 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. The 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. The existence of √x for a given positive real number x (visual proof to be emphasized).
4. Definition of nth root of a real number.
5. 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 numbers and a and b are integers.
6. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws).

00:42:29

00:55:17

00:22:03

00:56:18

01:02:00

00:26:48

00:29:49

00:26:31

00:41:46

00:16:45

### Lecture 11: Real Numbers Part- 12

00:25:49

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.

00:31:17

00:38:39

00:27:17

00:31:53

01:02:06

00:48:20

01:01:27

01:02:47

01:01:00

00:52:17

00:46:52

### Lecture 12: Polynomials part-12

00:51:06

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. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

00:55:53

### Lecture 2: Linear Equations In Two Variable Part-2

01:25:40

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

### Lecture 1: Co-ordinate Geometry

00:22:23

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.

### Lecture 1: Euclid's Geometry

00:17:09

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° 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 180°.
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.

00:34:42

00:30:51

00:26:50

00:42:43

00:45:54

00:29:34

00:29:16

00:56:34

00:34:19

### Lecture 10: Lines & Angles Part- 10

00:40:52

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.

00:27:51

00:29:59

00:26:03

00:40:37

00:33:20

00:34:04

00:24:45

00:36:04

00:29:18

00:29:48

### Lecture 11: Triangles Part- 11

00:16:00

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.

00:43:58

00:50:19

00:39:24

00:20:21

00:24:15

00:39:12

00:28:27

00:20:06

00:20:48

00:14:44

00:19:23

00:31:43

00:20:38

### Lecture 14: Quadrilaterals Part-12

00:24:33

Study Khazana aim to explaining the chapter of class 9 Area and Parallelograms and Triangles. The combinations of areas of parallelograms and triangles are given to prove in most of the question. Proof and questions based on “Parallelograms on the same base and between the same parallels have the same area” will be asked. Example of median may be used as theorem in most of the questions. In this chapter will we cover the following topics –
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 between the same parallel. Sameer Kohli faculty of Study Khazana provides a video lectures to students on this chapter to make them to understand this topic easily.

00:31:21

00:28:07

00:31:58

00:21:39

00:29:02

00:26:42

00:31:38

00:40:48

### Lecture 9: Areas of Parallelograms & Triangles Part-9

00:19:26

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment 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 (or their respective centers) 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 either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

01:06:43

00:58:53

00:37:00

00:40:26

00:34:36

00:22:59

### Lecture 7: Circles Part- 7

00:54:03

1. Construction of bisectors of line segments and angles of measure 60°, 90°, 45° etc., equilateral triangles.
2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.

00:34:51

00:16:51

### Lecture 3: Constructions Part- 3

00:39:57

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

00:40:23

00:36:47

00:25:45

00:23:42

00:42:58

### Lecture 6: Heron's Formula Part-6

00:32:44

Study Khazana provides study material on surface area and volume for class 9 by Mr.Sameer Kohli.
We provide 13 video lecture in this topic, students will covered the following concepts in this topic such as- Surface Area of a Cuboid and a Cube, Surface Area of a Right Circular Cylinder, Surface Area of a Right Circular Cone, Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone,Volume of a Sphere.

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

00:51:48

00:46:42

00:48:12

00:42:51

00:48:19

00:47:14

00:46:13

00:42:20

00:48:17

00:13:51

00:23:01

00:22:49

### Lecture 13: Surface Areas & Volumes Part-12

00:17:41

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.

00:52:21

00:35:43

00:29:09

00:38:26

### Lecture 5: Statistics Part-4

00:30:38

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).

00:24:07

00:54:54

### Lecture 3: Probability Part-3

00:06:28

Published    08-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. #### Sameer Kohli

 Phone: 85********24 Email: sam********@gmail.com Address: 319,Joshi Road Karol Bagh, Institute:

##### About Us

Mr. Kohli, founder of Jupiter Education Planet, is a visionary in the field of education and holds an experience of more than 15 years as a Mathematics and Science teacher. Owing to his student-friendly teaching style, he has been able to build an unflinching reputation for himself. He is not only an excellent teacher who has delivered exceptional results throughout his career, but also has a deep insight into child and parent psychology. Over the years, he has acquired expertise in the areas of motivation and counselling of parents and children to help them take better decisions. With a passion to change lives for the better, Mr. Kohli knows the right approach to help children in optimum decision making at both personal and professional level.

##### Qualification

B.Sc. (Hon.) (D.U.)

10 years

#### polynomial

smart learing, smart teaching.

Scroll to Top