# Class 9 Maths

Class 9 Maths is the base of secondary stage math learning that promotes various computational skills. It solidifies the mathematical understanding of concepts based on coordinate geometry, number system, algebra, trigonometry, mensuration, statistics, graphs, etc. Class 9 math helps students to gradually shift their concrete mathematical knowledge into abstract concepts and topics. Thus, studying each and every topic covered under Class 9 maths is highly important for students.

## Class 9 Maths - Syllabus

CBSE Class 9 Maths syllabus is thoroughly prepared to help young learners acquire basic mathematical concepts with ease. Class 9 Maths syllabus comprises topics related to fractions and more. Here is the complete syllabus of CBSE Class 9 Maths.

**NUMBER SYSTEMS**

NUMBER SYSTEM

Review of representation of natural numbers, integers, rational numbers on the number

line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

- Examples of non-recurring/non-terminating decimals. Existence of non-rational

numbers (irrational numbers)

- Recalling laws of exponents with integral powers. Rational exponents with positive

real bases (to be done by particular cases, allowing the learner to arrive at the general

laws.)

**ALGEBRA**

POLYNOMIALS

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.

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 with algebraic and graphical solutions being

done simultaneously

**COORDINATE GEOMETRY**

The Cartesian plane, coordinates of a point, names and terms associated with the

coordinate plane, notations, plotting points in the plane.

**GEOMETRY**

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 that 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 so formed is equal to the sum

of the two interior opposite angles.

### INTRODUCTION TO EUCLID'S GEOMETRY

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.

TRIANGLES

Congruence of Triangles, Congruency Rules: SAS Congruence, ASA Congruence, SSS Congruence, RHS Congruence, Triangle inequalities, Relation between ‘angle and facing side'.

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 (motivate) its converse.

CIRCLES

Through examples, arrive at definition of circle and related concepts-radius, circumference,

diameter, chord, arc, secant, sector, segment, subtended angle.

- (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) Equal chords of a circle (or of congruent circles) are equidistant from the

centre (or their respective centres) and conversely.

- (Motivate) 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) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is

180° and its converse.

CONSTRUCTION

- 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.

**MENSURATION**

HERON’S FORMULA

Area of a triangle using Heron's formula (without proof).

SURFACE AREAS AND VOLUMES

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right

circular cylinders/cones.

**STATISTICS & PROBABILITY**

STATISTICS

Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped/grouped, bar graphs, histograms.

PROBABILITY

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).

## Develop Class 9 Maths Skills

Class 9 maths focuses on developing various real life skills in students. Students progress their basic mathematical skills related to trigonometry, geometry, statistics, probability, linear equations, polynomials and so on. A thorough understanding of these Class 9 maths concepts can be implemented through various interactive activities and visualization. Here are some of the basic class 9 maths skills and concepts that are applicable in further grades.

**Numbers and Quantity**

In class 9 students extend their understanding of numbers to rational and irrational numbers and also work with exponents, decimals and various measurement units. Class 9 maths emphasis on using these numbers in algebraic expressions, equations and calculations to define and solve real-life problems.

**Trigonometry**

Trigonometry is one of the important topics covered under class 9 maths. Students should understand and implement various formulas as well as theorems based on this topic through practice.

## Class 9 Maths Tips and Tricks

Class 9 maths is an important part of academics that establishes a firm foundation for the following years. Here are some useful class 9 maths tips and tricks for students to learn and score well in exams.

**Follow Daily Practice Routine**

Class 9 maths is the basis for various higher-level maths skills thus students must implement a well-defined preparation strategy. Students should sincerely perform their everyday practice.

**Solve Previous Years Question Papers**

Practicing question papers from previous years will help students to get an idea of the complexity level of the exam. It will also benefit students in enhancing their speed and accuracy

**Cover Full Syllabus**

Covering full syllabus of class 9 maths is a must for students to clarify all their doubts before exams.

**Refer Reliable Study materia**l

Refer reliable study material like NCERT Solutions and NCERT textbooks for the preparation of class 9 maths. These are the best preparation resources as the class 9 maths exam is set according to them.

visual curriculum