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Cubes and Cube Roots
6-
Introduction, Cube, Properties of Cubes and Its Related Sums 38 minLecture1.1
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Cube Roots, Cube Root of a Cube Number 22 minLecture1.2
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Cube and its properties related Sum – [Under Construction] 35 minLecture1.3
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Method of finding Cube Roots – [Under Construction] 21 minLecture1.4
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Chapter Notes – Cubes and Cube RootsLecture1.5
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NCERT Solutions – Cubes and Cube Roots Exercise 7.1Lecture1.6
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Exponents and Powers
10-
Introduction, Laws of Exponents, Points to be Remember While solving Sums, BODMAS Rule 43 minLecture2.1
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Sums Related to Laws of Exponents 46 minLecture2.2
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Sums and Word Problems Related to laws of Exponent, Use of Exponents to Express Small Numbers in Standard Form 54 minLecture2.3
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Sums Based on Laws of Exponents – [Under Construction] 46 minLecture2.4
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Words Problems – [Under Construction] 48 minLecture2.5
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Introduction based Example – [Under Construction] 10 minLecture2.6
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Problem Based on Fraction Number – [Under Construction] 06 minLecture2.7
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Represent Smaller Number into exponents – [Under Construction] 09 minLecture2.8
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Chapter Notes – Exponents and PowersLecture2.9
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NCERT Solutions – Exponents and Powers Exercise 12.1,12.2Lecture2.10
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Linear Equations in One Variable
5-
Introduction, Algebraic Expression, Equations, Solution of linear Equations in One Variable-By Inverse Method, Transposition Method 01 hour 11 minLecture3.1
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Solving Equation By Cross Multiplication Method, Problems Based on Numbers 56 minLecture3.2
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Problems Based on Numbers Cont., Geometry, Age, Money Matters 01 hour 05 minLecture3.3
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Chapter Notes – Linear Equations in One VariableLecture3.4
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NCERT Solutions – Linear Equations in One Variable Exercise 2.1,2.2,2.3,2.4,2.5,2.6Lecture3.5
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Rational Numbers
6-
Introduction of Numbers, Rational Numbers, Properties of Numbers-Closure Property, Commutative Property 01 hour 04 minLecture4.1
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Commutative Property Cont., Associative Property 52 minLecture4.2
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Identity-Additive Inverse & Multiplicative Inverse and its Related Sums, Distributivity-Distributivity of Multiplication Over Addition and Subtraction 01 hour 11 minLecture4.3
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Combined Questions 35 minLecture4.4
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Chapter Notes – Rational NumbersLecture4.5
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NCERT Solutions – Rational Numbers Exercise 1.1, 1.2Lecture4.6
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Direct and Inverse Proportions
4-
Introduction, Direct Proportion and Inverse Proportion and Its related Sums, Time and Work Related Sums 01 hour 27 minLecture5.1
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Sums Based On Direct and Inverse Proportion – [Under Construction] 01 hour 30 minLecture5.2
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Chapter Notes – Direct and Inverse ProportionsLecture5.3
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NCERT Solutions – Direct and Inverse Proportions Exercise 13.1, 13.2Lecture5.4
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Square and Square Roots
5-
Introduction and Prime Factorizing Number 01 hour 20 minLecture6.1
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Shortcut Method: Diagonal Method for Squaring NUmber 05 minLecture6.2
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Methods for Finding Square Roots 01 hour 06 minLecture6.3
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Chapter Notes – Square and Square RootsLecture6.4
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NCERT Solutions – Square and Square Roots Exercise 6.1, 6.2, 6.3, 6.4Lecture6.5
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Chapter Notes – Direct and Inverse Proportions
1. Direct Proportion:
For any ratio x/y, if on changing the values of x & y, the ratio x/y does not change. Then, we say that x and y are in direct proportion.
In other words, one quantity is a constant multiple of the other quantity i.e. if x = ky where k is a constant. Then, we say that x and y are in direct proportion.
Example: Consider the per hour wages paid a company to its employees.
| No. of working hours | Paid Wages (in Rs.) |
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
| 4 | 400 |
| 5 | 500 |
| 6 | 600 |
| 7 | 700 |
| 8 | 800 |
Here, if we consider x as no. of working hours and y as paid wages, then we can find the direct proportion between the two quantities. Moreover, the answer of ratio remains same for each case.
If we consider x = 1 and y =100, we get x/y = 1/100.
Now, we consider x = 7 and y = 700, we get x/y = 7/700 = 1/100.
Thus, in any case ratio x/y will remain constant.
2. Inverse Proportion:
For any ratio x/y, if on increasing x by certain amount the quantity y decreases by the same amount. Then, we say that x and y are in inverse proportion.
In other words, if the product of two quantities is constant i.e xy = k where k is constant. Then, we say that x and y are in inverse proportion.
Example: Consider the speed and time relationship for five trains to travel same distance.
| Train No. | Speed (in kmph) | Time Taken (in Hrs) |
| 1 | 25 | 5 |
| 2 | 50 | 2.5 |
| 3 | 75 | 1.67 |
| 4 | 100 | 1.25 |
| 5 | 125 | 1 |
Here, we can see that as the speed increases the time taken to travel decreases.
Let us consider x as speed and y as time taken.
For train 1, x = 25 and y = 5. So, xy = 125.
For train 4, x = 100 and y = 1.25. So, xy = 125.
Thus, in any case product xy will remain constant.