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
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3.1 Introduction
3.2 Cartesian System
3.3 Plotting a Point in the Plane if its Coordinates are given
3.4 Summary
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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
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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
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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
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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
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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
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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
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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
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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
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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
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15.1 Introduction
15.2 Probability – an Experimental Approach
15.3 Summary
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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…
