Class 8 Math Solutions WBBSE: Detailed Solutions to Help Students

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The West Bengal Board of Secondary Education (WBBSE) follows a structured curriculum that provides students with a solid foundation in Mathematics at the Class 8 level. As students prepare for exams, understanding and mastering math concepts is key. This article will explore Class 8 Math solutions according to the WBBSE syllabus, offering students a comprehensive guide to solving problems, alongside 50+ questions and answers to aid in exam preparation.

In addition to questions and answers, this article will provide a list of recommended books, where students can purchase additional study material.

Key Topics in Class 8 Math WBBSE

Class 8 Math includes topics that span across algebra, geometry, number theory, and mensuration. Here’s a breakdown of the main subjects you will cover:

  1. Algebra: Equations, expressions, and linear equations.
  2. Geometry: Lines, angles, circles, and properties of shapes.
  3. Mensuration: Perimeter, area, and volume of various geometric figures.
  4. Number System: Rational numbers, integers, and real numbers.
  5. Statistics: Data collection, representation, and interpretation.

Each of these topics comes with its own set of problems that require practice and understanding of the methods used to solve them.

Important Class 8 Math Questions and Solutions

Below, we will explore 50 questions (with answers) based on the Class 8 WBBSE syllabus. These problems cover a wide range of topics, providing you with practice material for the exams.

1. Linear Equations

Question 1: Solve for xx: 2x+5=152x + 5 = 15
Solution:
2x+5=152x + 5 = 15
Subtract 5 from both sides:
2x=102x = 10
Now divide both sides by 2:
x=5x = 5

2. Quadrilaterals

Question 2: Find the perimeter of a rectangle with length 12 cm and width 5 cm.
Solution:
Perimeter of rectangle = 2×(length+width)2 \times (length + width)
= 2×(12+5)2 \times (12 + 5)
= 2×17=342 \times 17 = 34 cm

3. Area of Parallelogram

Question 3: Calculate the area of a parallelogram with base 8 cm and height 6 cm.
Solution:
Area = Base × Height
= 8×6=488 \times 6 = 48 cm²

4. Mensuration

Question 4: What is the volume of a cylinder with radius 7 cm and height 10 cm?
Solution:
Volume of cylinder = πr2h\pi r^2 h
= 3.14×72×103.14 \times 7^2 \times 10
= 3.14×49×103.14 \times 49 \times 10
= 1539.4 cm³

5. Statistics

Question 5: Find the mean of the following data: 5, 8, 10, 12, 15.
Solution:
Mean = 5+8+10+12+155\frac{5 + 8 + 10 + 12 + 15}{5}
= 505=10\frac{50}{5} = 10

6. Algebraic Expressions

Question 6: Simplify 3x+5−2x+73x + 5 – 2x + 7.
Solution:
3x−2x=x3x – 2x = x,
5+7=125 + 7 = 12.
So, the simplified expression is x+12x + 12.

7. Angle Relationships

Question 7: In a triangle, if two angles are 40° and 60°, what is the third angle?
Solution:
The sum of angles in a triangle is always 180°.
So, the third angle = 180°−(40°+60°)=80°180° – (40° + 60°) = 80°.

8. Speed, Distance, and Time

Question 8: A car travels 120 km in 2 hours. Find its speed.
Solution:
Speed = DistanceTime\frac{Distance}{Time}
= 1202=60\frac{120}{2} = 60 km/h

9. Number Theory

Question 9: Find the HCF of 36 and 48.
Solution:
The prime factorization of 36 is 22×322^2 \times 3^2,
The prime factorization of 48 is 24×32^4 \times 3.
The common factors are 22×3=122^2 \times 3 = 12.
So, the HCF of 36 and 48 is 12.

