## Maths

## CLASS 10

## NCERT Textbook & Solution

## TERM - I

Class 10 Maths NCERT textbook has 15 chapters in which TERM I has 8 chapters.

All the questions and answers that are present in the CBSE NCERT Books has been included in this page. We have provided all the Class 10 Maths NCERT Solutions with a detailed explanation i.e., we have solved all the question with step by step solutions in understandable language. So students having great knowledge over NCERT Solutions Class 10 Maths can easily make a grade in their board exams.

We have given Key concepts, Learning Objectives and Learning Outcomes so that students can understand what to study and what concept he will be using while solving certain type of prolems.

Working on NCERT Solutions for Class 10 will help students to get an idea about how to solve the problems. With the help of these NCERT Solutions for Class 10 Maths you can easily grasp basic concepts better and faster. Moreover, it is a perfect guide to help you to score good marks in CBSE board examination. Just click on the chapter wise links given below to practice the NCERT Solutions for the respective chapter.

We have extensively covered all exercises and every single question of all units of the NCERT Class 10 Mathematics textbook.

The detailed syllabus has been discussed below along with the Key Concepts and Learning outcomes. So that learning can be Joyful.

## Chapter 1

## Real Numbers

- Euclid’s Division
- Fundamental Theorem of Arithmetic
- Irrational Numbers
- Decimal Representation of Irrational Numbers

- Apply Euclid Division Algorithm and obtain HCF of two positive integers in the context of the given problem.
- Apply Euclid Division Algorithm and prove results of positive integers in the form of `ax+b` where `a` and `b` are constants.
- Use the Fundamental Theorem of Arithmetic and calculate HCF and LCM of the given numbers in the context of the given problem.
- Recall the properties of irrational number and prove that whether the sum/difference/product/quotient of two numbers is irrationals or not.
- Apply theorems of irrational number and prove whether a given number is irrational or not.
- Apply theorems of rational numbers and find out about the nature of their decimal representation and their factors.

Generalises properties of numbers and relations among them studied earlier, to evolve results, such as, Euclid’s division algorithm, fundamental theorem of arithmetic in order to apply them to solve problems related to real life contexts.

## Chapter 2

## Polynomials

- Geometrical meaning of Zeroes of a Polynomial.
- Relationship between Zeroes and Coefficients of a Polynomial.
- Division Algorithm for Polynomials.

- Recall degree of polynomial and find the number of zeroes of polynomial.
- Analyse the graph of the polynomials and find the number of zeroes of polynomial.
- Compute zeroes of the polynomials and verify the relationship between zeroes and the coefficients.
- Compute the sum and product of zeroes of the polynomial and find the quadratic polynomial.
- Divide the two given polynomials and verify the division algorithm.
- Divide the given polynomial with its known zero and find all the other zeroes of that polynomial.

Uses algebraic and graphical method of finding zeroes of a polynomial in order to establish a relationship between them.

## Chapter 3

## Pair of Linear Equations in Two Variables

- Introduction and Properties of Linear equations and nonlinear equations.
- Graphical Method of Solution of a pair of Linear Equations.
- Algebraic method for solving Equations.
- Equations Reducible to a Pair of Linear Equations in Two Variables.

- State the properties of linear equation and classify the given equations as linear or nonlinear.
- Interpret the concepts of linear equations and represent any given situation algebraically and graphically.
- Plot the lines corresponding to the given two linear equations and comment on the nature/behaviour of the lines representing the linear equations.
- Use different algebraic methods and solve a pair of linear equations.
- Use the most appropriate algebraic method and solve the given pair of linear equations.
- Use the concepts of pair of linear equations in two variables and represent any given situation algebraically and find its solution.
- Calculate the ratio of coefficients of linear equations and discuss the nature of pair of linear equations.
- Rewrite the given equations using substitution method which are reducible to a pair of linear equations and find the solution of those equations.

Uses graphical and other methods in order to finds solutions of pairs of linear equations in two variables.

## Chapter 6

## Triangles

- Similar figures.
- Similarity of triangles.
- Criteria for similarity of Triangles.
- Areas of Similar Triangles.
- Pythagoras Theorem.

