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9 Find Math home Tutors, Online Tutors, home Tuition & Private Tutors for Class
IX
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First Term Exam Syllabus for Math Class IX
UNIT I : NUMBER SYSTEMS
1. REAL NUMBERS
 Review of representation of natural numbers, integers, rational numbers on the number line
 Representation of terminating / nonterminating recurring decimals on the number line through successive magnification
 Rational numbers as recurring/terminating decimals
 Examples of nonrecurring / non terminating decimals such as √2, √3, √5 etc
 Existence of nonrational 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
 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.)
 Rationalization (with precise meaning) of real numbers of the type (& their combinations)
UNIT II : ALGEBRA
1. POLYNOMIALS
 Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms
 zero polynomial
 Degree of a polynomial
 Constant, linear, quadratic, cubic polynomials
 monomials
 binomials
 trinomials
 Factors and multiples
 Zeros/roots of a polynomial / equation
 State and motivate the Remainder Theorem with examples and analogy to integers
 Statement and proof of the Factor Theorem
 Factorization of ax2 + bx + c, a ≠ 0 where a, b, 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 polymonials
 Simple expressions reducible to these polynomials
UNIT III : GEOMETRY
1. 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. (Axim) 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
 (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180o and the converse
 (Prove) If two lines intersect, the vertically opposite angles are equal
 (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines
 (Motivate) Lines, which are parallel to a given line, are parallel
 (Prove) The sum of the angles of a triangle is 180o
 (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interiors 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 Congruene)
 (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 inequalities and relation between 'angle and facing side' inequalities 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
 graph of linear equations as examples
 focus on linear equations of the type Ax + By + C = 0 by writing it as y = mx + c
UNIT V : MENSURATION
1. AREAS
 Area of a triangle using Hero's formula (without proof) and its application in finding the area of a quadrilateral
Second Term Exam Syllabus for Math Class IX
UNIT II : ALGEBRA (Contd.)
2. LINEAR EQUATIONS IN TWO VARIABLES
 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
 problems from real life
 including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously
UNIT III : GEOMETRY
4. 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 (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 base and between the same parallels are equal in area and its converse
6. CIRCLES
 Through examples, arrive at definitions of circle related concepts
 radius
 circumference
 diameter
 chord
 arc
 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 line 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 noncollinear points
 (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center(s) 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 line segment joining two points subtendes equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle
 (Motivate) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180o and its converse
7. CONSTRUCTIONS
 Construction of bisectors of line segments & angles, 60o, 90o, 45o 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
UNIT V : MENSURATION (Contd.)
2. SURFACE AREAS AND VOLUMES
 Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones
UNIT VI : STATISTICS AND PROBABILITY
1. STATISTICS
 Introduction to Statistics
 Collection of data
 presentation of data — tabular form, ungrouped / grouped
 bar graphs
 histograms (with varying base lengths)
 frequency polygons, qualitative analysis of data to choose
 the correct form of presentation for the collected data. Mean, median, mode of ungrouped data
2. PROBABILITY
 History
 Repeated experiments and observed frequency approach to probability Focus is on empirical probability
the experiments to be drawn from real  life situations, and from examples used in the chapter on statistics)
