# Revised CBSE Syllabus 2021 for Class 9 Mathematics

Revised CBSE Syllabus 2021 for Class 9 Mathematics

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real life problems and other subject   areas, greater emphasis has been laid on applications of various concepts.

The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject  as a separate discipline. It   is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying  these  with further observations form inherent part of Mathematics learning at this stage. The  proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc.

The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments.

# Objectives

The broad objectives of teaching of Mathematics at secondary stage are to help the learners to:

consolidate the Mathematical knowledge and skills acquired at the upper primary stage;   acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols and underlying processes and skills;

develop mastery of basic algebraic skills; develop drawing skills;

feel the flow of reason while proving a result or solving a problem;

apply the knowledge and skills acquired to solve problems and wherever  possible, by  more  than one method;

to develop ability to think, analyze and articulate logically;

to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of gender biases;

to develop necessary skills to work with modern technological devices and mathematical

software’s.

to develop interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns, etc.

to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;

to develop interest in the subject by participating in related competitions;   to acquaint students with different aspects of Mathematics used in daily life; to develop an interest in students to study Mathematics as a discipline.

# COURSE STRUCTURE CLASS –IX

 Units Unit Name Marks I NUMBER SYSTEMS 08 II ALGEBRA 17 III COORDINATE GEOMETRY 04 IV GEOMETRY 28 V MENSURATION 13 VI STATISTICS & PROBABILITY 10 Total 80

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (10 Periods)
1. Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as , and their representation on the number
3. Rationalization (with precise meaning) of real numbers of the type

and          (and their combinations) where x and y are natural number and a and b are integers.

1. 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 )

# UNIT II: ALGEBRA

1. POLYNOMIALS (15) 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. 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:

+

and their use in factorization of polynomials.

# 2.     LINEAR EQUATIONS IN TWO VARIABLES                                             (10) Periods

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.

# UNIT III: 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 IV: GEOMETRY

1. 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
2. (Prove) If two lines intersect, vertically opposite angles are
3. (Motivate) Results on corresponding angles, alternate angles, interior angles  when  a transversal intersects two parallel
4. (Motivate) Lines which are parallel to a given line are
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

1. TRIANGLES (15) 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).

1. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
2. (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 (RHS Congruence)
3. (Prove) The angles opposite to equal sides of a triangle are
4. (Motivate) The sides opposite to equal angles of a triangle are

1. (Prove) The diagonal divides a parallelogram into two congruent
2. (Motivate) In a parallelogram opposite sides are equal, and
3. (Motivate) In a parallelogram opposite angles are equal, and
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and
5. (Motivate) In a parallelogram, the diagonals bisect each other and
6. (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

1. CIRCLES (12) Periods

Through examples, arrive at definition of circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate)  its
2. (Motivate) 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.
3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and
4. (Prove) 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
5. (Motivate) Angles in the same segment of a circle are
6. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its

# 6.        CONSTRUCTIONS                                                                              (5) Periods

1. Construction of bisectors of line segments and angles of measure 60o, 90o, 45o, equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.

# UNIT V: MENSURATION

1. AREAS (2) Periods

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

# 2.        SURFACE AREAS AND VOLUMES                                                           (12) Periods

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres)  and  right  circular cylinders/cones.

# UNIT VI: STATISTICS & PROBABILITY

1. STATISTICS (6) Periods

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

1. PROBABILITY (9) Periods

History, Repeated experiments and observed frequency approach to probability.

Focus is on empirical probability. (A large amount of time to be devoted to groupand 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).

MATHEMATICS QUESTION PAPER DESIGN

CLASS – IX (2020-21)

Time: 3 Hrs.                                                                                                                          Max. Marks: 80

 S. No. Typology of Questions Total Marks % Weightage (approx.) 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 43 54 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 19 24 3 Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations   Evaluating: Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria.   Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 18 22 Total 80 100

 INTERNAL ASSESSMENT 20 MARKS Pen Paper Test and Multiple Assessment (5+5) 10 Marks Portfolio 05 Marks Lab Practical (Lab activities to be done from the prescribed books) 05 Marks