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A compilation of mathematical formulas and problem-solving techniques relevant to various topics, including age problems, work-hour problems, clock angles, algebraic expressions, speed-distance problems, fractions, percentages, statistics (range, mean, mode, median), geometry, probability, ratios, profit and discount problems, equation solving, and basic calculations. It includes examples and step-by-step solutions for each topic, making it a useful reference for students. The document also covers concepts such as permutations, combinations, marble size calculations, bridge length problems, and logarithmic properties. It serves as a quick reference guide for mathematical concepts and problem-solving strategies.
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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
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:
The mode is the value that appears the most. 7 9 11 6 13 6 6 3 11 To work out the mode:
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 * 2^8 D. 3 * 2^9 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.
7:PERMUTATION If here are 5 student , in how many ways they can sit? 5!=54321=
8:COMBINITION
5 combinition 2 = 5!/2!(5-2)!= 5!/2!3!=54321/2132*1= Exp. How many different 4-person teams can b made from a group of 9 players? =9!/5!(9-5)!=
9:MARBLE SIZE Marble size is 20cm*30cm. How many marbles are required to cover a square with side 3m?
3m=300cm Area=300* No of marbles=Area/Marble size =300300/2030=
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- Similarly…. What is the number 3 less than the double of specific value of x..? 2x+
Log(x.y)=log x+logy Log(x/y)=logx-log y ln e= ln x^2=2ln x
14: Clock Angles
Cube : Let each edge of a cube be of length a. Then,
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 = ΠR^2 , where R is the radius. Circumference of a circle = 2ΠR. I). Circumference of a semi-circle = ΠR. II). Area of semi-circle = ΠR^2 / 2.
Cylinder : Let radius of base = r and Height (or length) = h. Then,
I=sqrt of - I^2=- I^4=
Average formula:
Let a 1 ,a 2 ,a 3 ,......,an be a set of numbers, average = (a 1 + a 2 + a 3 ,+......+ an)/n
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= 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)
If a=3 find (a^2)^3-a=? a^6-a=3^6-3=
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′.
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Answer: The square root of 2809 is 53. Try for 6084…. Ans 78
How much speed of train must be increased if time is reduced by 20% … S=vt….suppose s=100, t= V=100/10= 20% les time=10-2= V=100/8=12. 12.5-10=2.5 hence 25%
Largest of 13 consecutive intgrs whose sum os 0? -6 to 6 Largest = Leat no of among three digits whose sum is 18= 5..bcz X+X+1+X+2=18………………3X=15X=5……… 5+6+7=
26: Sum Of Series: Sn=n(a1+an)/
Example. Sum of numbers from 1,2,3…….. a1=1; an= n= Sn=100(1+100)/2=
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 )
Concept of Percentage :
Some Important Formulae : I. ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2 II. (1 2 + 2^2 + 3^2 + ..... + n^2 ) = n ( n + 1 ) (2n + 1) / 6 III. (1 3 + 2^3 + 3^3 + ..... + n^3 ) = n^2 (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
