Free NCERT Solutions for Class 10 Maths PDF format in Hindi and English medium are available to download. * NCERT Solutions* & Exemplar books provide excellent practice including higher order thinking skills (HOTS) for each chapter. So, it is advised to explore these books to make your knowledge foundation better. Some of the books are available as named Revision Book which are confined to latest

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## NCERT Solutions for Class 10 Maths PDF

### Chapter 1: Real Numbers

In class 9, we have studied rational numbers and irrational numbers collectively forming real numbers. Here we will learn the division algorithm (Euclid’s division lemma) and fundamental theorem of arithmetic. Getting LCM and HCF using prime factorisation and Euclid’s division lemma. Proving square roots of 2, 3, 5 are irrational numbers.

**NCERT Solutions Chapter 1 Real Numbers (Hindi & English Medium)****NCERT Book for class 10 Maths (All Chapters)****Revision Book for Class X Maths (All Chapters)****NCERT Exemplar Problems Solutions**

### Chapter 2: Polynomials

We have learnt Degree and coefficient of terms of polynomial and their factorization in class 9. Now we will find the relationship between the zeroes and their coefficient. Use of factor theorem to find the zeroes of the polynomials with degree 2, 3 or 4.

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

You have studied a linear equation in one variable and two variables in previous class. Now there is solution of pair of linear equations in class 10, using various methods like graphically, elimination, substitution and cross multiplication. Reduction of given equations into simple linear equations and get their solution

### Chapter 4: Quadratic Equations

Solution of quadratic equations by different methods – Factorization, Completing the square method and using quadratic formula. Checking the nature of roots using discriminant. Questions based on daily life.

### Chapter 5: Arithmetic Progression

To check whether the given sequence is in Arithmetic Progressions or not. To find the missing term of the AP and sum of the given sequence. To determine AP when sum to n terms is given. Some application base questions from daily life.

### Chapter 6: Triangles

Proof of Basic Proportionality theorem (Thales theorem) and question based on this theorem. Proof of Pythagoras theorem and its converse. Area theorem and its applications. Questions based on other theorems which are given for motivation only (proof will not be asked in the examination).

### Chapter 7: Coordinate Geometry

### Chapter 8: Introduction to Trigonometry

### Chapter 9: Some Applications of Trigonometry

### Chapter 10: Circles

### Chapter 11: Constructions

### Chapter 12: Area Related to Circles

### Chapter 13: Surface Areas and Volumes

### Chapter 14: Statistics

### Chapter 15: Probability

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**COORDINATE GEOMETRY**

LINES (In two-dimensions)

Review: Concepts of coordinate geometry, graphs of linear equations. Distance between two points. Section formula (internal division). Area of a triangle.

**INTRODUCTION TO TRIGONOMETRY**

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0 degree and 90 degree. Values (with proofs) of the trigonometric ratios of 30, 45 and 60. Relationships between the ratios.

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

**HEIGHTS AND DISTANCES**

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30, 45, 60.

**CIRCLES**

Tangent to a circle at a point.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. (Prove) The lengths of tangents drawn from an external point to circle are equal.

**CONSTRUCTIONS**

1. Division of a line segment in a given ratio (internally).

2. Tangent to a circle from a point outside it.

3. Construction of a triangle similar to a given triangle.

**AREAS RELATED TO CIRCLES**

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60, 90 and 120 only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

**SURFACE AREAS AND VOLUMES**

(i) Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken.)

**STATISTICS**

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

**PROBABILITY**

Classical definition of probability. Simple problems on single events (not using set notation).