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 (18 Periods)
1. Review of representation of natural numbers, integers, rational numbers on the number line.
Representation of terminating / non-terminating recurring decimals on the number line
through successive magnification. 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. Existence of √ for a given positive real number x and its representation on the number line
with geometric proof.
5. 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.
6. 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 (23) 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.
2. LINEAR EQUATIONS IN TWO VARIABLES (14) 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. 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 lie on a line. Graph of linear equations
in two variables. Examples, problems from real life, including problems on Ratio and
Proportion and 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. INTRODUCTION TO EUCLID'S GEOMETRY (6) 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. 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 (13) Periods

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is
O
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 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.
3. TRIANGLES (20) 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).
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.
7. (Motivate) Triangle inequalities and relation between ‘angle and facing side' inequalities
in triangles.
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. AREA (7) Periods

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 (15) 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) There is one and only one circle passing through three given non-collinear
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 (10) Periods

1. Construction of bisectors of line segments and angles of measure 60 , 90o, 45o etc.,
o

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
1. AREAS (4) Periods
Area of a triangle using Heron's formula (without proof) and its application in finding the
area of a quadrilateral.

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 (13) Periods
Introduction to Statistics: Collection of data, presentation of data — tabular form,
ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency
polygons. Mean, median and mode of ungrouped data.
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 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).
 QUESTIONS PAPER DESIGN 2018–19
CLASS–IX
Mathematics (Code No. 041) Marks: 80

S. Typology of Questions Very Short Short Long Total %

No. Short Answer-I Answer- Answer Marks Weightage
Answer (SA) (2 II (SA) (3 (LA) (4 (approx.)
(VSA) Marks) Marks) Marks)
(1
Mark)
1 Remembering-(Knowledge 2 2 2 2 20 25%
based- Simple recall questions, to
know specific facts, terms, concepts,
principles or theories; Identify, define,
or recite, information)
2 Understanding- 2 1 1 4 23 29%
(Comprehension- to be familiar
with meaning and to understand
conceptually, interpret, compare,
contrast, explain, paraphrase, or
interpret information)
3 Application (Use abstract 2 2 3 1 19 24%
information in concrete situation, to
apply knowledge to new situation; Use
given content to interpret a situation,
provide an example, or solve a
problem)
4 Higher Order Thinking Skills - 1 4 - 14 17%
(Analysis & Synthesis- Classify,
compare, contrast, or differentiate
between different pieces of
information; Organize and /or integrate
unique pieces of information from
variety of sources )
5 Evaluation ( Judge, and/or justify - - - 1 4 5%
the value or worth of a decision or
outcome, or to predict outcomes based
on values)
Total 6x1=6 6x2=12 10x3=30 8x4=32 80 100%

INTERNAL ASSESSMENT 20 Marks

 Periodical Test 10 Marks
 Note Book Submission 05 Marks
 Lab Practical (Lab activities to be done from the prescribed books) 05 Marks