- Distinguish between congruency and similarity and understand the concept of similar figures.
- Compute the angles and ratio of sides of polygons and determine their similarity.
- Compute the angles and ratio of sides of triangles and determine their similarity.
- Apply basic proportionality theorem and its converse and determine the ratio of sides in the given triangle(s).
- Apply various criteria of similarity and prove whether given triangles are similar or not.
- Show similarity of triangles and solve real life problems.
- Compute the square of the ratio of the corresponding sides of triangles and find the area of similar triangles.
- Compute the area of similar triangles and find the relation between their sides, medians, mid points of the triangles.
- Apply the theorem that if a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and prove Pythagoras Theorem.
- Prove Pythagoras theorem and its converse and solve real life problems.
- Apply Pythagoras theorem and its converse and determine that whether a given triangle is al right-angled triangle or not.

- Uses reasoning in order to differentiate between congruent and similar figures.
- Uses different geometric criteria established earlier such as basic proportionality theorem etc. in order to establish properties for similarity of two triangles.

## Chapter 7

## Coordinate Geometry

- Basics of Graphs.
- Distance Formula.
- Section Formula.
- Area of a Triangle.

- Identify `x` and `y` coordinate and plot points on the graph.
- Apply and derive distance formula and determine the distance between two coordinates on the graph.
- Apply distance formula and solve various mathematical and real-life problems graphically.
- Apply and derive section formula and divide the line segment in a given ratio.
- Apply distance and section formula and determine the vertices/diagonals/mid points of given geometrical shapes.
- Apply and derive the formula of area of triangle geometrically and determine the area of quadrilateral/triangle.

Derives formulae to establish relations for geometrical shapes in the context of a coordinate plane, such as finding the distance between two given points, in order to determine coordinates of a point between any two given points, to find area of a triangle etc.

## Chapter 8

## Introduction to Trigonometry

- Trigonometric Ratios.
- Trigonometric Ratios of Some Specific Angles.
- Trigonometric Ratios of Complementary Angles.
- Trigonometric Identities.

- Describe trigonometry and study the relationship between side and angle of a triangle.
- Define and distinguish various trigonometric ratios and describe and verify sine, cosine, tangent, cosecant, secant, cotangent of an angle.
- Use given trigonometric ratio(s) and find and verify other trigonometric ratios/angles of the triangle.
- Compute the trigonometric ratio 0°, 30°, 45°, 60° and 90° and use these for different angles.
- Compute the trigonometric ratio of complimentary angles and apply the values in solving contextual problems.
- Compute and apply trigonometric identities and simplify and solve mathematical problems.

Determines all trigonometric ratios with respect to a given acute angle (of a right triangle) in order to use them in solving problems in daily life contexts like finding heights of different structures or distances from them.

## Chapter 12

## Areas Related to Circles

- Perimeter and Area of a Circle – A Review
- Areas of Sector and Segment of a Circle
- Areas of combinations of plane figures

- Describe the relationship between circumference and diameter of a circle and define `\pi`.
- Apply the concepts of circumference and area of circle for solving problems on various circular objects in real life.
- Describe sector and segment of a circle and differentiate between the two.
- Describe minor and major sector of a circle and differentiate between the two.
- Describe minor and major segment of a circle and differentiate between the two.
- Apply the formula of area of sector and segment of a circle, and compute the area of a specified region.
- Calculate the length of an arc of a circle and comment whether it is the major arc or minor arc.
- Calculate the area of various combinations of plane figures and apply the concepts of circles, quadrilaterals and triangles.

## Chapter 15

## Probability

Probability- A Theoretical Approach.

- Differentiate between Empirical Probability and Theoretical Probability and find the two for a variety of cases.
- Calculate the probability of given events in an experiment and comment whether they are Complementary Events/Sure Events/Impossible Events.
- Represent using organized lists, tables, or tree diagrams and list the sample space for compound events.
- Calculate the probability of various events and rank them from most to least probable events.

Calculate and determine the probability of a given event.