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This is the first chapter of Maths which develops the base. This chapter will help students represent natural numbers, integers and rational number on the number line. Not only this, it will also help students to know about terminating, non-terminating number, recurring and non-recurring number. The chapter includes various topics-

• Introduction
• Irrational Number
• Real Number and their Decimal Expansion
•  Representing Real Number on number line
• Operations on Real Number
• Laws of exponents of Real Number
• Summary

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### Lecture 10: Number System Part-10

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This is first chapter of algebra unit. It will help students to know about definition of polynomials, coefficient of polynomials, zero polynomials. Students will also learn factors and theorem, and would recall of algebraic expression and identities. The chapter includes various topics-

• Introduction
• Polynomials in one variables
• Zeros of polynomials
• Reminder Theorem
• Factorisation of Polynomials
• Algebraic Identities
• Summary

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### Lecture 9: Polynomials Part-9

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This chapter will help students various theorems of lines and angles like lines which are parallel to the given lines are parallel; the sum of angles of triangles is 180 degree. Following are the topics covered in the chapter-

• Introduction
• Basic Terms and definitions
• Intersecting lines and Non-intersecting lines
• Pairs of angles
• Parallel lines and Transversals
• Lines parallel to the same line
• Angle sum property of a triangle
• Summary

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### Lecture 6: Lines & Angles Part-6

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This chapter will help students to understand linear equations in two variables and its graphical representation. Following are the topics included in the video-

• Introduction
• Linear Equations
• Solution of Linear Equation
• Graph of a linear equation in two variables
• Equations of line parallel to x-axis and y-axis
• Summary

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### Lecture 5: Linear Equation in Two Variables Part-5

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This chapter will help students to know about the Cartesian planes, points of coordinates and plotting points and other. It is a scoring chapter but it is very important to focus on the graph representations. Following are the topics covered in the chapter-

• Introduction
• Cartesian System
• Plotting a point in the plane if its coordinates are given
• Summary

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### Lecture 3: Coordinate Geometry Part-3

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This chapter will help students to understand various theorems of triangles, like side opposite to the various angles of triangles are equal, the angle opposite to the same side of triangle are equal etc. Following are the topics covered in the chapter-

• Introduction
• Congruence of Triangles
• Criteria for Congruence of Triangles
• Some properties of Triangles
• Some more criteria for Congruence of Triangles
• Inequalities of Triangles
• Summary

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### Lecture 8: Triangles Part-8

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This chapter will help students to know about various theorems and derivatives of quadrilaterals and its types. Following are the topic covered in the chapter-

• Introduction
• Angle Sum Property of a Quadrilaterals
• Properties of a parallelogram
• Another properties of a quadrilateral to be a parallelogram
• The mid-point theorem
• Summary

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This chapter will help students to understand the concept of area and recall area as a rectangle. There are various theorems and derivatives given in this chapter will help students in solving various problems. Following are the topic covered in the chapter-

• Introduction
• Figures on the same base and between the same parallels
• Parallelograms on the same base and between the same parallels
• Triangles on the same base and same parallels
• Summary

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### Lecture 5: Areas Of Parallelo Grams & Triangles Part-5

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This chapter will help students to understand the definition of a circle and related concepts like radius, circumference, diameter, chord etc. There are various theorems and derivatives given in the chapter which will help students to solve questions. Following are the topics covered in the chapter-

• Introduction
• Circle and its related terms: A Review
• Angle Subtended by a Chord at a point
• The perpendicular from a Circle to a chord
• Circle through three points
• Equal chord and their distance from the centre
• Angle subtended by an arc of a circle
• Summary

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### Lecture 8: Circles Part-8

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This chapter will help students to understand the construction of bisectors of line segment and angles of measure 60, 90 and 45 degree. Construction of triangles given its base, sum and difference of other two sides and one base angle. Following are the topics covered in the chapter-

• Introduction
• Basic Construction
• Some construction of a Triangle
• Summary

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### Lecture 3: Constructions part-3

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This chapter will help students to understand area of triangles using heron’s formula (without proof) and its application in finding the area of quadrilaterals.       Following are the topics covered in the chapter-

• Introduction
• Area of Triangle by Heron’s formula
• Application of Heron’s formula in finding in areas of quadrilaterals
• Summary

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### Lecture 2: Heron's Formula Part-2

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This chapter will help students to understand surface areas and volume of cubes, cuboids, spheres and right circular cylinder and cones.
Following are the topics covered in the chapter-

• Introduction
• Summary

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### Lecture 9: Surface Area & Volumes Part- 9

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This chapter will help students to know about basic of statistics, collection of data, and presentation of data (tabular form, grouped / ungrouped), bar graphs, histogram, and polygons Following are the topics covered in the chapter-

• Introduction
• Collection of Data
• Presentation of Data
• Geographical representation of Data
• Measures of Central Tendency
• Summary

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### Lecture 4: Statistics Part- 4

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This chapter will help students to know about the repeated experiments and observed frequency approach to probability and focus on empirical probability. Following are the topics covered in the chapter-

• Introduction
• Probability – an experimental approach
• Summary

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### Lecture 2: Probability Part- 2

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Published    06-Jan-2018      Bilingual

## MATHEMATICS COMPLETE COURSE OF CLASS 9TH CBSE

Study Khazana delivers CBSE Class 9th Mathematic, eighty eight video lectures by Rahul Bhujbal on Mathematics Complete Course with complete solutions using sample paper based on NCERT Syllabus. This chapter covers the following topic to make students understand the topic and covers the whole chapter with all the question and answers.

## 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?

In this chapter we will discuss - The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

## 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.
•

## 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?

In this chapter you we study Area of a triangle using Heron's formula (without proof) and its application in finding the area of a quadrilateral.

## 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

## HOW WE HELP THE STUDENTS???

These video lectures will make the subject easy for students. The free lecture is available as a demo. We provide mock exams after completion of the full course. These lectures are recording of the live session taken. It will include question and answers of the students undertaken during the class. CBSE Class 9th previous question papers and sample papers are also given to the students for practice. We have doubt sessions on YouTube related to students queries asked on WhatsApp. These classes are based on NCERT Syllabus. We offer pen drives and online-offline study mode to the students. We also have Android and IOS Study Khazana mobile app for helping students to study anywhere at any time.

#### RAHUL BHUJBAL

 Phone: 97********48 Email: rah********@gmail.com Address: 154 - A Nyay Khand - 3 Institute: Study Khazana