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 CBSE Syllabus 2017, providing even better strengths for learners. Students of class 10 must go through the Sample papers and Previous Year Board Papers issued by Central Board of Secondary Education as a supplementary practice for Science and maths. Books and their solutions of other subjects as Science, Social Science and Hindi are also available to download in PDF format. If you are having any suggestion for the improvement, you are welcome. The improvement of the website and its contents are based on your suggestion and feedback. Download NCERT solutions for Science, Social Science and Hindi.
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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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.
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.
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.)
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
Classical definition of probability. Simple problems on single events (not using set notation).