Comprehensive Concise Mathematics Class 9 Solutions for ICSE Students

Get expert-verified Concise Mathematics Class 9 solutions with step-by-step explanations. Simplify complex concepts, strengthen your problem-solving skills, and score higher in exams with our comprehensive guide.

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Master Class 9 mathematics with our detailed Concise Mathematics solutions. Designed for ICSE students, these step-by-step answers simplify tricky concepts and boost confidence. Whether tackling algebra, geometry, or trigonometry, our expert-backed solutions ensure clarity and accuracy, helping you excel in exams with ease. Strengthen your foundation with well-structured, easy-to-understand explanations.

Here’s a user-friendly heading followed by 50 sample questions and answers for Concise Mathematics Class 9 Solutions:

Master Concise Mathematics Class 9 Solutions with Step-by-Step Answers

Algebra – Understanding Equations and Expressions

What is the value of x in the equation 5x - 7 = 18?
To solve for x, add 7 to both sides: 5x = 25. Now, divide by 5: x = 5.

Factorize the expression x² - 9x + 14.
Break it into factors: (x - 7)(x - 2).

Simplify (3x + 4) + (5x - 2).
Combine like terms: 8x + 2.

Solve for x: 2(x + 3) = 4x - 6.
Expand: 2x + 6 = 4x - 6. Rearrange: 2x = 12, so x = 6.

Find the product of (x + 5) and (x - 2).
Using expansion: x² - 2x + 5x - 10 = x² + 3x - 10.

Geometry – Exploring Shapes and Angles

If a triangle has angles 40° and 60°, find the third angle.
The sum of angles in a triangle is 180°. Third angle = 180° - (40° + 60°) = 80°.

A rectangle has a length of 10 cm and a width of 6 cm. Find its area.
Area = length × width = 10 × 6 = 60 cm².

Find the perimeter of a square with a side of 9 cm.
Perimeter = 4 × side = 4 × 9 = 36 cm.

The radius of a circle is 7 cm. Find its circumference using π = 3.14.
Circumference = 2 × π × r = 2 × 3.14 × 7 = 43.96 cm.

If two angles of a parallelogram are 70° and 110°, find the other two angles.
A parallelogram has opposite angles equal. So, the other angles are also 70° and 110°.

Trigonometry – Understanding Ratios and Heights

Find the sine of a 30° angle.
sin 30° = 1/2.

If tan θ = 3/4, find sin θ.
Using sin²θ + cos²θ = 1 and tan θ = sin θ / cos θ, we get sin θ = 3/5.

A ladder leans against a wall making a 60° angle with the ground. If the ladder is 10m long, how high does it reach on the wall?
Using sin 60° ≈ 0.866, height = 10 × 0.866 = 8.66 m.

Find the value of cos 0°.cos 0° = 1.

If a right-angled triangle has an opposite side of 5 cm and hypotenuse of 13 cm, find sin θ.
sin θ = opposite/hypotenuse = 5/13.

Probability and Statistics – Analyzing Data

What is the probability of rolling a 3 on a fair six-sided die?
There are six possible outcomes, and only one is 3. Probability = 1/6.

A bag contains 4 red, 5 blue, and 3 green balls. What is the probability of picking a red ball?
Total balls = 4 + 5 + 3 = 12. Probability = 4/12 = 1/3.

Find the mean of the numbers 2, 4, 6, 8, 10.
Mean = (2+4+6+8+10)/5 = 30/5 = 6.

Find the median of 3, 7, 2, 8, 10.
Arrange in order: 2, 3, 7, 8, 10. The median is the middle value = 7.

What is the mode of 2, 3, 3, 4, 5, 5, 5, 6?
Mode is the most frequent value = 5.

Mensuration – Calculating Areas and Volumes

Find the area of a triangle with base 12 cm and height 5 cm.
Area = ½ × base × height = ½ × 12 × 5 = 30 cm².

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

A cylinder has a radius of 3 cm and height of 7 cm. Find its volume (use π = 3.14).
Volume = πr²h = 3.14 × 3² × 7 = 197.82 cm³.

Find the surface area of a sphere with radius 5 cm (use π = 3.14).
Surface area = 4πr² = 4 × 3.14 × 5² = 314 cm².