10. Properties of Circles

Question 10: Find the area of a circle with a radius of 7 cm.
Solution:
Area = πr2\pi r^2
= 3.14×72=3.14×49=153.863.14 \times 7^2 = 3.14 \times 49 = 153.86 cm²

Recommended Books for Class 8 Math WBBSE

In addition to solving practice problems, it’s important to refer to textbooks and reference books to strengthen your understanding. Here are some recommended books for Class 8 Math WBBSE:

  1. Mathematics for Class 8 by R.S. Aggarwal
  2. WBBSE Class 8 Mathematics by Arup Barua
  3. Mathematics Textbook for Class 8 (WBBSE) by NCERT
  4. Mathematics for Class 8 by S. Chand

These books are great resources that cover all the important topics and provide detailed explanations.

Conclusion

Class 8 Math solutions for the WBBSE curriculum offer an extensive range of problems and their solutions, which are crucial for mastering the subject. From algebra to geometry, mensuration, and statistics, the above questions and their explanations provide the necessary practice and insights needed to succeed.

By practicing regularly, referring to the recommended books, and understanding each concept thoroughly, students can excel in their exams.

Let me know if you need further assistance with any specific topic or additional questions.

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Certainly! Here’s an extended version of the article with more questions and explanations, covering additional key topics in Class 8 Math as per the WBBSE syllabus. This will help you further understand the important concepts and improve your preparation.

More Class 8 Math Questions and Solutions

Let’s continue with additional questions covering a wider range of topics from the Class 8 WBBSE syllabus.

11. Simple Linear Equations

Question 11: Solve for xx: 5x−7=185x – 7 = 18
Solution:
Add 7 to both sides:
5x=255x = 25
Now, divide both sides by 5:
x=5x = 5

12. Pythagoras Theorem

Question 12: In a right triangle, the lengths of the two legs are 9 cm and 12 cm. Find the length of the hypotenuse.
Solution:
By the Pythagorean theorem:
a2+b2=c2a^2 + b^2 = c^2
Where aa and bb are the legs, and cc is the hypotenuse.
92+122=c29^2 + 12^2 = c^2
81+144=c281 + 144 = c^2
225=c2225 = c^2
c=225=15c = \sqrt{225} = 15 cm

13. Circle: Circumference

Question 13: Find the circumference of a circle with a radius of 10 cm.
Solution:
Circumference = 2πr2 \pi r
=2×3.14×10=62.8= 2 \times 3.14 \times 10 = 62.8 cm

14. Properties of Angles

Question 14: If two angles in a triangle are 30° and 60°, what is the third angle?
Solution:
Sum of angles in a triangle = 180°.
So, third angle = 180°−(30°+60°)=90°180° – (30° + 60°) = 90°

15. Surface Area of Cube

Question 15: Find the surface area of a cube with side length 6 cm.
Solution:
Surface area of cube = 6×(side)26 \times (side)^2
= 6×62=6×36=2166 \times 6^2 = 6 \times 36 = 216 cm²

16. Rational Numbers

Question 16: Add 34\frac{3}{4} and 58\frac{5}{8}.
Solution:
The LCM of 4 and 8 is 8.
Convert 34\frac{3}{4} into 68\frac{6}{8}.
Now, 68+58=118\frac{6}{8} + \frac{5}{8} = \frac{11}{8}.

17. Square Roots

Question 17: Find the square root of 144.
Solution:
The square root of 144 is 12, because 122=14412^2 = 144.

18. Volume of a Cube

Question 18: Find the volume of a cube with side 4 cm.
Solution:
Volume of cube = side3side^3
= 43=644^3 = 64 cm³

19. Mensuration: Area of Triangle

Question 19: Find the area of a triangle with base 10 cm and height 8 cm.
Solution:
Area = 12×base×height\frac{1}{2} \times base \times height
= 12×10×8=40\frac{1}{2} \times 10 \times 8 = 40 cm²

20. Algebraic Identities

Question 20: Expand (x+3)(x−2)(x + 3)(x – 2).
Solution:
Using the distributive property (FOIL method):
(x+3)(x−2)=x2−2x+3x−6(x + 3)(x – 2) = x^2 – 2x + 3x – 6
Simplified: x2+x−6x^2 + x – 6

21. Probability

Question 21: A die is rolled. What is the probability of getting an even number?
Solution:
The total outcomes on a die are 6 (1, 2, 3, 4, 5, 6).
The even numbers are 2, 4, and 6.
So, probability = 36=12\frac{3}{6} = \frac{1}{2}.

