NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Euclid’s division lemma, Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

• Real Numbers Class 10 Ex 1.1
• Real Numbers Class 10 Ex 1.2
• Real Numbers Class 10 Ex 1.3
• Real Numbers Class 10 Ex 1.4

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Zeros of a polynomial. The relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.2
• Polynomials Class 10 Ex 2.3
• Polynomials Class 10 Ex 2.4

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and their graphical solution. Geometric representation of different possibilities of solutions/inconsistency.

Algebraic conditions for a number of solutions. A solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems must be included. Simple problems on equations reducible to linear equations.

• Pair of Linear Equations in Two Variables Class 10 Ex 3.1
• Pair of Linear Equations in Two Variables Class 10 Ex 3.2
• Pair of Linear Equations in Two Variables Class 10 Ex 3.3
• Pair of Linear Equations in Two Variables Class 10 Ex 3.4
• Pair of Linear Equations in Two Variables Class 10 Ex 3.5
• Pair of Linear Equations in Two Variables Class 10 Ex 3.6
• Pair of Linear Equations in Two Variables Class 10 Ex 3.7

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations

Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). A solution of the quadratic equations (only real roots) by factorization, by completing the square and by using the quadratic formula. The relationship between discriminant and the nature of roots.

Situational problems based on quadratic equations related to day to day activities to be incorporated.

• Quadratic Equations Class 10 Ex 4.1
• Quadratic Equations Class 10 Ex 4.2
• Quadratic Equations Class 10 Ex 4.3
• Quadratic Equations Class 10 Ex 4.4

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

The motivation for studying Arithmetic Progression Derivation of the nth term and some of the first n terms of A.P. and their application in solving daily life problems.

• Arithmetic Progressions Class 10 Ex 5.1
• Arithmetic Progressions Class 10 Ex 5.2
• Arithmetic Progressions Class 10 Ex 5.3
• Arithmetic Progressions Class 10 Ex 5.4

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Definitions, examples, counter examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to some of the squares on the other two sides, the angles opposite to the first side is a right angle.

• Triangles Class 10 Ex 6.1
• Triangles Class 10 Ex 6.2
• Triangles Class 10 Ex 6.3
• Triangles Class 10 Ex 6.4
• Triangles Class 10 Ex 6.5
• Triangles Class 10 Ex 6.6

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

Lines (In two-dimensions)
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). Area of a triangle.

• Coordinate Geometry Class 10 Ex 7.1
• Coordinate Geometry Class 10 Ex 7.2
• Coordinate Geometry Class 10 Ex 7.3
• Coordinate Geometry Class 10 Ex 7.4

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

1. 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^o and 90^o. Values (with proofs) of the trigonometric ratios of 30^o, 45^o and 60^o. Relationships between the ratios.

• Introduction to Trigonometry Class 10 Ex 8.1
• Introduction to Trigonometry Class 10 Ex 8.2
• Introduction to Trigonometry Class 10 Ex 8.3
• Introduction to Trigonometry Class 10 Ex 8.4

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

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

Heights and Distances: Angle of elevation, Angle of Depression
Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30^o, 45^o, 60^o.

• Some Applications of Trigonometry Class 10 Ex 9.1

NCERT Solutions for Class 10 Maths Chapter 10 Circles

Tangent to a circle at, the point of contact.

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 a circle are equal.

• Circles Class 10 Ex 10.1
• Circles Class 10 Ex 10.2

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.

• Constructions Class 10 Ex 11.1
• Constructions Class 10 Ex 11.2

NCERT Solutions for Class 10 Maths 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 a central angle of 60°, 90°, and 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

• Areas Related to Circles Class 10 Ex 12.1
• Areas Related to Circles Class 10 Ex 12.2
• Areas Related to Circles Class 10 Ex 12.3

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes

1. 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.

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

• Surface Areas and Volumes Class 10 Ex 13.1
• Surface Areas and Volumes Class 10 Ex 13.2
• Surface Areas and Volumes Class 10 Ex 13.3
• Surface Areas and Volumes Class 10 Ex 13.4
• Surface Areas and Volumes Class 10 Ex 13.5

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

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

• Statistics Class 10 Ex 14.1
• Statistics Class 10 Ex 14.2
• Statistics Class 10 Ex 14.3
• Statistics Class 10 Ex 14.4

NCERT Solutions for Class 10 Maths Chapter 15 Probability

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

• Probability Class 10 Ex 15.1
• Probability Class 10 Ex 15.2