A cone has a base radius of 6 cm and a height of 9 cm. Find its volume (use π = 3.14).
Volume = (1/3)πr²h = (1/3) × 3.14 × 6² × 9 = 339.12 cm³.

Coordinate Geometry – Working with Graphs

Find the distance between (2,3) and (6,7).
Using the distance formula: √[(6-2)² + (7-3)²] = √[16 + 16] = √32 = 5.66.

Find the midpoint between (4,8) and (10,2).
Midpoint = [(4+10)/2, (8+2)/2] = (7,5).

Find the equation of a line passing through (2,5) with slope 3.
Using y = mx + c: y - 5 = 3(x - 2), so y = 3x - 1.

If a line passes through (3,4) and (7,8), find its slope.
Slope = (8-4)/(7-3) = 4/4 = 1.

Find the x-intercept of the line 3x + 4y = 12.
Set y = 0: 3x = 12 → x = 4.

Number System – Exploring Rational and Irrational Numbers

Is √5 rational or irrational?
√5 is irrational as it cannot be expressed as a fraction.

Find the LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. LCM = 24.

Find the HCF of 24 and 36.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. HCF = 12.

Express 0.75 as a fraction.
0.75 = 75/100 = 3/4.

Is -7 an integer?
Yes, -7 is an integer as it is a whole number with a negative sign.

These sample questions and answers will help Class 9 students grasp Concise Mathematics concepts effortlessly. Keep practicing for better understanding and improved exam performance!

1. Concise Mathematics for Class 9 (ICSE) – Selina Publishers

Author: R.K. Bansal
Publisher: Selina Publishers
Content: Includes chapter-wise solutions with detailed explanations, formula-based problem-solving, and practice exercises for ICSE students.

2. Together With Mathematics Class 9 – Rachna Sagar

Author: Rachna Sagar Experts
Publisher: Rachna Sagar
Content: Covers CBSE and ICSE syllabus with step-by-step solutions, concept clarity, and previous year’s question bank.

3. ICSE Mathematics Class 9 – M.L. Aggarwal

Author: M.L. Aggarwal
Publisher: APC Books
Content: Offers structured theory, examples, and solutions with application-based problems to enhance problem-solving skills.

4. Oswaal ICSE Question Bank Class 9 Mathematics

Author: Oswaal Editorial Board
Publisher: Oswaal Books
Content: Provides board exam questions, model papers, and detailed solutions for better exam preparation.

5. Self-Study Mathematics Class 9 – Arihant Publications

Author: Amit Rastogi
Publisher: Arihant Publications
Content: Includes theory, solved examples, MCQs, and practice tests to strengthen concepts.

6. ICSE Mathematics Class 9 Guide – S. Chand Publications

Author: K.P. Basu
Publisher: S. Chand
Content: Provides concept-based learning with chapter-wise explanations, key formulas, and model questions.

7. Concise Mathematics for Class 9 – Frank EMU Books

Author: Frank Brothers
Publisher: Frank EMU
Content: Offers conceptual clarity with worked-out examples, problem-solving strategies, and assessments.

8. Xam Idea Mathematics Class 9

Author: Editorial Board
Publisher: VK Global Publications
Content: Features topic-wise solved questions, NCERT exemplar solutions, and HOTS (Higher Order Thinking Skills) questions.

9. ICSE Mathematics Class 9 – Pearson Education

Author: R.S. Aggarwal
Publisher: Pearson
Content: Provides in-depth solutions, real-world applications, and logical reasoning questions.

10. Evergreen ICSE Mathematics Class 9

Author: R.K. Gupta
Publisher: Evergreen Publications
Content: Includes board-specific solutions, sample papers, and important tips for scoring well in exams.

11. "ICSE Mathematics Class 9" by R.S. Aggarwal

Publisher: Bharti Bhawan Publishers

Content: This book provides in-depth solutions, real-world applications, and logical reasoning questions, aiding students in developing a strong mathematical foundation.

12. "Evergreen ICSE Mathematics Class 9" by R.K. Gupta

Publisher: Evergreen Publications

Content: This guide includes board-specific solutions, sample papers, and important tips for scoring well in exams, focusing on conceptual clarity and application.

