formulas for maths questions
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Question Types
• Age problems
• Work hours problems
• Clock angles and Sector area
• Algebraic expressions
• Speed distance problems
• Fractions & Percentages
• Range, mean, Mod
• Simple Geometry problems
• Basic Arithmetic
• Probability
• Ratios
• Profit, Discount problems
• Equation solving for Variables
Quantitative Sections Formulas
• Speed Distance and Time
Distance = Speed * Time
Example:
If a man running at 15 kmph passed a bridge in 9 seconds, what is the length of the bridge?
Solution: As S=v*t
Length=(15*1000/ 3600)*9=37. 5m
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• Mean Value
• The mean average is not always a whole number.
• The mean is the total of the numbers divided by how many numbers there are.
• To work out the mean:
• Add up all the numbers.
7 + 9 + 11 +6+13 + 6 + 6 + 3 + 11 = 72
• Divide the answer by how many numbers there are. There are 9 numbers.
72 / 9 = 8
So the mean value is 8.
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• Mode Value
• The mode is the value that appears the most.
• 7 9 11 6 13 6 6 3 11
• To work out the mode:
• Put the numbers in order: 3 6 6 6 7 9 11 11 13
• Look for the number that appears the most. 6 appears more than any other number.
So the mode value is 6.
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• Median value
• The median is the middle value.
• To work out the median:
• Put the numbers in order: 3 6 6 6 7 9 11 11 13
• 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 7.5.
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• Range
• The range is the difference between the biggest and the smallest number.
• To work out the range:
• Put the numbers in order:
3 6 6 6 7 9 11 11 13
• Subtract the smallest number from the biggest number:
13 - 3 = 10
So the range of this set of numbers is 10.
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• Sum of given Series
Sum = ((First Term+ Last Term) /2 )* Number of Terms
Example:
• .what is the avg of first 20 multiples of 7?
So series for first 20 multiples of 7 is 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
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• Probability
Probability that event A occurs P(A) = n(A) / n(S).
where
n(A) - number of event occurs in A
n(S) - number of possible outcomes
Example:
What is the probability of sum 9 on both of two dice when rolled together?
Solution:
Total outcomes for two dices=6*6=36
Events whose sum is 9 are (3,6),(6,3),(4,5),(5,4)=4
Probability of sum 9=4/36=1/9
• Marble Size, Number of Marbles
Example: • Marble size is 20cm*30cm. How many marbles are required to cover a square with side 3m?
• 3m= 300cm
• Area of Square=300*300
• No of marbles=Area /Marble size
• =300*300/ 20*30= 150
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• LOG PROPERTIES
• 1) Multiplication inside the log can be turned into addition outside the log
• Log(x.y)=log x+logy
• 2) Division inside the log can be turned into subtraction outside the log
• Log(x/y)=logx - logy
• 3) An exponent on everything inside a log can be moved out front as a multiplier
• In x^2=21n x
• In e=1
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• Clock hands and Angles
• Angle traced by hour hand in 12 hrs = 360°.
• Angle traced by minute hand in 60 min. = 360°.
Example:
• 5:35 express hour hand in degree?
• As 12 Sectors on clock=360 degree
• 5*30+30*35/60=150+17.5=167.5 degrees
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• WORK SHARE
• Amount of Work/Time=Output(Rate)
Example:
• 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.
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• AGE PROBLEM
• Example:
• 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
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• Percentage % 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
Share of cheapest mobile= 100*100/450=22.22%
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• 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
Commission = cost of service * commission rate
• Loss = C.P — S.P
• Gain% = Gain* 100 / C.P
• Loss % = Lost* 1 00 / C. P
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• Sector Area
• Sector Area=pi* r^2*angle
Example:
A clock's minute hand is 10cm long. What area it will cover from 9
0am to 9:35am?
• Solution:
r=10 cm
Area=pi* r^2* angle
Area=3.14*10*10*(7/12)
Area=183.3 cm^2
Note: for 35 minute, minute hand position will be at 7 angle with position as 7/12 or angle= 210/360
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• Solving Expressions
Example:
What is the value of x? If 3^ (1+x) + 5*3^x -8=0
Solution:
3 * 3^x +5 * 3^x=8
3^x (3+5)=8
3^x=1
3^x=3^0
Hence x=0
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• AREA & CIRCUMFERENCE OF CIRCLE
• Area= pi*r^2
• C=2*pi*r
• 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 triangle=sqrt3 *s^2 /4
• Perimeter=3s
• Area of rectangle= L*W
• Perimeter=2(L+W)
• Volume of cylinder = pi*r^2*h
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• Cube :
• Let each edge of a cube be of length a. Then,
• 1. Volume = a^3 cubic units.
• 2. Surface area = 6a^2 sq. units.
• 3. Diagonal =sqrt 3a units.
Example:
What is the volume of a cube whose surface area is 294?
A.125
b.216
c.294
d.343
• SOLUTION:
Surface Area of Cube= 6*a^2=294
a^2=49
So a=7
Volume of Cube= a^3
a^3=7^3=343
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• Cylinder :
• Let radius of base = r and Height (or length) = h. Then,
• 1. Volume = (π * r^2 * h) cubic units.
• 2. Curved surface area = (2*π * r * h) sq. units.
• 3. Total surface area = 2*π * r*(h + r) sq. units.
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• i values
• I=sqrt of -1
• I^2=-1
• I^4=1
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• Average formula:
Let a1, a2,a3,........an be a set numbers, average = (a1 + a2 + a3 + ....... +an)/n
• Average= sum of elements/no of elements
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• RATIO
• 3:b=x:c
• X=?
• 3c=bx
• X=3c/b