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…
