# CBSE Class 9 Math Syllabus

Introduction to real numbers

Real numbers as a system containing both rational as well as irrational numbers.

Symbols R to represent real number system.

Representation of real numbers on real line.

Infinitness of rational and irrational numbers.

Algebra of real numbers

Sum, difference, product, quotient of rational numbers. Sum and difference of irrational numbers, product of two irational numbers.

Quotient of two irrational numbers.

Properties of rational numbers w.r.t addition and multiplication.

Properties of real numbers w.r.t additional and multiplication .

## Unit 2: Algebra

Review and recall

VAriables, constant, algebraic expression, equation

Introduction to polynomials

Definition of polynomials, degree of polynomials, No. of terms in a polynomial of degree n, Types of polynomial based on numbers of terms-monomial,

equations and its representation on number line, expressing word statements into linear equations.

Linear equation in one variable, solution of linear equations and its representation on number line, expressing word statements into linear equations.

Quadratic equations

Quadratic equation in one variable, to verify the solution of given quadratic equation

Patterns

Number patterns and geometric patterns

## Unit 3: Coordinate Geometry

Cartesian system in two dimension

Introduction of terms like axes, quadrants, origin, abscissa, ordinate, ordered pair, Cartesian coordinates, Cartesian plane, independent and dependent variables

Point in a plane

Representation of a given point in Cartesian plane in the form of ordered pair. Plotting of a given point in the plane

## Unit 4:Lines, Angles and Triangles

Basic Geometrical terms

Point, Line, line segment, collinear points, non collinear points; Angle: right angle, acute angle, obtuse angle, straight angle, reflex angle, supplementary angles, complementary angles; Parallel lines, perpendicular lines, transversal; Triangle: scalene, isosceles, equilateral, acute angled, obtuse angled, right angled; Median, altitude, bisector of an angle, perpendicular bisector of a line segment

Lines and AnglesPractise Now

Pair of angles: adjacent angles, linear pair, vertically opposite angles; Linear pair axiom; Parallel lines and transversal: exterior angles, interior angles, corresponding angles, alternate interior angles, interior angles on the same side of traversal; corresponding angle axiom and converse, if a transversal intersects two parallel lines then each pair of alternate interior angles are equal and converse, if a transversal intersects two parallel lines then each pair of interior angles on the same

Properties of parallelogram

Exploration of following properties of parallelogram:
- In a parallelogram, pair of opposite sides is of equal length and the converse.
- A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and is of equal length
- The diagonals of a parallelogram bisect each other and the converse
- A parallelogram is a rectangle if its diagonal has equal length and the converse.
- A parallelogram is a rhombus if its diagonals are perpendicular to each other and the converse

A parallelogram is a square if its diagonals are equal and are at right angles and the converse
Problems based on above properties.
Logical proofs of above theorems and problems based on them

Mid-point Theorem

The line segment joining the midpoint of any two

sides of a triangle is parallel to the third side and equal to half of it.

Area of triangle

Triangles on the same base and between the same parallels are equal in area.
The area of a triangle is equal to half the product of one of
its base and the corresponding altitude.
If a triangle and a parallelogram are on the same base and
between same parallels then area of triangle is equal to half of the area of the parallelogram.
Problems based on above results.

## Unit 6: Circles

Review and recall basic terms

Definition of circle, centre, radius, diameter, Interior of circle,
circular region, exterior of circle ,arc, chord, minor segment, major segment, minor arc, major arc, sector of circle, minor sector, major sector, semicircular region, circumference of circle, angle subtended by the chord at a point on the circle, angle subtended by the arc at the centre of circle, concentric circles, intersecting circles, congruent circles, concyclic points

rhombus, trapezium.

Heron's formula Practise Now

Area of triangle using Heron's formula and its application in finding area of quadrilateral

Surface Area of solid shapes Practise Now

Surface Area of cube, cuboids, curved surface area and total surface area of cylinder, cone, sphere and hemisphere

Applications in daily life

Applications in finding the area of field, land etc

## Unit 8: Volume of Solids

Introduction to volume

Volume as product of area of base and height

Volume of cubes and cuboidsPractise Now

Formulae for finding volume of cube and cuboid of given dimension.

Volume of right circular cylinder and right circular cone. Practise Now

Volume of a hollow right circular cylinder. Volume of metal required to cast a solid right circular

Angle of elevation and angle of depression

Describing angle of elevation and angle of depression for a given point. Drawing of figure for given problems involving one right triangle as well quadrilateralas two right angle triangles.

## Unit 10: Introduction to Statistics and Probability

Introduction to statistics

Significance of conducting survey, collecting data, interpreting data etc.

Meaning and definition of statistics.

Types of data w.r.t. source

Primary data and secondary data

Classification of data

Ungrouped data and grouped data class interval, class-marks, upper limit, lower limit, frequency, range, cumulative frequency, class-size, discrete data and continuous data

Analysis of Data

Measure of central tendency: Mean, median, mode of ungrouped data Interpretation of Bar graph,