FORMULA SHEET
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
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.
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
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.
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:
1.
Put the numbers in
order:
3 6 6 6 7 9 11 11 13
3 6 6 6 7 9 11 11 13
2.
The number in the middle
of the list is the median.
So the median value is 7.
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
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:
1.
Put the numbers in
order:
3 6 6 6 7 9 11 11 13
3 6 6 6 7 9 11 11 13
2.
Subtract the smallest
number from the biggest number:
13 - 3 = 10
So the range of this set of numbers is 10.
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 avg of first 20 multiples of 7?
7,14,21…….41
Sum=((7+140)/2)*20
Sum=73.5*20
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!=5*4*3*2*1=120
8:COMBINITION
5 combinition
2 = 5!/2!(5-2)!= 5!/2!*3!=5*4*3*2*1/2*1*3*2*1=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 20cm*30cm. How many marbles are required to cover a square with side
3m?
3m=300cm
Area=300*300
No
of marbles=Area/Marble size
=300*300/20*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
5*30+30*35/60=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= pi*r^2
C=2*pi*r
16: AREA OF SQUARE,triangle,rectangle
Area
of square= s^2
Perimeter=4s
Area
of triangle= b*h/2
Perimeter=
sum of all sides
Area
of Equilateral triabgle=sqrt3 *s^2/4
Perimeter=3s
Area
of rectangle= L*W
Perimeter=2(L+W)
Volume
of cylinder = pi*r^2*h
Volume
of cube=a^3
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Area
of a rectangle = (Length × Breadth).
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Perimeter
of a rectangle = 2(Length + Breadth).
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Area
of a square = (side)2 = 1 / 2
(diagonal)2
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Area
of 4 walls of a room = 2 (Length + Breadth) × Height.
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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.
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Circumference
of a circle = 2ΠR.
I).
Circumference of a semi-circle = ΠR.
II).
Area of semi-circle = ΠR2 / 2.
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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,
1. Volume = (∏r2h) cubic units.
2. Curved surface area = (2∏rh) sq. units.
3. 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
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 1st sub+passed in 2nd sub+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 1st
sub+failed in 2nd sub+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 it wll 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′.
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 intgrs
whose sum os 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
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Loss = (C.P.) - (S.P.).
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Gain Percentage: (Gain %)
Gain % = (Gain x 100 / C.P)
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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
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
Falak Sher Buzdar
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