First Term Syllabus
1. REAL NUMBERS
1. Review of representation of natural numbers, integers, rational numbers on the
number line. Representation of terminating / nonterminating recurring decimals,
on the number line through successive magnification. Rational numbers as recurring/terminating
decimals.
2. Examples of nonrecurring / nonterminating decimals. Existence of nonrational
numbers (irrational numbers) such as √2, √3 and their representation on the number
line. Explaining that every real number is represented by a unique point on the
number line and conversely, every point on the number line represents a unique real
number.
3. Existence of √x for a given positive real number x (visual proof to be emphasized).
4. Definition of nth root of a real number.
5. Recall of laws of exponents with integral powers. Rational exponents with positive
real bases (to be done by particular cases, allowing learner to arrive at the general
laws.)
6. Rationalization (with precise meaning) of real numbers of the type (and their
combinations) of rational numbers in terms of terminating/nonterminating recurring
decimals.
UNIT II: ALGEBRA
1. POLYNOMIALS
Definition of a polynomial in one variable, its coefficients, with examples and
counter examples, its terms, zero polynomial. Degree of a polynomial. Constant,
linear, quadratic and cubic polynomials; monomials, binomials, trinomials. Factors
and multiples. Zeros of a polynomial. State and motivate the Remainder Theorem with
examples. Statement and proof of the Factor Theorem. Factorization of (ax2 + bx
+ c, a + 0 where a, b and c are real numbers, and of cubic polynomials using the
Factor Theorem) dt quadratic & cubic polynomial.
Recall of algebraic expressions and identities. Further verification of identities
of the type (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, (x ± y)3 = x3 ± y3 ±
3xy (x ± y), x³ ± y³ = (x ± y) (x² ± xy + y²), x3 + y3 + z3  3xyz = (x + y + z)
(x2 + y2 + z2  xy  yz  zx) and their use in factorization of polymonials. Simple
expressions reducible to these polynomials.
UNIT III: GEOMETRY
1. INTRODUCTION TO EUCLID'S GEOMETRY
History  Geometry in India and Euclid's geometry. Euclid's method of formalizing
observed phenomenon into rigorous mathematics with definitions, common/obvious notions,
axioms/postulates and theorems. The five postulates of Euclid. Equivalent versions
of the fifth postulate. Showing the relationship between axiom and theorem, for
example:
• (Axiom) 1. Given two distinct points, there exists one and only one line through
them. • (Theorem)
2. (Prove) Two distinct lines cannot have more than one point in common.
2. LINES AND ANGLES
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles
so formed is 180° and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles
when a transversal intersects two parallel lines.
4. (Motivate) Lines which are parallel to a given line are parallel.
5. (Prove) The sum of the angles of a triangle is 180°.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed
is equal to the sum of the two interior opposite angles.
3. TRIANGLES
1. (Motivate) Two triangles are congruent if any two sides and the included angle
of one triangle is equal to any two sides and the included angle of the other triangle
(SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of
one triangle is equal to any two angles and the included side of the other triangle
(ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are
equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of
one triangle are equal (respectively) to the hypotenuse and a side of the other
triangle.
5. (Prove) The angles opposite to equal sides of a triangle are equal. 6. (Motivate)
The sides opposite to equal angles of a triangle are equal.
7. (Motivate) Triangle inequalities and relation between 'angle and facing side'
inequalities in triangles.
UNIT IV: COORDINATE GEOMETRY
1. COORDINATE GEOMETRY
The Cartesian plane, coordinates of a point, names and terms associated with the
coordinate plane, notations, plotting points in the plane, graph of linear equations
as examples; focus on linear equations of the type Ax + By + C = 0 by writing it
as y = mx + c.
UNIT V: MENSURATION
1. AREAS
Area of a triangle using Heron's formula (without proof) and its application in
finding the area of a quadrilateral. Area of cyclic quadrilateral (with proof) 
Brahmagupta's formula
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.)
2. LINEAR EQUATIONS IN TWO VARIABLES
Recall of linear equations in one variable. Introduction to the equation in two
variables. Focus on linear equations of the type ax+by+c=0. Prove that a linear
equation in two variables has infinitely many solutions and justify their being
written as ordered pairs of real numbers, plotting them and showing that they seem
to lie on a line. Examples, problems from real life, including problems on Ratio
and Proportion and with algebraic and graphical solutions being done simultaneously.
UNIT III: GEOMETRY (Contd.)
4. QUADRILATERALS
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides
is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two
sides is parallel to the third side and (motivate) its converse.
5. AREA
Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same parallels have the
same area.
2. (Motivate) Triangles on the same (or equal base) base and between the same parallels
are equal in area
6. CIRCLES
Through examples, arrive at definitions of circle related concepts, radius, circumference,
diameter, chord, arc, secant, sector, segment subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate)
its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the
chord and conversely, the line drawn through the center of a circle to bisect a
chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given noncollinear
points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant
from the center (or their respective centers) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the angle subtended
by it at any point on the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtends equal angle at two other
points lying on the same side of the line containing the segment, the four points
lie on a circle.
8. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral
is 180° and its converse.
7. CONSTRUCTIONS
1. Construction of bisectors of line segments and angles of measure 60°, 90°, 45°
etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides
and one base angle.
3. Construction of a triangle of given perimeter and base angles.
UNIT V: MENSURATION (Contd.)
2. SURFACE AREAS AND VOLUMES
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and
right circular cylinders/cones.
UNIT VI: STATISTICS
Introduction to Statistics: Collection of data, presentation of data  tabular form,
ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency
polygons, qualitative analysis of data to choose the correct form of presentation
for the collected data. Mean, median, mode of ungrouped data.
UNIT VII: PROBABILITY
History, Repeated experiments and observed frequency approach to probability. Focus
is on empirical probability. (A large amount of time to be devoted to group and
to individual activities to motivate the concept; the experiments to be drawn from
real  life situations, and from examples used in the chapter on statistics).