CLASS –X (2021-22) FIRST TERM

UNIT-NUMBER SYSTEMS

1. REAL NUMBER

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and 

after illustrating and motivating through examples. Decimal representation of rational 

numbers in terms of terminating/non-terminating recurring decimals.

UNIT-ALGEBRA

2. POLYNOMIALS 

Zeroes of a polynomial. Relationship between zeroes and coefficients of quadratic 

polynomials only.

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 number of solutions. Solution of a 

pair of linear equations in two variables algebraically - by substitution and by elimination. 

Simple situational problems. Simple problems on equations reducible to linear 

equations.

UNIT-COORDINATE GEOMETRY

4. COORDINATE GEOMETRY

 LINES (In two-dimensions) 

 Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. 

Section formula (internal division)

 UNIT-GEOMETRY

 5. 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. (Motivate) 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. (Motivate) In a triangle, if the square on one side is equal to sum of the squares on the 

other two sides, the angle opposite to the first side is a right angle.

UNIT- TRIGONOMETRY

6. INTRODUCTION TO TRIGONOMETRY 

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well 

defined). Values of the trigonometric ratios of 300

, 450 and 600

. Relationships between the 

ratios. 

TRIGONOMETRIC IDENTITIES 

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

UNIT-MENSURATION

7. 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° and 90° only. 

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

UNIT- STATISTICS & PROBABILITY

 8. PROBABILITY 

Classical definition of probability. Simple problems on finding the probability of an 

event.