CURRICULUM IX MATHEMATICS TERM 01

MATHEMATICS CLASS -IX

(CODE NO. 041)

General Instructions:

l                  As per CCE guidelines, the syllabus of Mathematics for classes IX and X has been divided term wise.

l      The units specified for each term shall be assessed through both Formative and

Summative Assessments.

l      In each term, there will be two Formative Assessments, each carrying 10% weightage.

l      The Summative Assessment in term I will carry 30% weightage and the Summative

Asssessment in term II will carry 30% weightage.

l                  Listed  laboratory  activities  and  projects  will  necessarily  be  assessed  through formative assessments.

COURSE STRUCTURE CLASS -IX

First Term                                                                                                    Marks: 90

Units		Marks
I	NUMBER SYSTEMS	17
II	ALGEBRA	25
III	GEOMETRY	37
IV	COORDINATE GEOMETRY	11
V	MENSURATION
	Total (Theory)	90

UNIT I: NUMBER SYSTEMS

1.     REAL NUMBERS                                                                                 (18 Periods)

1.     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 recurring/

terminating decimals.

2.     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, viz. every point on the number line represents a unique real number.

3.     Existence of   x  for a given positive real number x and its representation on the number line with geometric proof.

4.     Definition of nth root of a real number.

5.     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.)

6.     Rationalization (with precise meaning) of real numbers of the type

      1      

a + b  x

and       1       (and their combinations) where x and y are natural number and

x +   y

a and b are integers.

UNIT II: ALGEBRA

1.     POLYNOMIALS                                                                                    (23) 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. 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. Verification of identities:(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.

UNIT III : GEOMETRY

1.     INTRODUCTION TO EUCLID'S GEOMETRY                                               (6) Periods

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.

2.     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 converse.

2.     (Prove) If two lines intersect, vertically opposite angles are equal.

3.     (Motivate) Results on corresponding angles, alternate angles, interior angles when a

transversal intersects two parallel lines.

4.     (Motivate) Lines which are parallel to a given line are parallel.

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 angles.

3.      TRIANGLES                                                                                      (20) 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).

2.     (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).

3.     (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4.     (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. (RHS Congruence)

5.     (Prove) The angles opposite to equal sides of a triangle are equal.

6.     (Motivate) The sides opposite to equal angles of a triangle are equal.

7.     (Motivate) Triangle  inequalities and  relation  between  ‘angle  and  facing  side'

inequalities in triangles.

UNIT IV: 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 V: MENSURATION

1.      AREAS                                                                                                (4) Periods

Area of a triangle using Heron's formula (without proof) and its application in finding

the area of a quadrilateral