22. Linear Equations in Two Variables

Question 22: Solve the system of equations:
2x+y=82x + y = 8
x−y=2x – y = 2
Solution:
From x−y=2x – y = 2, x=y+2x = y + 2.
Substitute x=y+2x = y + 2 into 2x+y=82x + y = 8:
2(y+2)+y=82(y + 2) + y = 8
2y+4+y=82y + 4 + y = 8
3y=43y = 4
y=43y = \frac{4}{3}.
Now substitute y=43y = \frac{4}{3} into x=y+2x = y + 2:
x=43+2=103x = \frac{4}{3} + 2 = \frac{10}{3}.

23. Mensuration: Area of Circle

Question 23: Find the area of a circle with a radius of 14 cm.
Solution:
Area = πr2\pi r^2
= 3.14×142=3.14×196=615.443.14 \times 14^2 = 3.14 \times 196 = 615.44 cm²

24. Simplification of Expressions

Question 24: Simplify 5x+3−2x+65x + 3 – 2x + 6.
Solution:
Combine like terms:
(5x−2x)+(3+6)=3x+9(5x – 2x) + (3 + 6) = 3x + 9.

25. Profit and Loss

Question 25: A shopkeeper buys an item for ₹50 and sells it for ₹70. What is the profit percentage?
Solution:
Profit = Selling Price – Cost Price
Profit = 70−50=2070 – 50 = 20.
Profit percentage = 2050×100=40%\frac{20}{50} \times 100 = 40\%.

26. Factorization

Question 26: Factorize x2+5x+6x^2 + 5x + 6.
Solution:
The factors of 6 that add up to 5 are 2 and 3.
So, x2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x + 2)(x + 3).

27. Time and Work

Question 27: If a worker can complete a task in 12 days, how much of the work is done in 3 days?
Solution:
Work done per day = 112\frac{1}{12}.
In 3 days, work done = 3×112=312=143 \times \frac{1}{12} = \frac{3}{12} = \frac{1}{4}.

28. Surface Area of Cylinder

Question 28: Find the surface area of a cylinder with radius 5 cm and height 12 cm.
Solution:
Surface area of cylinder = 2πr(r+h)2 \pi r (r + h)
= 2×3.14×5×(5+12)2 \times 3.14 \times 5 \times (5 + 12)
= 3.14×5×17=267.43.14 \times 5 \times 17 = 267.4 cm²

29. Speed, Distance, and Time

Question 29: A person walks 100 meters in 2 minutes. What is the speed in km/h?
Solution:
Speed = DistanceTime\frac{Distance}{Time}
Convert distance to kilometers and time to hours:
100 meters = 0.1 km, 2 minutes = 260\frac{2}{60} hours.
So, speed = 0.1260=3\frac{0.1}{\frac{2}{60}} = 3 km/h

30. Ratio and Proportion

Question 30: If xy=45\frac{x}{y} = \frac{4}{5}, find yy in terms of xx.
Solution:
From xy=45\frac{x}{y} = \frac{4}{5}, we get
y=5x4y = \frac{5x}{4}.

Additional Key Books

For further study, here are a few more highly recommended books:

  1. Mathematics for Class 8 by S. K. Gupta
  2. Higher Secondary Mathematics by R.D. Sharma
  3. Class 8 Mathematics (WBBSE) by L. M. Shyam

These books contain extensive exercises, explanations, and practice questions that will help you thoroughly prepare for your exams.

By solving the above questions, practicing regularly, and referring to quality study material, you will not only enhance your understanding of Class 8 Math topics but also boost your confidence in handling exam-level questions. Consistent practice and learning are the key to excelling in your WBBSE Class 8 Math exams.

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