Mathematics Class 10 Syllabus
Course Structure
First Term (SAI)
Units

Marks

I.

Number System

11

II.

Algebra

23

III.

Geometry

17

IV.

Trigonometry

22

V.

Statistics

17


Total

90

Second Term (SAII)
Units

Marks

II.

Algebra (contd.)

23

III.

Geometry (contd.)

17

IV.

Trigonometry (contd.)

8

V.

Probability

8

VI.

Coordinate Geometry

11

VII.

Mensuration

23


Total

90

First Term Syllabus
UNIT I: NUMBER SYSTEMS
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/nonterminating recurring decimals.
UNIT II: ALGEBRA
1. POLYNOMIALS
Zeros of a polynomial. Relationship
between zeros and coefficients of quadratic polynomials. Statement and simple
problems on division algorithm for polynomials with real coefficients.
2. 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 number of
solutions. 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.
UNIT III: GEOMETRY
1. 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 on 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 sum of the squares on the other two sides, the angles
opposite to the first side is a right traingle.
UNIT IV: TRIGONOMETRY
1 . INTRODUCTION TO TRIGONOMETRY
Trigonometric ratios of an acute angle
of a rightangled triangle. Proof of their existence (well defined); motivate
the ratios, whichever are defined at 0° and 90°. Values (with proofs) of
the trigonometric ratios of 30°, 45° and 60°. Relationships between the
ratios.
2. TRIGONOMETRIC IDENTITIES
Proof and applications of the identity
sin^{2}A + cos^{2}A = 1. Only simple identities to be given.
Trigonometric ratios of complementary angles.
UNIT V: STATISTICS AND PROBABILITY
1. STATISTICS
Mean, median and mode of grouped data
(bimodal situation to be avoided). Cumulative frequency graph.
Second Term Syllabus
UNIT II: ALGEBRA (Contd.)
3. QUADRATIC EQUATIONS
Standard form of a quadratic equation
ax^{2}+bx+c=0, (a ≠ 0). Solution
of the quadratic equations (only real roots) by factorization, by
completing the square and by using quadratic formula. Relationship
between discriminant and nature of roots.
Situational problems based on quadratic
equations related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS
Motivation for studying Arithmetic
Progression Derivation of the n^{th} term
and sum of the first n terms of A.P. and their
application in solving daily life problems.
UNIT III: GEOMETRY (Contd.)
2. CIRCLES
Tangents to a circle motivated by
chords drawn from points coming closer and closer to the point.
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 circle are equal.
3. CONSTRUCTIONS
1. Division of a line segment in a given
ratio (internally).
2. Tangent to a circle from a point
outside it.
3. Construction of a triangle similar to a
given triangle.
UNIT IV: TRIGONOMETRY
3. HEIGHTS AND DISTANCES
Simple and believable 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 V: STATISTICS AND PROBABILITY
2. PROBABILITY
Classical definition of probability.
Simple problems on single events (not using set notation).
UNIT VI: COORDINATE GEOMETRY
1. LINES (In twodimensions)
Concepts of coordinate geometry, graphs
of linear equations. Distance formula. Section formula (internal division).
Area of a triangle.
UNIT VII: MENSURATION
1. 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°, 90° and 120° only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)
2. SURFACE AREAS AND VOLUMES
(i) Problems
on finding 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.
(ii) 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.)