta & Anubhuti Gangal
Publisher: Arihant Publications
This book is excellent for students preparing for competitive exams, with detailed explanations and a variety of practice questions. It covers a wide spectrum of topics, ensuring students get ample practice with both theoretical concepts and practical problems.
"Mathematics for Class 10" by R.S. Aggarwal
Publisher: S. Chand & Company
R.S. Aggarwal’s books are a go-to for many students aiming to clear their Math exams. This book includes step-by-step explanations of the concepts, followed by extensive exercises to practice. It is highly recommended for mastering topics such as algebra, geometry, and trigonometry.
"Target WBBSE Class 10 Mathematics" by S. P. Bakshi
Publisher: Kundan Prakashan
A focused guide for WBBSE students, this book offers in-depth coverage of every topic in the Class 10 Math syllabus. It contains numerous solved examples, unsolved questions, and practice papers to help students evaluate their progress.
"Elementary Mathematics for Class 10" by S. L. Loney
Publisher: Pearson India
S. L. Loney is renowned for his clear, concise approach to teaching mathematics. This book is ideal for understanding the fundamentals of geometry, algebra, and trigonometry. It provides problems that require a deeper understanding of concepts, making it ideal for students looking to excel.
"WBBSE Class 10 Mathematics" by Dr. K. S. Kundu
Publisher: Goyal Publishers
Dr. K.S. Kundu’s book is well-suited for Class 10 WBBSE students, as it includes topic-wise solutions along with model papers and previous years’ questions. It offers a balanced mix of theoretical explanations and practice problems.
"New Mathematical Problem Solving" by R. S. Aggarwal
Publisher: S. Chand & Company
This book is particularly useful for students looking to sharpen their problem-solving skills. It presents a variety of questions from various mathematical concepts, helping students develop a practical understanding of the subject.
"WBBSE Class 10 Mathematics" by B.D. Sharma
Publisher: Vikas Publishing House
B.D. Sharma’s book is great for students who want to approach their math preparation with clarity. The content is organized in an easy-to-understand format, with a mixture of solved examples and practice sets to build student confidence.
"Mathematics Success for Class 10" by M.S. Sethi
Publisher: Orient Blackswan
This book is ideal for students who are looking for structured content to succeed in their Class 10 exams. With easy-to-follow explanations, this book is filled with chapter-wise solved examples, short-answer questions, and long-answer questions.
"Class 10 Mathematics - Self Study" by J.B. Gupta
Publisher: Goyal Publishers
As the name suggests, this book is tailored for self-learners. It provides a thorough overview of all topics with extensive practice sets that can help students prepare for their exams without external assistance.
"Mathematics for Class 10" by C.B. Sharma
Publisher: Dhanpat Rai & Co.
This book provides an excellent explanation of both basic and advanced mathematical topics. It focuses on conceptual clarity, with multiple solved examples and challenging exercises for practice.
"Modern's ABC of Mathematics for Class 10" by M.L. Aggarwal
Publisher: Modern Publishers
An ideal book for students who wish to practice more application-based questions, it includes problems from various topics, such as geometry, algebra, and statistics. The book emphasizes real-world applications of mathematical concepts.
"Class 10 Mathematics (WBBSE) - Exam-Oriented" by P. R. Soni
Publisher: S.K. Publications
P.R. Soni’s book is perfect for exam-oriented students. It provides ample practice questions with a focus on key topics and common problem types that frequently appear in exams.
"A Textbook of Mathematics for Class 10" by P.K. Sinha
Publisher: Gyan Publishing House
This book is great for students who want to thoroughly cover the syllabus. It offers well-explained examples, followed by practice sets that allow students to gain confidence in their problem-solving abilities.
"Practice Book of Mathematics for Class 10" by S.K. Bansal
Publisher: Pustak Mahal
This practice book is designed to boost problem-solving skills. It contains a variety of questions ranging from basic to difficult, offering thorough practice and reinforcing the learning of core concepts.
"Success in Mathematics for Class 10" by A.K. Sharma
Publisher: Vikas Publishing
Known for its focus on concept clarity, this book covers all chapters systematically with both solved and unsolved problems to ensure students get enough practice to excel in their exams.
"R.D. Sharma’s Mathematics for Class 10" (WBBSE)
Publisher: Dhanpat Rai & Co.
R.D. Sharma's work remains one of the most popular among students for its comprehensive coverage and clear explanations. This book offers a detailed understanding of mathematical concepts, followed by practice questions that students can attempt on their own.
"Class 10 Mathematics - Master Practice" by G.R. Sharma
Publisher: Arihant Publications
This book is specifically designed for competitive exam aspirants and those aiming for a perfect score in WBBSE. It provides practice questions in a variety of formats and includes detailed solutions to help students grasp difficult concepts easily.
Class 10 WBBSE Math Solution: A Guide to Preparing Effectively
Class 10 mathematics can be a challenging subject for many students, especially when it comes to the West Bengal Board of Secondary Education (WBBSE). However, with the right approach and resources, students can master the concepts and perform exceptionally well in their exams. In this guide, we will explore some effective strategies and recommended resources to help students tackle the Math syllabus with confidence.
The Class 10 WBBSE Math syllabus is extensive, covering subjects such as algebra, geometry, trigonometry, statistics, and coordinate geometry. Each of these topics requires a solid understanding of core concepts, as well as ample practice. One of the best ways to prepare is by breaking down the syllabus into manageable sections and tackling one section at a time. For instance, students should start with the basics of algebra and gradually move on to more complex areas like trigonometry.
When it comes to practicing, a good book can make all the difference. Books such as R.D. Sharma’s Mathematics for Class 10 and S. K. Gupta’s Comprehensive Mathematics are widely regarded for their clarity and extensive problem sets. These books not only explain concepts in an easy-to-understand manner but also provide a wide variety of practice problems ranging from basic to advanced levels. By practicing these problems regularly, students can improve their problem-solving skills and gain a deeper understanding of the subject.
Another crucial aspect of effective preparation is time management. Students should set aside dedicated time each day for math practice. It is helpful to start with easier problems and gradually work towards more challenging questions. This will help build confidence and reduce anxiety as the exams approach. Additionally, students can use sample papers and previous years’ question papers to get an idea of the types of questions that are likely to appear in the exams.
Understanding the patterns of questions is another important aspect of exam preparation. For example, in algebra, students may encounter questions on solving linear equations, quadratic equations, or word problems. By practicing these types of questions regularly, students can gain familiarity with the exam format and develop strategies to solve them efficiently. Similarly, topics such as geometry and trigonometry require a clear understanding of theorems and formulas, so regular revision of these concepts is crucial.
In addition to books, online resources, such as video tutorials and interactive practice tests, can be helpful for students who need extra help in specific areas. These resources often provide step-by-step solutions and explanations, which can enhance understanding and provide alternative methods to solve problems.
It is also essential for students to review their mistakes regularly. By going over incorrect answers and understanding where they went wrong, students can avoid making the same mistakes in the future. This practice of self-assessment can significantly improve performance in exams.
Lastly, students should make sure to stay positive and keep their morale high throughout their preparation. Confidence plays a key role in exam success, and maintaining a positive attitude will help students stay focused and motivated until the final day of the exam.
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