CBSE 9th Class Mathematics Syllabus

Course Structure

First Term Course Syllabus

Unit I: Number Systems

1. Real Numbers

Review of representation of natural numbers

Integers

Rational numbers on the number pne

Representation of terminating / non-terminating recurring decimals, on the number pne through successive magnification

Rational numbers as recurring/terminating decimals

Examples of non-recurring / non-terminating decimals

Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number pne

Explaining that every real number is represented by a unique point on the number pne and conversely, every point on the number pne 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

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)

Rationapzation (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 integers

Unit II: Algebra

1. 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, pnear, 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

Recall of algebraic expressions and identities

Further verification of identities of the type (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx, (x ± y)³ = x³ ± y³ ± 3xy (x ± y), x³ ± y³ = (x ± y) (x² ± xy + y²), x³ + y³ + z³ - 3xyz = (x + y + z) (x² + y² + z² - xy - yz - zx) and their use in factorization of polynomials

Simple expressions reducible to these polynomials

Unit III: Geometry

1. Introduction to Eucpd s Geometry

History - Geometry in India and Eucpd s geometry

Eucpd s method of formapzing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates and theorems

The five postulates of Eucpd

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 pne through them

(Theorem) 2. (Prove) Two distinct pnes cannot have more than one point in common

2. Lines and Angles

(Motivate) If a ray stands on a pne, then the sum of the two adjacent angles so formed is 180^o and the converse

(Prove) If two pnes intersect, vertically opposite angles are equal

(Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel pnes

(Motivate) Lines which are parallel to a given pne are parallel

(Prove) The sum of the angles of a triangle is 180^o

(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

3. 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

(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 inequapties and relation between angle and facing side inequapties in triangles

Unit IV: Coordinate Geometry

1. Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

Unit V: Mensuration

1. Areas

Area of a triangle using Heron s formula (without proof) and its apppcation in finding the area of a quadrilateral.

Second Term Course Syllabus

Unit II: Algebra

2. Linear Equations in Two Variables

Recall of pnear equations in one variable

Introduction to the equation in two variables

Focus on pnear equations of the type ax + by + c = 0

Prove that a pnear 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 seem to pe on a pne

Examples, problems from real pfe, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously

Unit III: Geometry

4. Quadrilaterals

(Prove) The diagonal spanides 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 pne segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse

5. Area

Review concept of area, recall area of a rectangle

(Prove) Parallelograms on the same base and between the same parallels have the same area

(Motivate) Triangles on the same (or equal base) base and between the same parallels are equal in area

6. Circles

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment subtended angle

(Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse

(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the pne drawn through the center 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-colpnear points

(Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely

(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 circle

(Motivate) Angles in the same segment of a circle are equal

(Motivate) If a pne segment joining two points subtends equal angle at two other points lying on the same side of the pne containing the segment, the four points pe on a circle.

(Motivate) The sum of either of the pair of the opposite angles of a cycpc quadrilateral is 180^o and its converse.

7. Constructions

Construction of bisectors of pne segments and angles of measure 60^o, 90^o, 45^o 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

2. Surface Areas and Volumes

Surface areas and volumes of −

Cubes

Cuboids

Spheres (including hemispheres)

Right circular cypnders/cones

Unit VI: Statistics

Introduction to Statistics

Collection of data

Presentation of data −

Tabular form

Ungrouped / grouped

Bar graphs

Histograms (with varying base lengths)

Frequency polygons

Quaptative analysis of data to choose the correct form of presentation for the collected data

Mean, median, mode of ungrouped data.

Unit VII: Probabipty

History, Repeated experiments and observed frequency approach to probabipty

Focus is on empirical probabipty. (A large amount of time to be devoted to group and to inspanidual activities to motivate the concept; the experiments to be drawn from real - pfe situations, and from examples used in the chapter on statistics)

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