MATHEMATICS (IX-X)

COURSE STRUCTURE
CLASS –IX
Units Unit Name Marks

I NUMBER SYSTEMS 10
II ALGEBRA 20
III COORDINATE GEOMETRY 04
IV GEOMETRY 27
V MENSURATION 13
VI STATISTICS 06
Total 80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18) Periods

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 real bases
(to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26) 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. 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.

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 2. LINEAR EQUATIONS IN TWO VARIABLES (16) 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.

UNIT III: COORDINATE GEOMETRY

COORDINATE GEOMETRY (7) Periods

The Cartesian plane, coordinates of a point, names and terms associated with the
coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID'S GEOMETRY (7) Periods

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.

2. LINES AND ANGLES (15) 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) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22) 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).
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).

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 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.

4. QUADRILATERALS (13) 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 (17) Periods

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.

UNIT V: MENSURATION

1. AREAS (5) Periods

Area of a triangle using Heron's formula (without proof)

2. SURFACE AREAS AND VOLUMES (17) Periods

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

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UNIT VI: STATISTICS
STATISTICS (15) Periods

Bar graphs, histograms (with varying base lengths), and frequency polygons.

MATHEMATICS
QUESTION PAPER DESIGN
CLASS – IX (2024-25)

Time: 3 Hrs. Max. Marks: 80

%
S. Total
Typology of Questions Weightage
No. Marks
(approx.)

Remembering: Exhibit memory of previously learned material by

recalling facts, terms, basic concepts, and answers.
1 Understanding: Demonstrate understanding of facts and ideas by 43 54
organizing, comparing, translating, interpreting, giving descriptions,
and stating main ideas

Applying: Solve problems to new situations by applying acquired 19 24

2
knowledge, facts, techniques and rules in a different way.

Analysing :
Examine and break information into parts by identifying motives or
causes. Make inferences and find evidence to support
generalizations

Evaluating:
18 22
3 Present and defend opinions by making judgments about
information, validity of ideas, or quality of work based on a set of
criteria.

Creating:
Compile information together in a different way by combining
elements in a new pattern or proposing alternative solutions
Total 80 100

INTERNAL ASSESSMENT 20 MARKS

Pen Paper Test and Multiple Assessment (5+5) 10 Marks
Portfolio 05 Marks
Lab Practical (Lab activities to be done from the prescribed books) 05 Marks