COURSE STRUCTURE CLASS –IX

Units Unit Name Marks
I NUMBER SYSTEMS 08
II ALGEBRA 17
III COORDINATE GEOMETRY 04
IV GEOMETRY 28
V MENSURATION 13
VI STATISTICS & PROBABILITY 10
Total 80
UNIT I: NUMBER SYSTEMS
1. REAL NUMBERS (10 Periods)
1. Review of representation of natural numbers, integers, 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.
3. 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.
4. 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.)
UNIT II: ALGEBRA
1. POLYNOMIALS (15) Periods
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. 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. 
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2. LINEAR EQUATIONS IN TWO VARIABLES (10) Periods
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. Graph of linear equations in two
variables. Examples, problems from real life with algebraic and graphical solutions being
done simultaneously.
UNIT III: COORDINATE GEOMETRY
 COORDINATE GEOMETRY (6) Periods
The Cartesian plane, coordinates of a point, names and terms associated with the
coordinate plane, notations, plotting points in the plane.
UNIT IV: GEOMETRY
1. LINES AND ANGLES (13) Periods
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) 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 180O
.
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.
2. TRIANGLES (15) Periods
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). 
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2. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three
sides of the other triangle (SSS Congruence).
3. (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)
4. (Prove) The angles opposite to equal sides of a triangle are equal.
5. (Motivate) The sides opposite to equal angles of a triangle are equal.
4. QUADRILATERALS (10) Periods
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.
5. CIRCLES (12) Periods
Through examples, arrive at definition of circle and 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) 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) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180°
and its converse.
6. CONSTRUCTIONS (5) Periods
1. Construction of bisectors of line segments and angles of measure 60o
, 90o
, 45o
 etc., equilateral
triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base
angle. 
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UNIT V: MENSURATION
1. AREAS (2) Periods
Area of a triangle using Heron's formula (without proof)
2. SURFACE AREAS AND VOLUMES (12) Periods
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right
circular cylinders/cones.
UNIT VI: STATISTICS & PROBABILITY
1. STATISTICS (6) Periods
Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped /
grouped, bar graphs
2. PROBABILITY (9) Periods
History, Repeated experiments and observed frequency approach to probability.
Focus is on empirical probability. (A large amount of time to be devoted to groupand 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).