MATHEMATICS CLASS -IX
(CODE NO. 041)
General Instructions:
l As per CCE guidelines, the syllabus of Mathematics for classes IX and X has been divided term wise.
l The units
specified for each term shall
be assessed through
both Formative and
Summative Assessments.
l In each term, there
will be two Formative Assessments, each carrying 10% weightage.
l The Summative
Assessment in term I will carry 30% weightage and the Summative
Asssessment in term II will carry 30% weightage.
l Listed laboratory activities and projects
will
necessarily
be
assessed
through
formative assessments.
COURSE STRUCTURE CLASS -IX
First Term
Marks:
90
|
Units
|
|
Marks
|
|
I
|
NUMBER SYSTEMS
|
17
|
|
II
|
ALGEBRA
|
25
|
|
III
|
GEOMETRY
|
37
|
|
IV
|
COORDINATE GEOMETRY
|
11
|
|
V
|
MENSURATION
|
|
|
Total (Theory)
|
90
|
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.
2. Examples of non-recurring/non-terminating
decimals. Existence of non-rational 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, viz. every
point on the number line represents a unique
real number.
3. Existence
of x for a given positive
real number x and its representation on the
number line with geometric proof.
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
1
a + b x
and 1 (and their combinations) where
x and y are natural
number and
x + y
a and b are
integers.
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:(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 polynomials.
UNIT III : 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 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.
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.
UNIT IV: 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 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
+ y +
)2
- 
times each of the equal sides . Find the
length of each side and area of the triangle.