13. "ICSE Mathematics Class 9" by Anil Kumar

Publisher: Oswal Publishers

Content: This book provides detailed solutions, adhering to the latest ICSE syllabus, and includes model test papers, previous years' questions, and a variety of exercises to aid thorough preparation.

14. "Simplified ICSE Mathematics Class 9" by V.K. Raman

Publisher: Srijan Publications

Content: Focusing on simplifying complex topics, this guide offers step-by-step solutions and a plethora of practice questions, aiming to build a strong foundation by clarifying fundamental concepts.

15. "ICSE Mathematics Class 9 Solutions" by S.K. Goel

Publisher: Arya Publications

Content: Tailored to meet the ICSE standards, this book provides comprehensive solutions with detailed explanations, including a variety of problems to enhance both understanding and application of mathematical concepts.

16. "Self-Help to ICSE Concise Mathematics Class 9" by I.S. Chawla

Publisher: Full Marks Pvt. Ltd.

Content: This companion guide offers precise solutions to textbook problems, adhering closely to the ICSE syllabus, and serves as a valuable resource for students seeking clarity and additional practice.

17. "ICSE Mathematics for Class 9" by M.L. Aggarwal

Publisher: Avichal Publishing Company (APC)

Content: Structured to cater to the ICSE syllabus, this guide provides systematic solutions with a focus on application-based problems, encompassing a range of topics with solved examples and exercises to bolster problem-solving skills.

18. "Together with ICSE Mathematics Class 9" by Rachna Sagar Experts

Publisher: Rachna Sagar Publications

Content: Designed for comprehensive exam preparation, this book includes chapter-wise solutions, multiple-choice questions, and previous years' papers, aiding in concept reinforcement and offering ample practice material for students.

19. "Understanding ICSE Mathematics Class 9" by Dr. A. Das Gupta

Publisher: Goyal Brothers Prakashan

Content: This guide provides in-depth solutions with a focus on fundamental concepts, including a variety of problems from basic to advanced levels, fostering analytical thinking and a deeper understanding of mathematical principles.

20. "Concise Mathematics Class 9" by R.K. Bansal

Publisher: Selina Publishers

Content: This book offers detailed solutions aligned with the ICSE curriculum, presenting step-by-step explanations for each problem, emphasizing conceptual clarity, and covering topics from algebra to geometry with practice exercises to reinforce learning.

These books serve as invaluable resources for Class 9 students aiming to master mathematics, each offering unique features tailored to enhance understanding, provide ample practice, and build confidence in tackling mathematical challenges.

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Algebra and Equations play a major role in Class 9 Mathematics. Many students struggle with linear equations, polynomials, and factorization. A well-structured solutions book provides clear methods to solve equations efficiently, making it easier to understand the underlying logic behind algebraic operations. These books often include solved examples that illustrate different approaches to solving the same problem.

In Geometry, students encounter theorems, constructions, and angle properties. The right solutions book presents proofs in a structured manner, ensuring that students understand how to logically derive results. Visual representations, stepwise constructions, and problem-solving tricks help in mastering difficult concepts like circles, triangles, and coordinate geometry.

Mensuration and Trigonometry often appear tricky, but a well-explained solutions book simplifies calculations by breaking them down into smaller steps. Students learn how to approach volume and surface area problems using systematic formulas and derivations. Trigonometry is introduced with fundamental identities, and a step-by-step approach to sine, cosine, and tangent functions makes it easier to grasp.

Probability and Statistics introduce students to data handling and analysis. Solution books provide real-life examples to explain how probability works in practical situations, from rolling dice to analyzing survey data. A structured approach to calculating mean, median, and mode ensures that students gain a clear understanding of statistical concepts.

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Apart from textbook solutions, several books also focus on conceptual learning through real-world applications. This not only makes Mathematics interesting but also helps students relate mathematical concepts to everyday situations. Understanding the relevance of these topics in fields like engineering, economics, and data science encourages students to develop a deeper appreciation for the subject.

A well-structured Mathematics solution book isn’t just about finding the right answers—it’s about understanding the "why" behind each solution. Clear explanations, multiple solution methods, and interactive exercises help students become independent problem solvers. Whether it's algebraic expressions, coordinate geometry, or probability, a reliable guide ensures that students grasp every concept with clarity and ease

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