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Importance of Statistics in Different Fields The Circle and Parts of a Circle Formulas of Integration Quartile Deviation and its… Click here to read more
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From basic to higher mathematics
Concept of Proportion
“A statement of equality of two ratios is called proportion.” Four numbers, a, b, c, d, are said to be… Click here to read more
Direct Proportion
Suppose the price of one piece of soap is 20 Rs. If a person wants to buy one dozen pieces… Click here to read more
Inverse Proportion
Suppose that 20 men build a house in 6 days. If the number of men is increased to 30 then they… Click here to read more
Compound Proportion
“The proportion involving two or more quantities is called Compound Proportion.” Rules for Solving Compound Proportions \[\begin{array}{*{20}{c}} {{\text{Quantity 1}}}&{{\text{Quantity 2}}}&{{\text{Quantity… Click here to read more
Introduction to Analytic Geometry
Geometry is one of the most ancient branches of mathematics, concerned with the properties of space and object – points,… Click here to read more
Coordinate System
Cartesian coordinates are defined through the use of two coordinate lines, one horizontal and the other vertical. Let their point of intersection be $$O$$,… Click here to read more
More Examples of Integration
Example: \[\int {\frac{{{{\text{x}}^2} + 2\sqrt {{\text{x}} – 1} }}{{2{{\text{x}}^2}\sqrt {{\text{x}} – 1} }}{\text{dx}}} \] Solution: We have \[\int {\frac{{{{\text{x}}^2} +… Click here to read more
Examples of Integration
Evaluate: (i) $$\int {\left( {3{{\text{x}}^6} – 2{{\text{x}}^2} + 7{\text{x}} + 1} \right)} {\text{ dx}}$$ (ii) $$\int {\frac{{{{\text{t}}^2} – 2{{\text{t}}^4}}}{{{{\text{t}}^4}}}{\text{ dt}}}… Click here to read more
Basic Integral Formulas
1) $$\int {1dx = x + c} $$ 2) $$\int {adx = ax + c} $$ Where $$a$$is any constant…. Click here to read more
Concept of Anti Derivatives or Integration
The inverse process of derivatives is called anti–derivatives or integration. “A function $$f\left( {\text{x}} \right)$$being given and it is required… Click here to read more
Introduction to Differential Calculus
In the seventeenth century, Sir Isaac Newton, an English mathematician (1642–1727), and Gottfried Wilhelm Leibniz, a German mathematician (1646–1716), considered… Click here to read more
Average and Instantaneous Rate of Change
A variable which can assign any value independently is called the independent variable, and the variable which depends on some independent… Click here to read more
Examples of Average and Instantaneous Rate of Change
Example: Let $$y = {x^2} – 2$$ (a) Find the average rate of change of $$y$$ with respect to $$x$$… Click here to read more
Derivative of a Function
Let $$y = f(x)$$ be a given function of $$x$$. Give to $$x$$ a small increment $$\Delta x$$ and let… Click here to read more
Introduction to Functions
In mathematics, the term function is very famous. If we look at the historical background the term, function was first used… Click here to read more
Concept of Functions
Let A and B be any two non–empty sets. Then a function ‘$$f$$’ is a rule or law which associates… Click here to read more
Examples of Functions
Example: Find the range of the function $$f\left( {\text{x}} \right) = \frac{{{\text{x}} + 1}}{{{\text{x}} – 1}}$$. Solution: We have \[f\left(… Click here to read more
Types of Functions
Constant Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from ‘A’ to ‘B’ is… Click here to read more
Nature of Functions
One – One Function: Let ‘A’ and ‘B’ be any two non–empty sets, then a function ‘$$f$$’ from A to… Click here to read more
Concept of Limit
Meaning of the Phrase “Tend to Zero”: Suppose a variable ‘x’ assumes in succession a set of values. \[1,\;\frac{1}{{10}},\;\frac{1}{{{{10}^2}}},\;\frac{1}{{{{10}^3}}},\;\frac{1}{{{{10}^4}}},\; \cdots… Click here to read more
Subgroups
Let $$G$$ be a group and $$H$$ any subset of $$G$$. Let $$a,b$$ be any two elements of $$H$$. Now… Click here to read more
Profit and Loss
For the purpose of comparison, we usually express the actual profit or loss as a percentage of cost price. For… Click here to read more
Concept of Discount
In most cases, retailers cannot sell defective items, old items, etc. at the retail-selling price. If these items are sold… Click here to read more
Concept of Commission
A commission is the payment an agent gets for selling or buying something on behalf of another person. It is… Click here to read more
Concept of Rate
Before defining rate, first we consider some examples. 1. If one dozen eggs cost 24 Rs., what is the cost… Click here to read more
Concept of Percentages
Comparing fractions is not an easy task, especially when the two fractions have different denominators. For example, you are asked… Click here to read more
Expressing One Quantity as a Percentage of Another Number
In a school, 56 out of 70 teachers are female. What percentage of the teachers is female? What percentage of them… Click here to read more
Percentage Changing
The change in the value of an item can be expressed as a percentage increase or decrease of the original… Click here to read more
Concept of Ratio
Sometimes we have to deal with quantities that require comparison. Suppose in a class of 45 students, 15 of the… Click here to read more
Uses of Ratio and Continued Ratio
Ratio is used for calculating continued ratio, proportion, rates, and percentage as well as continued proportion. Ratio can also be… Click here to read more
Continued Proportion
Quantities are said to be in continued proportion if the first is related to the second, the second is related… Click here to read more