The Central Board of Secondary Education (CBSE) is one of the
most prestigious and preferred educational boards in India. It
aims to provide a holistic and healthy education to all its
learners so that students can get adequate space to develop
mentally and physically. CBSE is known for its comprehensive
syllabus and well structured exam pattern which helps students
to get a detailed idea about the entire curriculum. There are
around 20,102 schools under the board which follows the NCERT
The CBSE Class 9 can be called as the foundation for higher
classes and thus it is very important for students to learn the
topics thoroughly. For example, if a student takes up science
after their board exams, topics like mechanics and waves, etc.
would also be included in higher classes. So, learning the
topics properly from an early stage is very crucial. The
curriculum is designed in a way that the students learn and
develop their sense of individuality which naturally shapes
their future. The guidelines for CBSE Class 9 are issued by the
board and the NCERT. So, the schools affiliated to the CBSE
board follows the NCERT syllabus. It is important that subjects
like science and maths are learnt properly by understanding each
concept and topic as these topics would be included in higher
standards. For proper preparation, knowing the syllabus is very
important along with solving various sample questions.
Exam Structure and Important Chapters
Linear equations in two variables
Introduction to euclid's geometry
Lines and angles
Areas of parallelograms and triangles
Heron’ s formula
Surface areas and volumes
Statistics and Probability
Unit I: Number Systems
1. Real Numbers
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
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, every point on the number line
represents a unique real number.
Existence of √x for a given positive real number x (visual
proof to be emphasized).
Definition of nth root of a real number.
Rationalization (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 number and a and b are
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
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.
2. Linear equations 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.
Unit III: Coordinate Geometry
1. Coordinate Geometry
The Cartesian plane, coordinates of a point, notations, plotting
points in the plane.
Unit IV: Geometry
1. Introduction to Euclid's geometry
(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
If a ray stands on a line, then the sum of the two adjacent
angles so formed is 180° and the converse.
If two lines intersect, vertically opposite angles are equal.
Results on corresponding angles, alternate angles, interior
angles when a transversal intersects two parallel lines.
Lines which are parallel to a given line are parallel.
The sum of the angles of a triangle is 180°.
If a side of a triangle is produced, the exterior angle so
formed is equal to the sum of the two interior opposite angles.
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).
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).
Two triangles are congruent if the three sides of one triangle
are equal to three sides of the other triangle (SSS
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.
The angles opposite to equal sides of a triangle are equal.
(The sides opposite to equal angles of a triangle are equal.
Triangle inequalities and relation between 'angle and facing
side' inequalities in triangles.
The diagonal divides a parallelogram into two congruent
In a parallelogram opposite sides are equal, and conversely.
In a parallelogram opposite angles are equal, and conversely.
A quadrilateral is a parallelogram if a pair of its opposite
sides is parallel and equal.
In a parallelogram, the diagonals bisect each other and
In a triangle, the line segment joining the mid points of any
two sides is parallel to the third side and (motivate) its
Review concept of area, recall area of a rectangle.
Parallelograms on the same base and between the same parallels
have the same area.
Triangles on the same (or equal base) base and between the same
parallels are equal in area.
Through examples, arrive at definitions of circle related concepts,
radius, circumference, diameter, chord, arc, secant,
sector, segment subtended angle.
Equal chords of a circle subtend equal angles at the center and
(motivate) its converse.
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.
There is one and only one circle passing through three given
Equal chords of a circle (or of congruent circles) are
equidistant from the center (or their respective
centers) and conversely.
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
Angles in the same segment of a circle are equal.
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.
The sum of either of the pair of the opposite angles of a cyclic
quadrilateral is 180° and its converse.
Construction of bisectors of line segments and angles of measure
60°, 90°, 45° etc., equilateral triangles.
Construction of a triangle given its base, sum/difference of the
other two sides and one base angle.
Construction of a triangle of given perimeter and base angles.
Unit V: Mensuration
Area of a triangle using Heron's formula and its application
2. SURFACE AREAS AND VOLUMES
Surface areas and volumes of cubes, cuboids, spheres and right
Unit VI: Statistics & Probability
Introduction to Statistics: bar graphs, histograms (with varying
base lengths), frequency polygons, qualitative analysis of data to
choose the correct form of presentation for the collected data.
Mean, median, mode of ungrouped data.
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).
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