Through the years, from the time of the Kothari Commission, there have been several committees looking at ways of making the school curriculum meaningful and enjoyable for the learners. Based on the understanding developed over the years, a National Curriculum Framework (NCF) was finalised in 2005. As part of this exercise, a National Focus Group on Teaching of Mathematics was formed. Its report, which came in 2005, highlighted a constructivist approach to the teaching and learning of mathematics. The essence of this approach is that children already know, and do some mathematics very naturally in their surroundings, before they even join school. The syllabus, teaching approach, textbooks etc., should build on this knowledge in a way that allows children to enjoy mathematics, and to realise that mathematics is more about a way of reasoning than about mechanically applying formulae and algorithms.

NCERT Solutions for Class 10 are solved by experts of AskGuru in order to help students to obtain excellent marks in their board examination. All the questions and answers that are present in the CBSE NCERT Books has been included on this page. The CBSE Class 10 board exams are the first public exams that every student has to face. The structure of this exam is to test the candidate’s practical as well as theoretical knowledge. Hence, it is important for students to have a clear understanding of the concepts and relating them to real-world applications will help them have strong practical knowledge as well.

NCERT Solutions for Class 10 Maths for all the exercises from Chapters 1 to 15 are provided here.

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Chapter 1

Real Numbers

Euclid’s division lemma, Fundamental Theorem of Arithmetic, Proofs of irrationality of √2, √3, √5 Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

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Chapter 4

Quadratic Equations

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization; and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

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Chapter 7

Coordinate Geometry

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Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

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Chapter 10

Circles

Tangent to a circle at, point of contact.

 

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

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

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Chapter 13

Surface Areas and Volumes

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. 

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

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Chapter 2

Polynomials

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. division algorithms for polynomials with real coefficients.

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Chapter 5

Arithmetic Progressions

Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

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Chapter 8

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 0ㅇ and 90ㅇ. Values of the trigonometric ratios of 30ㅇ, 45ㅇ and 60ㅇ. Relationships between the ratios. Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

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Chapter 11

Constructions

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

Tangents to a circle from a point outside it. 

Construction of a triangle similar to a given triangle.

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Chapter 14

Statistics

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

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Chapter 3

Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for the number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. 

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Chapter 6

Triangles

Definitions, examples, counter-examples of similar triangles. Theorems on similarity

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Chapter 9

Some Applications of Trigonometry

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°.

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Chapter 12

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 the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)

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Chapter 15

Probability

The classical definition of probability. Simple problems on finding the probability of an event.