Real Numbers

12 Topics | 4 Quizzes

13 Topics | 4 Quizzes

Polynomials

Degree of a Polynomial

Types of polynomials based on the number of terms

Types of Polynomials based on Degree

Value of Polynomial

Zero of a Polynomial

Graph of a Linear Polynomial

Graph of Quadratic Polynomial

Factorisation of Polynomials

Splitting the middle term:

Relationship between Zeroes and Coefficients of a Polynomial

Division Algorithm

Algebraic Identities

Practice Questions 2 – Polynomials – Class X

Olympiad Questions – Polynomials – Class X

Concept Checkers – Polynomials – Class X

Practice Questions – Polynomials – Class X

Pair of Linear Equations in Two Variables

4 Topics | 4 Quizzes

Linear Equations

Pair of Linear Equations

Graphical method of solution of a pair of Linear Equations

Algebraic Methods of Solving a Pair of Linear Equations

Practice Questions 2 – Pair of Linear Equations in Two Variables – Class X

Olympiad Questions – Pair of Linear Equations in Two Variables – Class X

Concept Checkers – Pair of Linear Equations in Two variables – Class X

Practice Questions – Pair of Linear Equations in Two Variables – Class X

Quadratic Equations

7 Topics | 4 Quizzes

Quadratic Polynomial

Quadratic Equation

Standard form of Quadratic Equation

Types of Quadratic Equations

Roots of a Quadratic Equation

Methods to solve the Quadratic Equations

Nature of Roots

Practice Questions 2 – Quadratic Equations – Class X

Olympiad Questions – Quadratic Equations – Class X

Concept Checkers – Quadratic Equations – Class X

Concept Checkers – Quadratic Equation – Class X

Arithmetic Progressions

5 Topics | 4 Quizzes

Arithmetic Progressions

Finite or Infinite Arithmetic Progressions

The general form of an AP

Arithmetic Series

Sum of first n terms of an Arithmetic series

Olympiad Questions-Arithmetic Progression-ClassX

Practice Questions 2-Arithmetic Progression-ClassX

Concept Checkers – Arithmetic Progressions – Class X

Practice Questions – Arithmetic Progressions – Class X

8 Topics | 4 Quizzes

Centers of the Triangle

Similarity Criteria of Triangles

Basic Proportionality Theorem (Thales Theorem)

Converse of Basic Proportionality Theorem

Pythagoras Theorem (Baudhayan Theorem)

Practice Questions 2-Triangles-ClassX

Olympiad Questions-Triangles-ClassX

Concept Checkers – Triangles – Class X

Practice Questions – Triangles – Class X

Coordinate Geometry

9 Topics | 4 Quizzes

Cartesian coordinate system

Equation of a Straight Line

Distance formula

Section formula

Mid-point formula

Centroid of a Triangle

Area of a triangle given its vertices

Collinearity Condition

Using section formula

Concept Checkers – Coordinate Geometry – Class X

Practice Questions – Coordinate Geometry – Class X

Practice Questions 2-Coordinate Geometry-ClassX

Olympiad Questions-Coordinate Geometry-ClassX

Introduction to Trigonometry

7 Topics | 4 Quizzes

Trigonometry

Trigonometric Ratios

Relation between Trigonometric Ratios

Trigonometric Ratios of Some Specific Angles

Trigonometric Ratios of Complementary Angles

Range of Trigonometric Ratios from 0 to 90 degrees

Trigonometric Identities

Practice Questions 2-Introduction to Trigonometry-Class X

Olympiad Questions-Introduction to Trigonometry-Class X

Concept Checkers -Trigonometry – Class X

Practice Questions -Trigonometry – Class X

Some Applications of Trigonometry

5 Topics | 2 Quizzes

APPLICATION OF TRIGONOMETRY

Practice Questions-Some Applications of Trigonometry-Class X

Olympiad Questions-Some Applications of Trigonometry-Class X

Circles

5 Topics | 2 Quizzes

Introduction to Circles

Circle and line in a plane

Tangent to a Circle

Circle Theorems

Length of a tangent

Olympiad Questions-Circles-Class X

Practice Questions-Circles-Class X

Constructions

3 Topics | 2 Quizzes

Introduction

Division of a Line Segment

Construction of a Triangle similar to a given Triangle as per given Scale

Concept Checkers – Construction – Class X

Practice Questions-Construction-Class X

Areas Related to Circles

5 Topics | 3 Quizzes

Areas related to Circle

Area of a Sector of a Circle

Perimeter and Area of the Semi-circle

Areas of Segments of the Circle

Areas of Combinations of Plane Figures

Concept Checkers-Areas Related to Circles-Class X

Practice Questions-Areas Related to Circles-Class X

Olympiad Questions-Areas Related to Circles-Class X

Surface Areas and Volumes

4 Topics | 2 Quizzes

Introduction

Volume of a combination of solids

Conversion of Solid from One Shape to Another

Frustum of a Cone

Olympiad Questions-Surface area and volume-Class X

Practice Questions-Surface area and volumes-Class X

8 Topics | 2 Quizzes

Mean of Grouped Data (Without Class-Interval)

Mean of Grouped Data (With Class-Interval)

Mode of Grouped Data

Median of Grouped Data

Graphical Representation of Cumulative Frequency Distribution

Practice Questions-Statistics-Class X

Olympiad Questions-Statistics-Class X

Probability

4 Topics | 1 Quiz

Introduction

Sum of Probabilities

Sure or Certain Event

Complementary Events

Olympiad Questions-Probability-Class X

Mock Test 1-Class X

Mock Test 2 – Class X

Mock Test 3 – Class X

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Nature of Roots

Mathematics Class X Quadratic Equations Nature of Roots

From the quadratic formula, we can see that the two roots of the Quadratic Equation are –

[mathtype] $x = \dfrac{{ - b + \sqrt {{b^2} - 4ac} }}{{2a}}$ And [mathtype] $\dfrac{{ - b - \sqrt {{b^2} - 4ac} }}{{2a}}$

Or [mathtype] $x = \dfrac{{ - b \pm \sqrt D }}{{2a}}$

Where [mathtype] $D = {b^2} - 4ac$

The nature of the roots of the equation depends upon the value of D, so it is called the discriminant.

Based on the value of the discriminant,[mathtype] $D = {b^2} - 4ac$ , the roots of a quadratic equation can be of three types.

Case 1: If D>0, the equation has two distinct real roots.

Case 2: If D=0, the equation has two equal real roots.

Case 3: If D<0, the equation has no real roots.

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