CHAPTER 1 : REAL NUMBERS
1. Review of representation of natural numbers, integers, and rational numbers on the number
line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers
(irrational numbers) such as , and their representation on the number line. Explaining
that every real number is represented by a unique point on the number line and conversely,
viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers of the type
and (and their combinations) where x and y are natural number and a and b are
integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive

CHAPTER 1 : POLYNOMIALS
Definition of a polynomial in one variable, with examples and counter examples. Coefficients
of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant,
linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and
multiples. Zeros of a polynomial. Motivate and State 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.
Recall of algebraic expressions and identities. Verification of identities:
+
and their use in factorization of polynomials.

CHAPTER 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.Explain 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 lie on a line.

CHAPTER 1 : COORDINATE GEOMETRY
The Cartesian plane, coordinates of a point, names and terms associated with the
coordinate plane, notations.

CHAPTER 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. 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.

CHAPTER 2 : LINES AND ANGLES
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O
and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Lines which are parallel to a given line are parallel.

CHAPTER 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. (RHS Congruence)
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.

CHAPTER 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 in half of it and (motivate) its converse.

CHAPTER 5 : CIRCLES
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) Equal chords of a circle (or of congruent circles) are equidistant from the center
(or their respective centers) and conversely.
4.(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.
5.(Motivate) Angles in the same segment of a circle are equal.
6.(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.
7.(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180°
and its converse.

CHAPTER 1 : AREAS
Area of a triangle using Heron's formula (without proof)

CHAPTER 2 : SURFACE AREAS AND VOLUMES
Surface areas and volumes of spheres (including hemispheres) and right circular cones.

CHAPTER 1 : STATISTICS
Bar graphs, histograms (with varying base lengths), and frequency polygons.

Chemical Reactions and Equations: Chemical reactions, Chemical equation, Balanced
chemical equation, types of chemical reactions: combination, decomposition,
displacement, double displacement, precipitation, endothermic exothermic reactions,
oxidation and reduction.

Acids and Bases – definitions in terms of furnishing of H+ and
OH– ions, identification using indicators, chemical properties, examples and uses,
neutralization, concept of pH scale (Definition relating to logarithm not required),
importance of pH in everyday life; preparation and uses of Sodium Hydroxide,Bleaching
powder, Baking soda, Washing soda and Plaster of Paris

Properties of metals and non-metals; Reactivity series;
Formation and properties of ionic compounds; Basic metallurgical processes; Corrosion
and its prevention.

Covalent bonds – formation and properties of covalent
compounds, Versatile nature of carbon, Hydrocarbons – saturated and unsaturated
Homologous series. Nomenclature of alkanes, alkenes, alkyne and carbon compounds
containing functional groups (halogens, alcohol, ketones, aldehydes). Chemical
properties of carbon compounds (combustion, oxidation, addition and substitution
reaction). Ethanol and Ethanoic acid (only properties and uses), soaps anddetergents.

‘Living Being’. Basic concept of nutrition, respiration, transport and
excretion in plantsand animals.

Tropic movements in plants;
Introduction of plant hormones; Control and co-ordination in animals: Nervous system;
Voluntary, involuntary and reflex action; Chemical co-ordination: animal hormones.

Reproduction in animals and plants (asexual and sexual) reproductive
health - needand methods of family planning. Safe sex vs HIV/AIDS. Child bearing and
women’s health.

Heredity; Mendel’s contribution- Laws for inheritance of traits:
Sex determination; brief introduction.

Reflection of light by curved surfaces; Images formed by spherical mirrors, centre of
curvature, principal axis, principal focus, focal length, mirror formula (Derivation not
required), magnification.
Refraction; Laws of refraction, refractive index.
Refraction of light by spherical lens; Image formed by spherical lenses; Lens formula
(Derivationnot required); Magnification. Power of a lens.
Functioning of a lens in human eye, defects of vision and their corrections, applications
ofspherical mirrors and lenses.
Refraction of light through a prism, dispersion of light, scattering of light, applications in
daily life (excluding colour of the sun at sunrise and sunset).

Electric current, potential difference and electric current. Ohm’s law; Resistance,
Resistivity, Factors on which the resistance of a conductor depends. Series combination
of resistors, parallel combination of resistors and its applications in daily life. Heating
effect of electric current and its applications in daily life. Electric power, Interrelation
between P, V, I and R.

Magnetic field, field lines, field due to a current carrying
conductor, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming’s Left Hand Rule, Direct current. Alternating current: frequency of AC.
Advantage of AC over DC. Domestic electric circuits.

Eco-system, Environmental problems, Ozone depletion, waste
production and their solutions. Biodegradable and non-biodegradable substances.