COURSE STRUCTURE
CLASS –X (2021-22)
FIRST TERM
One Paper
90 Minute
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 30
, 45 and 60
. Relationships between the
ratios.
TRIGONOMETRIC IDENTITIES
Proof and applications of the identity . 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
UNIT-ALGEBRA
1. 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 quadratic formula. Relationship
between discriminant and nature of roots. Situational problems based on quadratic
equations related to day to day activities (problems on equations reducible to quadratic
equations are excluded)
2. ARITHMETIC PROGRESSIONS
Motivation for studying 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.
(Applications based on sum to n terms of an A.P. are excluded)
UNIT- GEOMETRY
3. CIRCLES
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.
4. CONSTRUCTIONS
1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
UNIT-TRIGONOMETRY
5. 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°, 45°, 60°.
UNIT-MENSURATION
6. 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.
2. 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).
UNIT-STATISTICS & PROBABILITY
7. STATISTICS
Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by
Direct Method and Assumed Mean Method only
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