ࡱ> pro[ |bjbj hΐΐe/Z OOO$sssss1 0000000$Q4660iO@0]1   RO0 0  ~/-"01Gs0`0s101n0)7f)7(0)7O08 00 1)7 : 9 CLASS-IX First Term Marks: 90  SYLLABUS / CURRICULUM MATHEMATICS (041) TERM I CLASS-IX (2014-15) S.NOMonthUnits / Chapters Detailed Split-up Syllabus Total No. of Periods 1APRIL 1.REAL NUMBERS 2.POLYNOMIALS1. REAL NUMBERS (18 Periods) 1. Review of representation of natural numbers, integers, and 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 such as "2, "3, "5 , etc. 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, every point on the number line represents a unique real number. 3. Rational numbers as recurring/terminating decimals. 4. Existence of "x for a given positive real number x (visual proof to be emphasized). 5. Definition of nth root of a real number. 6. 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.) 7. Rationalization (with precise meaning) of real numbers of the type (and their combinations)  EMBED Microsoft Equation 3.0  and  EMBED Microsoft Equation 3.0  , where x and y are natural number and a and b are integers. 2. POLYNOMIALS (23) Periods Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zeroes polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeroes/roots of a polynomial / equation State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Two skill based Maths Lab activities / Project 18 6 2 MAY & JUNE  1.POLYNOMIALS (contd.) . 1. POLYNOMIALS (23) Periods Factorization of ax2 + b x + 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), x y = (x y) (x x y + y), x3 + y3 + z3 3xyz = (x + y + z) (x2 + y2 + z2 x y y z z x) and their use in factorization of polynomials. Simple expressions reducible to these polynomials.  17 S.NO Month  Units / ChaptersDetailed Split-up SyllabusTotal No. of Periods  JULY 1. INTRODUCTION TO EUCLID'S GEOMETRY 2. LINES AND ANGLES 3. COORDINATE 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. Formative assessment-1  EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0  2. LINES AND ANGLES (10) 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, the 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. COORDINATE GEOMETRY (9) Periods The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting Points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y = m x + c . Two skill based Maths Lab activities / Project  6 10 9 S.NO Month Units / ChaptersDetailed Split-up SyllabusTotal No. of Periods  3AUGUST  1. AREAS 2.TRIANGLES  1. AREAS (4) Periods Area of a triangle using Hero's formula (without proof) and its application in finding the area of a quadrilateral 2. 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. 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 Two skill based Maths Lab activities / Project 4 20 4 SEPTEMBER  Revision for Summative Assessment -1  Revision for Summative Assessment I  10 Course Structure CLASS-IX TERM II  . PRESCRIBED BOOKS: 1. Mathematics - Textbook for class IX - NCERT Publication 2. Mathematics - Textbook for class X - NCERT Publication 3. Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication 4. Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication 5. A Handbook for Designing Mathematics Laboratory in Schools - NCERT Publication 6. Laboratory Manual - Mathematics, secondary stage - NCERT Publication SYLLABUS/CURRICULUM MATHEMATICS (041) TERM II CLASS-IX (2014-15) S.NOMonthUnits / Chapters Detailed Split-up Syllabus (Along with number of periods) Total no. of Periods 1October 1.LINEAR EQUATIONS IN TWO VARIABLES 2.Quadrilaterals  1. LINEAR EQUATIONS IN TWO VARIABLES (14) Periods Recall of linear equations in one variable. Introduction to the equation in two variables. Prove 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 seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously. 2. QUADRILATERALS (10) Periods 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse. Two skill based Maths Lab activities / Project  14 10 November 1. CONSTRUCTIONS 2.AREA  CONSTRUCTIONS (10) Periods Construction of bisectors of line segments and angles, 600, 900 , 450 angles, 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. 2. AREA (4) Periods 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 base and between the same parallels are equal in area and its converse  10 4November 3. CIRCLESCIRCLES (15) Periods Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse. 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) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center(s) and conversely. 5. (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. 6. (Motivate) Angles in the same segment of a circle are equal. 7. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 8. (Motivate) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180o and its converse. Two skill based Maths Lab activities / Project 15DECEMBER 1.PROBABILITY 2. SURFACE AREAS AND VOLUMES 1. PROBABILITY (12) Periods 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). 2. SURFACE AREAS AND VOLUMES (12) Periods Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones Two skill based Maths Lab activities / Project12 5JANUARY  1.SURFACE AREAS AND VOLUMES(contd.) 1. SURFACE AREAS AND VOLUMES (12) Periods Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones FORMATIVE ASSESEMENT -3  EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   EMBED Microsoft Equation 3.0   7JANUARY STATISTICS  1. 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