Cbse Class 9 Math Syllabus 2022-23
Class 9 cbse syllabus 2022-23
Unit with Marks
UNIT I: NUMBER SYSTEMS
1. Real Numbers
Review of representation of natural
numbers, integers, and 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.
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.
Definition of nth root of a real number.
Rationalisation (with precise
meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are
natural numbers and a and b are integers.
Recall of laws of exponents with integral powers. Rational exponents
with positive real bases (to be done by
particular cases, allowing learners to arrive at the general laws.)
UNIT II: ALGEBRA
2. Polynomials
Definition of a polynomial in one
variable, with examples and counterexamples.
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 ax^2 + 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 = x^2 + y^2 + z^2
+2xy + 2yz + 2xz
(x ± y)^3 = x^3 ± y^3 ± 3xy (x ±
y)
x^3 ± y^3 = (x ± y) (x^2 ± xy +
y^2)
x^3 + y^3 + z^3 – 3xyz = (x + y +
z) (x^2 + y^2 + z^2 – xy – yz – xz)
and their use in factorization of
polynomials.
3. 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.
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
4. Coordinate Geometry
The Cartesian plane, coordinates of
a point, names and terms associated with the
coordinate plane, notations, plotting points in the plane.
UNIT IV: GEOMETRY
5. Introduction to Euclid’s Geometry
History - Geometry in
India and Euclid’s geometry.
Euclid’s method of
formalising observed phenomena 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.
6. Lines and Angles
(Motivate) If a ray stands on a
line, then the sum of the two adjacent angles so formed is 180° and the converse.
(Prove) If two lines intersect,
vertically opposite angles are equal.
(Motivate) Results on
corresponding angles, alternate angles, interior angles when a transversal intersects two parallel
lines.
(Motivate) Lines which are parallel
to a given line are parallel.
(Prove) The sum of the
angles of a triangle is 180°.
(Motivate) If a side of a
triangle is produced, the exterior angle formed is equal to the sum of the two interior opposite angles.
7. Triangles
(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).
(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).
(Motivate) Two triangles are
congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS
Congruence).
(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).
(Prove) The angles opposite to
equal sides of a triangle are equal.
(Motivate) The sides opposite to
equal angles of a triangle are equal.
(Motivate) Triangle
inequalities and relation between ‘angle and facing side’ inequalities in triangles.
8. Quadrilaterals
(Prove) The diagonal divides a
parallelogram into two congruent triangles.
(Motivate) In a parallelogram
opposite sides are equal, and conversely.
(Motivate) In a parallelogram
opposite angles are equal, and conversely.
(Motivate) A quadrilateral is a
parallelogram if a pair of its opposite sides is parallel and equal.
(Motivate) In a parallelogram, the
diagonals bisect each other and conversely.
(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 (motivates) its converse
9. Areas of Parallelograms and Triangles (Deleted)
10. Circles
(Prove) Equal chords of a circle
subtend equal angles at the centre and (motivate) its converse.
(Motivate) The perpendicular from
the centre of a circle to a chord bisects the chord and conversely, the line drawn through the
centre of a circle to bisect a chord is
perpendicular to the chord.
(Motivate) There is one
and only one circle passing through three given non-collinear points.
(Motivate) Equal chords of a circle
(or of congruent circles) are equidistant from the centre (or their respective centres) and
conversely.
(Prove) The angle
subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the
circle.
(Motivate) Angles in the same
segment of a circle are equal.
(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.
(Motivate) The sum of either pair
of the opposite angles of a cyclic quadrilateral is 180° and its converse.
11. Constructions (Deleted)
UNIT V: MENSURATION
12. Heron’s Formula
Area of a triangle using Heron’s
formula (without proof) and its application in finding the area of a quadrilateral.
Application of Heron’s
Formula in finding the area of a
quadrilateral.
13. Surface Area and Volumes
Surface areas and volumes of cubes,
cuboids, spheres (including hemispheres) and
right circular cylinders/ cones.
UNIT VI: STATISTICS AND PROBABILITY
14. Statistics
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.
15. Probability (Deleted)
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