# Hi, I'm Sushil, I study in Class 9

And I Learn My Subjects Easily With Vikrant Academy®

## Hi, I'm Sushil, I study in Class 9

And I Learn My Subjects Easily With Vikrant Academy®

# MATHEMATICS

**Chapter 1: **

**NUMBER SYSTEMS**

1.1 Introduction

1.2 Irrational Numbers

1.3 Real Numbers and their Decimal Expansions

1.4 Representing Real Numbers on the Number Line

1.5 Operations on Real Numbers

1.6 Laws of Exponents for Real Numbers

1.7 Summary

2.1 Introduction

2.2 Polynomials in One Variable

2.3 Zeroes of a Polynomial

2.4 Remainder Theorem

2.5 Factorization of Polynomials

2.6 Algebraic Identities

2.7 Summary

Free-Download Full Chapter Questions Solved

3.1 Introduction

3.2 Cartesian System

3.3 Plotting a Point in the Plane if its Coordinates are given

3.4 Summary

Free-Download Full Chapter Questions Solved

4.1 Introduction

4.2 Linear Equations

4.3 Solution of a Linear Equation

4.4 Graph of a Linear Equation in Two Variables

4.5 Equations of Lines Parallel to x-axis and y-axis

4.6 Summary

5.1 Introduction

5.2 Euclid’s De

5.3 Equivalent Versions of Euclid’s Fifth Postulate

5.4 Summary

Free-Download Full Chapter Questions Solved

6.1 Introduction

6.2 Basic Terms and Definitions

6.3 Intersecting Lines and Non-intersecting Lines

6.4 Pairs of Angles

6.5 Parallel Lines and a Transversal

6.6 Lines Parallel to the same Line

6.7 Angle Sum Property of a Triangle

6.8 Summary

Free-Download Full Chapter Questions Solved

7.1 Introduction

7.2 Congruence of Triangles

7.3 Criteria for Congruence of Triangles

7.4 Some Properties of a Triangle

7.5 Some More Criteria for Congruence of Triangles

7.6 Inequalities in a Triangle

7.7 Summary

Free-Download Full Chapter Questions Solved

8.1 Introduction

8.2 Angle Sum Property of a Quadrilateral

8.3 Types of Quadrilaterals

8.4 Properties of a Parallelogram

8.5 Another Condition for a Quadrilateral to be a Parallelogram

8.6 The Mid-point Theorem

8.7 Summary

Free-Download Full Chapter Questions Solved

9.1 Introduction

9.2 Figures on the same Base and Between the same Parallels

9.3 Parallelograms on the same Base and between the same Parallels

9.4 Triangles on the same Base and between the same Parallels

9.5 Summary

Free-Download Full Chapter Questions Solved

10.1 Introduction

10.2 Circles and its Related Terms : A Review

10.3 Angle Subtended by a Chord at a Point

10.4 Perpendicular from the Centre to a Chord

10.5 Circle through Three Points

10.6 Equal Chords and their Distances from the Centre

10.7 Angle Subtended by an Arc of a Circle

10.8 Cyclic Quadrilaterals

10.9 Summary

11.1 Introduction

11.2 Basic Constructions

11.3 Some Constructions of Triangles

11.4 Summary

Free-Download Full Chapter Questions Solved

12.1 Introduction

12.2 Area of a Triangle – by Heron’s Formula

12.3 Application of Heron’s Formula in finding Areas of Quadrilaterals

12.4 Summary

Free-Download Full Chapter Questions Solved

13.1 Introduction

13.2 Surface Area of a Cuboid and a Cube

13.3 Surface Area of a Right Circular Cylinder

13.4 Surface Area of a Right Circular Cone

13.5 Surface Area of a Sphere

13.6 Volume of a Cuboid

13.7 Volume of a Cylinder

13.8 Volume of a Right Circular Cone

13.9 Volume of a Sphere

10.10 Summary

Free-Download Full Chapter Questions Solved

14.1 Introduction

14.2 Collection of Data

14.3 Presentation of Data

14.4 Graphical Representation of Data

14.5 Measures of Central Tendency

14.6 Summary

Free-Download Full Chapter Questions Solved

15.1 Introduction

15.2 Probability – an Experimental Approach

15.3 Summary

Free-Download Full Chapter Questions Solved

# Question & Answers (Solved)

## Chapter – 1: Number Systems

Exercise – 1.1 1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0? Solution: We know that, a number is said to be…

## Chapter – 3: Coordinate Geometry

Exercise 3.1 1. How will you describe the position of a table lamp on your study table to another person? Solution: For describing the position of table lamp on the study table, we take two lines, a…

## Chapter – 4: Linear Equations in Two Variables

Exercise 4.1 1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and…

## Chapter – 5: Introduction to Euclid’s Geometry

Exercise 5.1 1. Which of the following statements are true and which are false? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are an infinite number of lines…

## Chapter – 7: Triangles

Exercise: 7.1 1. In quadrilateral ACBD, AC = AD and AB bisect ∠A (see Fig. 7.16). Show that ΔABC≅ ΔABD. What can you say about BC and BD? Solution: It is given that AC and AD are…

## Chapter – 8: Quadrilaterals

Exercise 8.1 1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral. Solution: Let the common ratio between the angles be = x. We…

## Chapter – 9: Areas of Parallelograms and Triangle

Exercise 9.1 1. Which of the following figures lie on the same base and in-between the same parallels? In such a case, write the common base and the two parallels. Solution: (i) Trapezium ABCD and ΔPDC lie…

## Chapter – 12: Heron’s Formula

Exercise: 12.1 1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the…

## Chapter – 13: Surface Area and Volumes

Exercise 13.1 1. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: (i)The…

## Chapter – 14: Statistics

Exercise 14.1 1. Give five examples of data that you can collect from your day-to-day life. Solution: Five examples from day-to-day life: 2. Classify the data in Q.1 above as primary or secondary data. Solution: Primary data:…

## Chapter – 15: Probability

Exercise 15.1 1. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Solution: According to the question, Total number…