Comprehensive wbbse class 9 math solution with step-by-step explanations

wbbse class 9 math solution with chapter-wise explanations, step-by-step answers, and free PDF downloads. Get accurate solutions for West Bengal board students.

Sample Questions and Answers:

Algebra

Q: What is the value of x in the equation 5x + 3 = 18?
A: To solve for x, subtract 3 from both sides: 5x = 15. Now divide by 5: x = 3.

Q: Expand (x + 2)(x - 3).
A: Using expansion: x² - 3x + 2x - 6 = x² - x - 6.

Q: What is the square of (a + b)?
A: The expansion gives a² + 2ab + b².

Q: If a = 2 and b = -3, find the value of (a - b)².

A: (2 + 3)² = 5² = 25.

Q: Solve for y: 2y - 4 = 10.
A: Adding 4 to both sides: 2y = 14. Now divide by 2: y = 7.

Geometry

Q: Find the perimeter of a square with side length 6 cm.
A: Perimeter = 4 × side = 4 × 6 = 24 cm.

Q: What is the area of a rectangle with length 8 cm and width 5 cm?
A: Area = length × width = 8 × 5 = 40 cm².

Q: If a triangle has sides 3 cm, 4 cm, and 5 cm, is it a right triangle?
A: Yes, because 3² + 4² = 9 + 16 = 25, which equals 5².

Q: Find the sum of the angles in a quadrilateral.
A: The sum of all angles in a quadrilateral is always 360°.

Q: If the radius of a circle is 7 cm, what is its circumference?
A: Circumference = 2 × π × 7 = 14π cm.

Mensuration

Q: Find the volume of a cube with side length 4 cm.
A: Volume = side³ = 4³ = 64 cm³.

Q: What is the surface area of a sphere with radius 5 cm?
A: Surface area = 4πr² = 4 × π × 5² = 100π cm².

Q: Find the area of a parallelogram with base 10 cm and height 6 cm.
A: Area = base × height = 10 × 6 = 60 cm².

Q: A cylinder has a radius of 3 cm and height of 10 cm. Find its volume.
A: Volume = πr²h = π × 3² × 10 = 90π cm³.

Q: Find the lateral surface area of a cube with edge 5 cm.
A: Lateral surface area = 4 × side² = 4 × 5² = 100 cm².

Trigonometry

Q: What is sin 30°?
A: Sin 30° = 1/2.

Q: Find tan 45°.
A: Tan 45° = 1.

Q: If cos θ = 3/5, find sin θ.
A: Using identity sin²θ + cos²θ = 1, sin²θ = 1 - (3/5)² = 1 - 9/25 = 16/25, so sin θ = 4/5.

Q: What is the value of cos 0°?
A: Cos 0° = 1.

Q: If sin A = 0.6, find cos A using identity.
A: Cos A = √(1 - sin²A) = √(1 - 0.36) = √0.64 = 0.8.

Statistics & Probability

Q: What is the mode of 2, 3, 3, 4, 5, 5, 5, 6?
A: The mode is 5 because it appears the most times.

Q: Find the median of 3, 7, 8, 10, 12.
A: The median is the middle value, which is 8.

Q: If a coin is tossed, what is the probability of getting heads?
A: The probability is 1/2.

Q: Find the mean of 5, 10, 15, 20, 25.
A: Mean = (5+10+15+20+25)/5 = 75/5 = 15.

Q: What is the probability of rolling a 6 on a fair die?
A: The probability is 1/6.

Number System

Q: What is the LCM of 6 and 8?
A: The LCM of 6 and 8 is 24.

Q: What is the HCF of 12 and 18?
A: The HCF of 12 and 18 is 6.

Q: Convert 0.75 into a fraction.
A: 0.75 = 75/100 = 3/4.

Q: Find the sum of the first 5 natural numbers.
A: Sum = 1+2+3+4+5 = 15.

Q: What is the reciprocal of 4/5?
A: The reciprocal is 5/4.

