Maths Is used daily in our Life, Its helpful in every where in every field, So, I made it easier for all people and collect all major formulas and equations which we use on daily basis, which is new and easy for every one..

Math Topics
 Age problems
 Work hours problems
 Clock angles and Sector area
 Algebraic expressions
 Speed distance problems
 Fractions & Percentages
 Range, mean, Mod, Median
 Simple Geometry problems
 Basic Arithmetic
 Probability
 Ratios
 Profit, Discount problems
 Equation solving for Variables
 Basic Calculations
 Square, Marble Size
 Bridge Length
 Fraction Based Gain, Loss
 Finding Share

1.Mean
The mean average is not always a whole number.
The mean is the total of the numbers dividedby how many numbers there are.
To work out the mean:

1. Add up all the numbers.
   7 + 9 + 11 + 6 + 13 + 6 + 6 + 3 + 11 = 72
2. Divide the answer by how many numbers there are.
   There are 9 numbers.
   72 ÷ 9 = 8
   So the mean value is 8.

2: Mode
The mode is the value that appears the most.
7 9 11 6 13 6 6 3 11
To work out the mode:

1. Put the numbers in order:
   3 6 6 6 7 9 11 11 13
2. Look for the number that appears the most.
   6 appears more than any other number.
   So the mode value is 6.
   3.Median
   The median is the middle value.
   To work out the median:
3. Put the numbers in order:
   3 6 6 6 7 9 11 11 13
4. The number in the middle of the list is the median.
   So the median value is 7.
   If there are two middle values, the median is halfway between them. Work out the median for this set of numbers:
   3 6 6 6 7 8 9 11 11 13
   There are two middle values, 7 and 8.
   The median is halfway between 7 and 8, so the median is
   4.Range
   The range is the difference between the biggest and the smallest number.
   To work out the range:
5. Put the numbers in order:
   3 6 6 6 7 9 11 11 13
6. Subtract the smallest number from the biggest number:
   13 - 3 = 10
   So the range of this set of numbers is 10.
   5.Sum of Series
   Sum of an series =
   Exp.what is the avgof first 20 multiples of 7?
   7,14,21…….41
   Sum=((7+140)/2)20
   Sum=73.520
   We have to find avg so
   Avg=73.5*20/20=73.5 ans

6.Probability
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A. 210
B. 29
C. 3 * 28
D. 3 * 29
E. None of these
The correct choice is (B) and the correct answer is 29.

If two dice are thrown what is the probability of soming a sum of 9.
(4,5)…(5,4)….(3,6)…..(6,3) Total 4 ways to become 9
So 4/36=1/9 ans
Factorial:
N!=N.(N-1).(N-2)…….…2.1

7:PERMUTATION
If here are 5 student , in how many ways they can sit?
5!=54321=120
8:COMBINITION
5 combinition 2 = 5!/2!(5-2)!= 5!/2!3!=54321/21321=10
Exp. How many different 4-person teams can b made from a group of 9 players?
=9!/5!(9-5)!=126
9:MARBLE SIZE
Marble size is 20cm30cm. How many marbles are required to cover a square with side 3m?
3m=300cm
Area=300300
No of marbles=Area/Marble size
=300300/20*30=150

12: LENGTH OF BRIDGE
If a man running at 15kmph passed a bridge in 9 seconds, what is the length of the bridge?
Length or Dist=speed * Time
15km=15000m
15000mpr=15000/3600 mps
So Length=15000*9/3600=37.5m

12: EQU MAKING
What is the number 3 more than the double of specific value of x..?
2x-3
Similarly….
What is the number 3 less than the double of specific value of x..?
2x+3

13:LOG PROPERTIES
Log(x.y)=log x+logy
Log(x/y)=logx-log y
ln e=1
ln x^2=2ln x
14: Clock Angles
Angle traced by hour hand in 12 hrs = 360°.
Angle traced by minute hand in 60 min. = 360°.

5:35 ..express hour hand in degree?
As 12Sectors on clock=360 degree
530+3035/60=150+17.5=167.5

14:WORK SHARE
Amount of Work/Time=Output(Rate)

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A=1/4
B+C=1/3
A+C=1/2
C=1/2-1/4=1/4
B=1/3-1/4=1/12
So B alone will do in 12 hours
15: AREA & CIRCUMFERENCE OF CIRCLE
Area= pir^2
C=2pir
16: AREA OF SQUARE,triangle,rectangle
Area of square= s^2
Perimeter=4s
Area of triangle= bh/2
Perimeter= sum of all sides
Area of Equilateral triabgle=sqrt3 s^2/4
Perimeter=3s
Area of rectangle= LW
Perimeter=2(L+W)
Volume of cylinder = pir^2h
Volume of cube=a^3
Area of a rectangle = (Length × Breadth).
Perimeter of a rectangle = 2(Length + Breadth).
Area of a square = (side)2 = 1 / 2 (diagonal)2
Area of 4 walls of a room = 2 (Length + Breadth) × Height.
Area of a triangle = 1 / 2 × Base × Height.
I). Area of a triangle = √s(s-a)(s-b)(s-c) where a, b, c are the sides of the triangle and s = 1/ 2 (a + b + c)
II). Area of parallelogram = (Base x Height).
Area of a rhombus = 1 / 2 (Product of diagonals).
III). Area of a trapezium =1 / 2 (sum of parallel sides) x distance between them.
Iv). Area of a circle = ΠR2, where R is the radius.
Circumference of a circle = 2ΠR.
I). Circumference of a semi-circle = ΠR.
II). Area of semi-circle = ΠR2 / 2.

