# Hi, I'm Shubham, I study in Class 10

And I Learn My Subjects Easily With Vikrant Academy®

## Hi, I'm Shubham, I study in Class 10

And I Learn My Subjects Easily With Vikrant Academy®

# MATHEMATICS

**Chapter 1:**

** Real Numbers**

1.1 Introduction

1.2 Euclid’s Division Lemma

1.3 The Fundamental Theorem of Arithmetic

1.4 Revisiting Irrational Numbers

1.5 Revisiting Rational Numbers and Their Decimal Expansions

1.6 Summary

2.1 Introduction

2.2 Geometrical Meaning of the Zeroes of a Polynomial

2.3 Relationship between Zeroes and Coefficients of a Polynomial

2.4 Division Algorithm for Polynomials

2.5 Summary

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3.1 Introduction

3.2 Pair of Linear Equations in Two Variables

3.3 Graphical Method of Solution of a Pair of Linear Equations

3.4 Algebraic Methods of Solving a Pair of Linear Equations

3.4.1 Substitution Method

3.4.2 Elimination Method

3.4.3 Cross-Multiplication Method

3.5 Equations Reducible to a Pair of Linear Equations in Two Variables

3.6 Summary

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4.1 Introduction

4.2 Quadratic Equations

4.3 Solution of a Quadratic Equation by Factorization

4.4 Solution of a Quadratic Equation by Completing the Square

4.5 Nature of Roots

4.6 Summary

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5.1 Introduction

5.2 Arithmetic Progressions

5.3 nth Term of an AP

5.4 Sum of First n Terms of an AP

5.5 Summary

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6.1 Introduction

6.2 Similar Figures

6.3 Similarity of Triangles

6.4 Criteria for Similarity of Triangles

6.5 Areas of Similar Triangles

6.6 Pythagoras Theorem

6.7 Summary

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7.1 Introduction

7.2 Distance Formula

7.3 Section Formula

7.4 Area of a Triangle

7.5 Summary

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8.1 Introduction

8.2 Trigonometric Ratios

8.3 Trigonometric Ratios of Some Specific Angles

8.4 Trigonometric Ratios of Complementary Angles 8.5 Trigonometric Identities

8.6 Summary

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10.1 Introduction

10.2 Tangent to a Circle

10.3 Number of Tangents from a Point on a Circle

10.4 Summary

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11.1 Introduction

11.2 Division of a Line Segment

11.3 Construction of Tangents to a Circle

11.4 Summary

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12.1 Introduction

12.2 Perimeter and Area of a Circle — A Review

12.3 Areas of Sector and Segment of a Circle

12.4 Areas of Combinations of Plane Figures

12.5 Summary

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13.1 Introduction

13.2 Surface Area of a Combination of Solids

13.3 Volume of a Combination of Solids

13.4 Conversion of Solid from One Shape to Another

13.5 Frustum of a Cone

13.6 Summary

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14.1 Introduction

14.2 Mean of Grouped Data

14.3 Mode of Grouped Data

14.4 Median of Grouped Data

14.5 Graphical Representation of Cumulative Frequency Distribution

14.6 Summary

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15.1 Introduction

15.2 Probability — A Theoretical Approach

15.3 Summary

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# Question & Answers (Solved)

## Chapter – 1: Real Number

Exercise 1.1 1. Use Euclid’s division algorithm to find the HCF of: i. 135 and 225 ii. 196 and 38220 iii. 867 and 255 Solutions: i. 135 and 225 As you can see, from the question 225…

## Chapter – 2: Polynomials

Exercise 2.1 1. The graphs of y = p(x) is given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Solutions: Graphical method to find zeroes:- Total number…

## Chapter – 3: Pair of Linear Equations in Two Variables

Exercise 3.1 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t…

## Chapter – 4: Quadratic Equation

Exercise 4.1 1. Check whether the following are quadratic equations: (i) (x + 1)2 = 2(x – 3) (ii) x2 – 2x = (–2) (3 – x) (iii) (x – 2)(x + 1) = (x – 1)(x + 3)…

## Chapter – 5: Arithmetic Progressions

Exercise 5.1 1. In which of the following situations, does the list of numbers involved make as arithmetic progression and why? (i) The taxi fare after each km when the fare is Rs 15 for the first…

## Chapter – 6: Triangles

Exercise 6.1 1. Fill in the blanks using correct word given in the brackets: – (i) All circles are __________. (Congruent, similar) Solution: Similar (ii) All squares are __________. (Similar, congruent) Solution: Similar (iii) All __________ triangles are similar….

## Chapter – 7: Coordinate Geometry

Exercise7.1 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (- a, – b) Solution: Distance formula to find the distance between two…

## Chapter – 8: Introduction to Trigonometry

Exercise 8.1 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C Solution: In a given triangle ABC, right angled at…

## Chapter – 9: Some Application of trigonometry

Exercise 9.1 1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the…

## Chapter – 10: Circles

Exercise: 10.1 1. How many tangents can a circle have? Solution: There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal distance from a point. Since there are…

## Chapter – 11: Constructions

Exercise 11.1 In each of the following, give the justification of the construction also: 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Construction…