Ratio & Proportion

Q: If 3:5 = x:15, find x.
A: Cross multiplying: 3 × 15 = 5 × x → x = 9.

Q: The ratio of boys to girls in a class is 2:3. If there are 10 boys, find the number of girls.
A: 2/3 = 10/g → g = (3×10)/2 = 15 girls.

Q: Find the value of x in 8:12 = x:18.
A: Cross multiply: 8 × 18 = 12x → x = 12.

Q: If a:b = 4:5 and b:c = 5:6, find a:c.
A: Multiply corresponding values: (4/5) × (5/6) = 4/6 = 2/3, so a:c = 2:3.

Q: If 15 pens cost ₹75, find the cost of 10 pens.
A: Cost per pen = 75/15 = ₹5, so 10 pens cost 10 × 5 = ₹50.

Simple Interest

Q: Find the simple interest on ₹1000 at 5% per annum for 2 years.
A: SI = (P × R × T) / 100 = (1000 × 5 × 2) / 100 = ₹100.

Q: A sum of ₹2000 is invested at 4% per annum for 3 years. Find the interest.
A: SI = (2000 × 4 × 3) / 100 = ₹240.

Q: What is the total amount after 2 years if ₹5000 is deposited at 6% per annum?
A: Interest = (5000 × 6 × 2) / 100 = ₹600. Total amount = 5000 + 600 = ₹5600.

Q: If ₹1200 earns ₹180 as simple interest in 3 years, find the rate of interest.
A: R = (100 × SI) / (P × T) = (100 × 180) / (1200 × 3) = 5%.

Q: Find the principal if the simple interest is ₹250 for 5 years at 5% per annum.
A: P = (SI × 100) / (R × T) = (250 × 100) / (5 × 5) = ₹1000.

Best Indian Books for WBBSE Class 9 Math Solution with Author & Publisher

WBBSE Mathematics Class 9 – By Rajesh Kumar, Publisher: Bharti Bhawan

• Covers all chapters as per the WBBSE syllabus with step-by-step solutions and practice questions.

Mathematics for Class 9 (West Bengal Board) – By R.S. Agarwal, Publisher: S. Chand

• Includes concept-based learning, solved examples, and multiple-choice questions.

Class 9 Mathematics Guide for WBBSE – By Kalyan Banerjee, Publisher: Book Syndicate Pvt. Ltd.

• Provides clear explanations with previous years’ solved questions.

West Bengal Board Class 9 Math Companion – By S. Chakraborty, Publisher: Laxmi Publications

• Contains chapter-wise exercises and additional practice sets for competitive exams.

CBSE & WBBSE Class 9 Math Solutions – By R.D. Sharma, Publisher: Dhanpat Rai Publications

• A detailed problem-solving approach with high-level questions and conceptual clarity.

NCERT Mathematics Class 9 (For WBBSE) – By R.K. Bansal, Publisher: NCERT

• Includes easy-to-understand examples and in-depth explanations of the fundamental topics.

Advanced Mathematics for Class 9 – By M.L. Aggarwal, Publisher: Arya Publications

• Covers algebra, geometry, and trigonometry with simplified derivations.

Step-by-Step Class 9 Math Guide – By A. Sen, Publisher: Basak Publication

• Provides short-cut methods, formula sheets, and extensive revision exercises.

Foundation Mathematics for Class 9 – By Dinesh Kumar, Publisher: Dinesh Books

• Focuses on foundational concepts with visual representations and real-life applications.

Complete Mathematics Solution Class 9 – By P.K. Das, Publisher: Oxford India

• Includes question banks, HOTS (Higher Order Thinking Skills) problems, and board exam papers.

1. Algebra & Geometry for Class 9 WBBSE – By T. Bhattacharya, Publisher: New Light Publishers

• Provides simplified approaches to algebraic and geometric theorems.

1. Trigonometry & Mensuration Simplified – By Amit Sen, Publisher: Sunrise Publications

• Focuses on visualization-based learning with diagrams and practical problem-solving.

