The Vikas Mathematics Practical Book for 9th class serves as a vital resource for students aiming to enhance their understanding of mathematical concepts through practical applications. This article provides detailed solutions to the exercises within the book, offering step-by-step explanations to facilitate effective learning.
Understanding the Vikas Mathematics Practical Book
The Vikas Mathematics Practical Book is designed to complement theoretical learning by providing practical exercises that reinforce mathematical principles. It covers a range of topics, including algebra, geometry, trigonometry, and statistics, with each chapter containing activities that encourage hands-on learning.
Key Features of the Book
- Comprehensive Coverage: Encompasses essential topics in the 9th-grade mathematics curriculum.
- Practical Exercises: Includes activities that promote the application of theoretical knowledge.
- Step-by-Step Solutions: Provides detailed answers to facilitate understanding.
- Illustrative Examples: Offers examples that demonstrate the application of concepts in real-life scenarios.
Detailed Solutions to Selected Exercises
Below are solutions to selected exercises from the Vikas Mathematics Practical Book for 9th class:
- Exercise 1: Number Systems
Question: Convert the decimal number 45 to binary.
Solution: Divide 45 by 2, noting the quotient and remainder at each step:
- 45 ÷ 2 = 22, remainder 1
- 22 ÷ 2 = 11, remainder 0
- 11 ÷ 2 = 5, remainder 1
- 5 ÷ 2 = 2, remainder 1
- 2 ÷ 2 = 1, remainder 0
- 1 ÷ 2 = 0, remainder 1
Reading the remainders from bottom to top, the binary representation of 45 is 101101.
- Exercise 2: Algebraic Expressions
Question: Simplify the expression: 3x + 5x – 2.
Solution: Combine like terms:
- 3x + 5x = 8x
Therefore, the simplified expression is 8x – 2.
- Exercise 3: Geometry
Question: Calculate the area of a triangle with a base of 10 cm and a height of 5 cm.
Solution: Use the formula for the area of a triangle:
- Area = (Base × Height) / 2
Substitute the given values:
- Area = (10 cm × 5 cm) / 2 = 50 cm² / 2 = 25 cm²
Thus, the area of the triangle is 25 cm².
- Exercise 4: Trigonometry
Question: Find the value of sin 30°.
Solution: From trigonometric tables or a calculator:
- sin 30° = 0.5
Therefore, sin 30° equals 0.5.
- Exercise 5: Statistics
Question: Find the mean of the following data set: 2, 4, 6, 8, 10.
Solution: Calculate the sum of the data:
- Sum = 2 + 4 + 6 + 8 + 10 = 30
Divide by the number of data points:
- Mean = 30 / 5 = 6
Thus, the mean of the data set is 6.
Recommended Books for Further Study
To deepen your understanding of 9th-grade mathematics, consider the following resources:
NCERT Mathematics Textbook for Class 9
A comprehensive textbook covering all essential topics with clear explanations and practice exercises.
Offers detailed solutions and a variety of problems to enhance problem-solving skills.
Provides in-depth coverage of mathematical concepts with illustrative examples.
Features a structured approach to learning with numerous practice questions.
Includes solved examples and exercises to build a strong foundation in mathematics.
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