COURSE STRUCTURE CLASS –X

Units Unit Name Marks
I NUMBER SYSTEMS 06
II ALGEBRA 20
III COORDINATE GEOMETRY 06
IV GEOMETRY 15
V TRIGONOMETRY 12
VI MENSURATION 10
VII STATISTICS & PROBABILTY 11
Total 80
UNIT I: NUMBER SYSTEMS
1. REAL NUMBER (8) Periods
 Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and
after illustrating and motivating through examples, Proofs of irrationality of
Decimal representation of rational numbers interms of terminating/non-terminating
recurring decimals.
UNIT II: ALGEBRA
1. POLYNOMIALS (4) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of quadratic
polynomials.
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.
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 quadratic formula. Relationship
between discriminant and nature of roots.
4. ARITHMETIC PROGRESSIONS (4) Periods
Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the
first n terms of A.P. 
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UNIT III: COORDINATE GEOMETRY
1. LINES (In two-dimensions) (10) Periods
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula.
Section formula (internal division).
UNIT IV: GEOMETRY
1. 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.
2. 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. 
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3. CONSTRUCTIONS (4) Periods
1. Division of a line segment in a given ratio (internally).
2. Tangents to a circle from a point outside it.
UNIT V: TRIGONOMETRY
1. INTRODUCTION TO TRIGONOMETRY (8) Periods
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.
2. TRIGONOMETRIC IDENTITIES (10) Periods
Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be
given.
3. 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°, 45°, 60°.
UNIT VI: MENSURATION
1. 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°and
90° only. Plane figures involving triangles, simple quadrilaterals and circle should be
taken.)
2. SURFACE AREAS AND VOLUMES (8) Periods
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 VII: STATISTICS AND PROBABILITY
1. STATISTICS (10) Periods
Mean, median and mode of grouped data (bimodal situation and step deviation method
for finding the mean to be avoided).
 2. PROBABILITY (10) Periods
Classical definition of probability. Simple problems on finding the probability of an
event.