MATHEMATICS COMPLETE COURSE OF CLASS 9TH CBSE

WHAT DO YOU STUDY IN NUMBER SYSTEM?

• 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.
• 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, 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.
• Rationalization (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.
• 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.)

WHAT DO YOU STUDY IN POLYNOMIALS?

•   Definition of a polynomial in one variable, with examples and counter examples 
• Define Coefficients of polynomial, terms of a polynomial and zero polynomial, Degree of a polynomial 
• Explain 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. ·        

WHAT DO YOU STUDY IN LINEAR EQUATION IN TWO VARIABLES?

•  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. 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 lie on a line. Graph of linear equations in two variables  

WHAT DO YOU STUDY IN COORDINATE GEOMETRY?

WHAT DO YOU STUDY IN EUCLID 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. 
• Concept of five postulates of Euclid. 
• Discuss Equivalent versions of the fifth postulate    

WHAT DO YOU STUDY LINES AND ANGLES?

• (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse.
• (Prove) If two lines intersect, 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 180°.
• (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.
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WHAT DO YOU STUDY IN 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 inequalities and relation between 'angle and facing side' inequalities in triangles.

WHAT DO YOU STUDY IN 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.

WHAT DO YOU STUDY IN AREA OF PARALLELOGRAM AND TRIANGLES?

•  Explain the 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.

WHAT DO YOU STUDY IN CIRCLE?

• (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 non-collinear 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.

WHAT DO YOU STUDY IN CONSTRUCTION?

• Construction of bisectors of line segments and angles of measure 60°, 90°, 45° 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.        

WHAT DO YOU STUDY IN HERON FORMULA?

WHAT DO YOU STUDY IN SURFACE AREAS AND VOLUMES?

• Discuss the Surface areas and volumes of cubes, 
• Explain cuboids, spheres, hemispheres 
• Describe right circular cylinders/cones

WHAT DO YOU STUDY IN STATISTICS?

• Introduction to Statistics 
• Explain Collection of data, presentation of data - tabular form, ungrouped / grouped, bar graphs,  
• Discus histograms (with varying base lengths), 
• What is a frequency polygon? 
• Describe qualitative analysis of data to choose the correct form of presentation for the collected data. 
• Explain Mean, median, mode of ungrouped data.  

WHAT DO YOU STUDY IN PROBABILITY?

• Define history of Probability 
• Discuss repeated experiments and observed frequency approach to probability 
• Explain empirical probability    

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