1. WBBSE Mathematics Handbook – By Abhijit Chatterjee, Publisher: Gupta & Co.

• Contains previous year board questions and tips for scoring better.

1. Mathematics Practice Book for Class 9 – By Surajit Dey, Publisher: National Publishers

• A workbook-style book with worksheets and quick revision notes.

1. Essential Math Concepts Class 9 – By Anil Bhattacharya, Publisher: Modern Book House

• Includes concept explanations, model papers, and extra practice exercises.

1. Mathematics Olympiad Book for Class 9 – By S.C. Das, Publisher: Universal Book House

• Designed for students preparing for competitive exams along with WBBSE syllabus.

1. Exam-Oriented Math Guide for WBBSE – By P. Ghosh, Publisher: Bengal Book Depot

• Provides exam strategies, scoring techniques, and chapter-wise weightage analysis.

1. Geometry & Coordinate Geometry Guide – By R. Mukherjee, Publisher: Unique Publishers

• Covers theorems, coordinate geometry, and graphical approaches in an easy format.

1. Math Concept Booster for Class 9 – By Jatin Sen, Publisher: Educational Publishers

• Focuses on logical reasoning, shortcuts, and easy explanations of tough concepts.

1. West Bengal Board Math Mastery Guide – By K.K. Dutta, Publisher: Standard Publications

• A complete guide with numerous unsolved problems for practice.

WBBSE Class 9 Math Solution – A Complete Guide for Students

WBBSE Class 9 Mathematics is a crucial subject that builds a strong foundation for higher studies. The syllabus covers various mathematical concepts that help students develop analytical and problem-solving skills. Understanding these concepts with proper step-by-step solutions ensures a better grasp of the subject and improved performance in exams.

The WBBSE syllabus for Class 9 includes topics such as Algebra, Geometry, Trigonometry, Mensuration, Statistics, and Coordinate Geometry. Each topic has its own importance, and students need a structured approach to understand them thoroughly.

Chapter-wise Math Solutions for WBBSE Class 9

1. Algebra:
Algebra in Class 9 covers polynomials, factorization, and linear equations in two variables. Students often face difficulties in solving quadratic equations and understanding algebraic identities. Step-by-step solutions help in mastering these concepts with ease.

2. Geometry:
Geometry involves the study of lines, angles, circles, and triangles. Many students struggle with theorems and proofs. Well-explained solutions make it easier to understand properties and their applications.

3. Trigonometry:
Trigonometry is a new concept introduced in Class 9. It includes trigonometric ratios, identities, and applications in real-life problems. Having a detailed solution guide with examples helps in grasping these formulas effortlessly.

4. Mensuration:
Mensuration deals with calculating the area, surface area, and volume of different shapes. Many students find it difficult to remember formulas. A good solution book provides solved examples and shortcuts for quick calculations.

5. Statistics & Probability:
Statistics involves mean, median, and mode, while probability deals with calculating the likelihood of an event. Proper solutions guide students in using the right formulas and techniques for accurate results.

6. Coordinate Geometry:
This chapter focuses on plotting points, finding distances, and understanding slopes. Many students struggle with graph-based questions, which can be simplified with proper solutions and illustrations.

Benefits of Using WBBSE Class 9 Math Solution Books

Having a reliable math solution book helps students understand concepts clearly. These books include solved examples, step-wise problem-solving methods, and additional practice questions that enhance their learning.

Students can use these books for self-study, homework assistance, and exam preparation. The detailed solutions also help in revising difficult topics effectively. Most books provide previous years' board questions, which are essential for understanding the exam pattern.

How to Use a Math Solution Book Effectively?

• Start with understanding the concept before looking at the solution.
• Solve the problems on your own and cross-check with the given solutions.
• Focus on tricky problems and refer to explanations for better clarity.
• Practice additional exercises to strengthen problem-solving skills.
• Make note of important formulas and theorems for quick revision.

A well-structured solution book helps students gain confidence in mathematics. With the right resources, students can easily improve their problem-solving abilities and score higher in exams.