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Area of a circle = π r. Length of an arc of a sector of a circle with radius r and angle with degree measure θ is= theta/360 *2*π *r. Area of a sector of a circle with radius r and angle with degree measure θ is theta/360 *π*r.

Class 10 Area Related To Circle Reduced Syllabus 2021

Areas Related to Circles (10 Periods)

 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° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

Class 10 Area Related To Circle Deleted Syllabus 2021

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant

Class 10 Circle Reduced Syllabus 2021

Circles (8 Periods)

Tangent to a circle at, 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.

Class 10 Circle Deleted Syllabus 2021

Class 10 Maths Some Application Of Trigonometry Mind Maps The height or length of an object or the distance between two distinct objects can be determined with the help of trigonometric ratios.

Class 10 Some Applications of Trigonometry Reduced Syllabus 2021

Heights and Distances: Angle of elevation, Angle of Depression. (8 Periods)

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.

Class 10 Some Applications of Trigonometry Deleted Syllabus 2021

Trigonometry (from Greek trigōnon, “triangle” and metron, “measure”) is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Class 10 Introduction to Trigonometry Reduced Syllabus 2021

Introduction to Trigonometry (8 Periods)

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values (with proofs) of the trigonometric ratios of 30^o, 45^o and 60^o. Relationships between the ratios.

Class 10 Introduction to Trigonometry Deleted Syllabus 2021

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight.

Class 10 Coordinate Geometry Reduced Syllabus 2021

COORDINATE GEOMETRY

1. Lines (In two-dimensions) (10 Periods)

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division). 

Class 10 Coordinate Geometry Deleted Syllabus 2021

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Class 10 Triangle Reduced Syllabus 2021

Triangles (10 Periods)

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) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Class 10 Triangle Deleted Syllabus 2021

An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. The sum of a finite arithmetic progression is called an arithmetic series

Class 10 Arithmetic Progressions Reduced Syllabus 2021

4. Arithmetic Progressions (4 Periods)

Motivation for studying Arithmetic Progression Derivation of the n^th term and sum of the first n terms of an A.P. 

Class 10 Arithmetic Progressions Deleted Syllabus 2021

What is Quadratic Equation? Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0. … The quadratic equation will always have two roots. The nature of roots may be either real or imaginary.

Class 10 Quadratic Equation Reduced Syllabus 2021

3. Quadratic Equations (10 Periods)

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.

Class 10 Quadratic Equation Deleted Syllabus 2021

An equation of the form Ax + By + C = 0 is called a linear equation in two variables x and y where A, B, C are real numbers. Two linear equations in the same two variables are called a pair of linear equations in two variables.

Class 10 Pair of linear equation in two variable reduced syllabus 2021

2. Pair of Linear Equations in Two Variables (11 Periods)

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.

Class 10 Pair of linear equation in two variable deleted syllabus 2021

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.

Class 10 Polynomial Reduced Syllabus 2021

1. Polynomials  (4 Periods)

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. 

Class 10 Polynomial Deleted Syllabus 2021