First Term Syllabus
UNIT I: NUMBER SYSTEMS
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
Pair of linear equations in two variables and their graphical solution. Geometric
representation of different possibilities of solutions/inconsistency.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
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 may be included.
UNIT II: 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 triangle.
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 sin2A + cos2A = 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.
Units

Chapter name

Marks

1

Algebra (contd.)

23

2

Geometry (contd.)

30

3

Trigonometry (contd.)

29

4

Probability

7


Total

90

Second Term Syllabus
UNIT II: ALGEBRA (Contd.)
3. QUADRATIC EQUATIONS
Standard form of a quadratic equation ax2+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 standard results of
finding the nth term and sum of first n terms and their application in solving daily
life problems.
4. ARITHMETIC PROGRESSIONS
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
UNIT V: STATISTICS AND PROBABILITY
Classical definition of probability. Connection with probability as given in Class
IX. Simple problems on single events, not using set notation.
UNIT VI: COORDINATE GEOMETRY
1. LINES (In twodimensions)
Review the concepts of coordinate geometry done earlier including graphs of linear
equations. Awareness of geometrical representation of quadratic polynomials. Distance
between two points and section formula (internal). 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.)