Math tricks PDF E book | PDF files of Math Book

Math short tricks and notes PDF file links are given in this article. You can get it here. Its for upcoming competitive exams like SSC, UPSC, Bank and other Exams

Math short tricks

What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:
x+2=6
That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

(Note point: this equation has the solution x=4, read how to solve equations.)

What is a Formula?

A formula is a special type of equation that shows the relationship between different variables.

A variable is a symbol like x or V that stands in for a number we don't know yet.
Ex. The formula for finding the volume of a box is:
V = lwh
V stands for volume, l for length, w for width, and h for height.

Cuboid

When l=10, w=4, and h=5, then:
V = 10 × 4 × 5 = 200
A formula will have more than one variable.
These are all equations, but only some are formulas:

x = 2y - 7    Formula (relating x and y)
a2 + b2 = c2    Formula (relating a, b and c)
x/2 + 7 = 0    Not a Formula (just an equation)

Without the Equals

Sometimes a formula is written without the "=":
Ex. The formula for the volume of a box is:
lwh
But in a way the "=" is still there, because we can write V = lwh if we want to.

Subject of a Formula

The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.
Ex. in the formula

s = ut + ½ at2

"s" is the subject of the formula

Changing the Subject

A very powerful thing that Algebra can do is to "rearrange" a formula so that another variable is the subject.
Ex. Rearrange the volume of a box formula (V = lwh) so that the width is the subject
Start with:    V = lwh
divide both sides by h:    V/h = lw
divide both sides by l:    V/(hl) = w
swap sides:    w = V/(hl)
So now when we want a box with a volume of 12, a length of 2, and a height of 2, we can calculate its width:
w =    V/(hl)
=    12 / (2 × 2)
=    12 / 4
=    3

Profit and Loss

Profit/loss = Sales price - Cost price

In case of profit

25% of Cost Price (1/4 of CP) = 20% of Selling Price (1/5 of SP)
Similarly, 1/3 of CP = 1/2 of SP

In case of loss

25% of Selling Price (1/4 of SP) = 20% of Cost Price (1/5 of CP)

Profit and Loss

Estimation

That's the most important technique. This is not a secret that every successful candidate is using this technique during exams.

Example - 112 × 92
Simply 112 × 9 = 1008
⇒ Add a zero 10080 and then add 224 to 10080.
⇒ Answer is 10304
You need to do all the calculations in your brain. Don't use paper. You need to divide complex calculations into parts and solve it in your brain without paper. That's how toppers do complex calculations during exams.
Right now it will be difficult for you to use this method but with practice, you will be able to do any complicated calculation within seconds.
Sencelry, 1/3 of SP = 1/2 of CP