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  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).

Lecture 1: Real Numbers Part- 1


Lecture 2: Real Numbers Part- 2


Lecture 3: Real Numbers Part-3


Lecture 4: Real Numbers Part-4


Lecture 5: Real Numbers Part-5


Lecture 6: Real Numbers Part-7


Lecture 7: Real Numbers Part-8


Lecture 8: Real Numbers Part-9


Lecture 9: Real Numbers Part- 10


Lecture 10: Real Numbers Part- 11


Lecture 11: Real Numbers Part- 12

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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.

Lecture 1: Polynomials Part-1


Lecture 2: Polynomials Part-2


Lecture 3: Polynomials Part-3


Lecture 4: Polynomials Part-4


Lecture 5: Polynomials Part-5


Lecture 6: Polynomials Part-6


Lecture 7: Polynomials Part-7


Lecture 8: Polynomials Part-8


Lecture 9: Polynomials Part-9


Lecture 10: Polynomials Part-10


Lecture 11: Polynomials Part-11


Lecture 12: Polynomials part-12

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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.

Lecture 1: Linear Equations In Two Variable Part-1


Lecture 2: Linear Equations In Two Variable Part-2

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

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.

  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.

Lecture 1: Lines & Angles Part-1


Lecture 2: Lines & Angles Part-2


Lecture 3: Lines & Angles Part-3


Lecture 4: Lines & Angles Part- 4


Lecture 5: Lines & Angles Part- 5


Lecture 6: Lines & Angles Part- 6


Lecture 7: Lines & Angles Part- 7


Lecture 8: Lines & Angles Part- 8


Lecture 9: Lines & Angles Part- 9


Lecture 10: Lines & Angles Part- 10

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  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.

Lecture 1: Triangles Part- 1


Lecture 2: Triangles Part- 2


Lecture 3: Triangles Part- 3


Lecture 4: Triangles Part- 4


Lecture 5: Triangles Part- 5


Lecture 6: Triangles Part- 6


Lecture 7: Triangles Part- 7


Lecture 8: Triangles Part- 8


Lecture 9: Triangles Part- 9


Lecture 10: Triangles Part- 10


Lecture 11: Triangles Part- 11

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  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.

Lecture 1: Quadrilaterals Part-1


Lecture 2: Quadrilaterals Part-2


Lecture 3: Quadrilaterals Part-3


Lecture 4: Quadrilaterals Part-4


Lecture 5: Quadrilaterals Part-5


Lecture 6: Quadrilaterals Part-5-1


Lecture 7: Quadrilaterals Part-5-2


Lecture 8: Quadrilaterals Part-6


Lecture 9: Quadrilaterals Part-7


Lecture 10: Quadrilaterals Part-8


Lecture 11: Quadrilaterals Part-9


Lecture 12: Quadrilaterals Part-10


Lecture 13: Quadrilaterals Part-11


Lecture 14: Quadrilaterals Part-12

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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.

Lecture 1: Areas of Parallelograms & Triangles Part-1


Lecture 2: Areas of Parallelograms & Triangles Part-2


Lecture 3: Areas of Parallelograms & Triangles Part-3


Lecture 4: Areas of Parallelograms & Triangles Part-4


Lecture 5: Areas of Parallelograms & Triangles Part-5


Lecture 6: Areas of Parallelograms & Triangles Part-6


Lecture 7: Areas of Parallelograms & Triangles Part-7


Lecture 8: Areas of Parallelograms & Triangles Part-8


Lecture 9: Areas of Parallelograms & Triangles Part-9

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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.

Lecture 1: Circles Part- 1


Lecture 2: Circles Part- 2


Lecture 3: Circles Part- 3


Lecture 4: Circles Part- 4


Lecture 5: Circles Part- 5


Lecture 6: Circles Part- 6


Lecture 7: Circles Part- 7

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  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.

Lecture 1: Constructions Part - 1


Lecture 2: Constructions Part - 2


Lecture 3: Constructions Part- 3

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

Lecture 1: Heron's Formula Part-1


Lecture 2: Heron's Formula Part-2


Lecture 3: Heron's Formula Part-3


Lecture 4: Heron's Formula Part-4


Lecture 5: Heron's Formula Part-5


Lecture 6: Heron's Formula Part-6

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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.

Lecture 1: Surface Areas & Volumes Part-1


Lecture 2: Surface Areas & Volumes Part-2


Lecture 3: Surface Areas & Volumes Part-3


Lecture 4: Surface Areas & Volumes Part-4


Lecture 5: Surface Areas & Volumes Part-5


Lecture 6: Surface Areas & Volumes Part-6


Lecture 7: Surface Areas & Volumes Part-7


Lecture 8: Surface Areas & Volumes Part-8


Lecture 9: Surface Areas & Volumes Part-8-2


Lecture 10: Surface Areas & Volumes Part-9


Lecture 11: Surface Areas & Volumes Part-10


Lecture 12: Surface Areas & Volumes Part-11


Lecture 13: Surface Areas & Volumes Part-12

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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.

Lecture 1: Statistics Part-1


Lecture 2: Statistics part-2-1


Lecture 3: Statistics Part-2-2


Lecture 4: Statistics Part-3


Lecture 5: Statistics Part-4

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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).

Lecture 1: Probability Part-1


Lecture 2: Probability Part-2


Lecture 3: Probability Part-3

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Published    08-Jan-2018      Bilingual

Sameer Kohli

Phone: 98********46 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.


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


10 years


smart learing, smart teaching.


STUDY KHAZANA is an e-treasure of knowledge and education with one aim of upbringing the level of education all over the India. In the journey of more than 25 years with 150 centers across the India we discovered that many student are out of the reach of proper education due to poverty.

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