RATIO

“In the ratio a / b which is written as a : b, is a mathematical operations ratio and fraction are written in the same manner but in fact, their meanings are different”

Formula: ax + bx = n for two parts

ax + bx + cx = n for three parts Proportion: A statement which represents that the two ratio are

equal is called proportion, eg: let the two ratios a/b and c/d be equal than equation a / b = c / d is a proportion or a / b :: c / d or a:b::c:d

Percentage: the word percent consist of two words ‘per’ and ‘cent’, per means each and cent means hundred

Commission: Amount of commission = Rate of

commission x Amount of sales / 100 Rate of commission = Amount of commission x 100 /

Amount of salesAmount of sales = Amount of commission x 100 / Rate

of commissio Amount of del – creder commission = Credit sales x

Rate commission / 100Profit and loss: Profit percent = Profit x 100 / cost

price, Cost price = profit x 100 / profit %.

SIMULATANEOUS EQUATIONS

“simultaneous equations have two variables, e.g:4 x + y = 2”

METHODS: Graphical method: to solve two simultaneous

equations in two variables by graphic method Substitutions method: this method consists of

expressing one variable in term of other in any one equation and substituting this value in other equation by solving this equation so formed

Comparison method: keeping one variable at one end and all other values at other end, do the same with other equation also and put these equation in front of each other by putting “=” sign in between, only one variable would be remaining to be found

Elimination method: “2X +Y = 8” – “2X - Y = 4”, answer is 2Y = 4, so Y = 2 and thereby X = 3.

ELEMENTARY MATRIX “Matrix gives a systematic method to write a system of

equations. Whatever be the size of that system of equations”

TYPES: Horizontal Matrix: more columns and less rows Vertical Matrix: less columns and more rows Row Matrix: more than one columns and one row Column Matrix: one column and more than one rows Vector Matrix: one column and one row Square Matrix: equal amount of columns and rows

THEORY OF LOGARITHM “if ax = n (a > 0, a ≠ 1) then the index x is called the

logarithms of the number n with respect to the base a and is expressed as Logan = x read as the logarithm of n to the base a is x”

Definition: The logarithm of a number to a given base is the index

or power to which the base must be raised to produce the number i.e. to make it equal to the given number for eg: 32 = 9 will be written as Log39 = 2

Anti-Logarithm: The antilogarithm function antilogb(y) is the

inverse function of the logarithm function logb(x); it can be written in closed form as by. The antilog notation was common before the advent of modern calculators and computers: tables of antilogarithms to the base 10 were useful in carrying out computations by hand

Differential calculus: The study of the definition, properties, and applications

of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the derivative function or just the derivative of the original function.

SIMPLE INTEREST

“The consideration of sum of money to be paid for the borrowed money”

Calculation: Principal x rate x months / (100 x 12) Compound Interest: When the simple interest is

added to the principal so that the amount become the principal for next period

Linear Programming: Linear programming (LP) is a mathematical method

for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations. More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

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