Cube :
Let each edge of a cube be of length a. Then,

1. Volume = a3 cubic units.
2. Surface area = 6a2 sq. units.
3. Diagonal =√ 3a units.
   Cylinder :
   Let radius of base = r and Height (or length) = h. Then,
4. Volume = (∏r2h) cubic units.
5. Curved surface area = (2∏rh) sq. units.
6. Total surface area = 2∏r(h + r) sq. units.

17: i values
I=sqrt of -1
I^2=-1
I^4=1
18:
Average formula:

Let a1,a2,a3,......,an be a set of numbers, average = (a1 + a2 + a3,+......+ an)/n
Average= sum of elements/no of elements
19: RATIO
3:b=x:c
X=?
3c=bx
X=3c/b
20: Algebra
a^n*a^m=a^m+n
a^n/a^m=a^n-m

19:
If Given Data is
Passed in 1st sub=x%.......Pass in 2nd sub=y%......failed in both sub=z%
Then we can find % of passing students in both sub by this formula
passed in both %= passed in 1stsub+passed in 2ndsub+failed in both-100%.

Similarly
If given data is
Failed in 1st sub=x%.......Failed in 2nd sub=y%....Passedin both sub=z%
Then we can find % of students failed in both sub by this formula
Failed in both %=failed in 1stsub+failed in 2ndsub+Passed in both-100%.
Through these formulas you can find % of failed or passed students in only one subject or both subjects
20:
If it is Sunday , what wil be after 100 days?
12*8=96=Sunday so +4=Thursday
After 100 days itwll b Friday

20:AGE PROBLEM
If father is double the age of his son. 20 years ago he was 12 times that of son. What is the age of father now?
F=2S
F-20=12(S-20)
2S-20=12S-240
10S=220
S=22
F=2S=44
21: % SHARE
A company sell three types of mobiles worth 100, 125, and 225. It sold equal no. of all mobiles. What is the percent share of cheapest mobile?
Total=100+125+225=450
225=50%
100+125=225=50%
100*50/225=22.22%
Simple Interest (S.I.) :
If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.
Let the principal = P, Rate = R% per annum (p.a) and Time = T years. Then ,

1. S.I. = (P x R x T / 100)
2. P = (100 x S.I. / R x T)
3. R = (100 x S.I / P x T)
4. T = (100 x S.I. / P x R).

22: SIMPLE EQU TO FIND VALUE OV VARIABLE
If a=3 find (a^2)^3-a=?
a^6-a=3^6-3=726

23: square root, perfect square
Find the square root of 2809.

1. The last digit is ’9′…so the last digit of the answer is either ’3′ or ’7′.
2. Out of the perfect squares in the list, which ones straddle ’28′? In this case, ’25′ and ’36′.
3. Choose ’25′ since its the lower one. The square root of ’25′ is ’5′. ’5′ is the first digit of our answer.
4. Which number is ’28′ closer to…’25′ or ’36′? It’s closer to ’25′ in this case, so we choose the smaller of our choices for the second digit. Our choices are ’3′ and ’7′; so we choose ’3′.
   Answer: The square root of 2809 is 53.
   Try for 6084…. Ans 78
   24:
   How much speed of train must be increased if time is reduced by 20% …
   S=vt….suppose s=100, t=10
   V=100/10=10
   20% les time=10-2=8
   V=100/8=12.5
   12.5-10=2.5 hence 25%
   25:
   Largest of 13 consecutive intgrswhose sumos 0 ? -6 to 6
   Largest =6
   Leat no of among three digits whose sum is 18= 5..bcz
   X+X+1+X+2=18………………3X=15X=5……… 5+6+7=18
   26: Sum Of Series:
   Sn=n(a1+an)/2

Example. Sum of numbers from 1,2,3……..100
a1=1;
an=100
n=100
Sn=100(1+100)/2=5050

27: Gain, Loss
Loss = (C.P.) - (S.P.).
Gain Percentage: (Gain %)
Gain % = (Gain x 100 / C.P)

Loss Percentage: (Loss %)

Loss % = (Loss x 100 / C.P )

28: Percentage:
Concept of Percentage :
By a certain percent, we mean that many hundredths. Thus, x percent means x hundredths, written as x%.
I. To express x% as a fraction: We have, x% = x / 100.
Thus, 48% = 48 / 100 = 12 / 25.
II. To express a / b as a percent :
We have a / b = (a / b × 100)%.
Percent to fraction: x% = x/100

Percentage formula: Rate/100 = Percentage/base

Properties of Logarithms :

1. loga(xy) = loga x + loga y
2. loga(x / y) = loga x - loga y
3. logx x = 1
4. loga 1 = 0
5. loga (xp) = p(loga x )
6. loga x = 1 / logxa

Some Important Formulae :
I. ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2
II. (1 2 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6
III. (1 3 + 23 + 33 + ..... + n3) = n2 (n + 1)2 / 4

Fractions formulas:

Consumer math formulas:

Discount = list price × discount rate

Sale price = list price − discount

Discount rate = discount ÷ list price

Sales tax = price of item × tax rate

Interest = principal × rate of interest × time

Tips = cost of meals × tip rate

Commission = cost of service × commission rate
BY
Ziad
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