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35 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Interest |
# simple interest = p*r*t /100 New amount = p ( 1+ r*t /100) # Compound interest = p[ ( 1+ r /n) ^(n*t) - 1 ] New amount = p ( 1+ r /n) ^(n*t) |
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Ratio |
#combined ratios |
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Fraction to decimal to percent |
1/100 = 0.01 = 1% 1/50 = 0.02 = 2% 1/25 = 0.04 = 4% 1/20 = 0.05 = 5% 1/10 = 0.10 = 10% 1/9 = 0.111 = 11.1% 1/8 = 0.125 = 12.5% 1/6 = 0.167 = 16.7 % 1/5 = 0.2 = 20% 1/4 = 0.25 = 25% 3/10 = 0.3 = 30% 1/3 = 0.333 = 33.3% 3/8 = 0.375 = 37.5% 2/5 = 0.4 = 40% 1/2 = 0.5 = 50% 3/5 = 0.6 = 60% 5/8 = 0.625 = 62.5% 2/3 = 0.667 = 66.7% 7/10 = 0.7 = 70% 3/4 = 0.75 = 75% 4/5 = 0.8 = 80% 5/6 = 0.833 = 83.3% 7/8 = 0.875 = 87.5% 9/10 = 0.9 = 90% 5/4 = 1.25 = 125% 4/3 = 1.33 = 133% 3/2 = 1.5 = 150% 7/4 = 1.75 = 175% |
# Fractions : preferred for multiplication or division # Decimals : preferred for addition or subtraction, for estimation, for comparison # percents : same as decimals # smart numbers : multiples of denominators when all the values are unknown and fractions only given Do not pick smart numbers when any amount or total is given. On percent problems smart number can be 100 # heavy division shortcut: use approximation # if the denominator has power of 10 minus 1, then mostly numerator gives you repeating decimals # terminating decimals: when denominator has factors of 2 or 5 or both # unit digit of numbers: keep only last digit and discard all others for any action # only unit digit contribute to the units digit of product # |
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Algebra |
# 0 raised to any power = 0 # 1 raised to any power = 1 # increasing power of fractions Positive fractions = decrease Proper fractions = decrease # anything raised to 0 = 1 # square root of x^2 = |x| # if an equation has square root then use only +ve root # if an equation contains square as power then use +ve as well as -ve root # no solution for even root of a -ve number #Imperfect square: whose square root is not integer |
# squares: 1.4^2 = 2 2^(1/2) = 1.4 1.7^2 = 3 3^(1/2) = 1.7 2.25^2 = 5 5^(1/2) = 2.25 13^2= 169 14^2 = 196 15^2 = 225 25^2= 625 # cubes: 4^3= 64 5^3= 125 |
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Fractions value on sign change |
# fractions b/w 0 and 1 Positive Square = smaller fraction Negative square = bigger fraction Positive cube = smaller fraction Negative cube = bigger fraction #fractions > 1 Positive Square = bigger fraction Negative square = smaller fraction Positive cube= bigger fraction Negative cube = smaller fraction |
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Functions |
Pick numbers to solve quickly |
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Maxima minima |
# When calculating range then take two cases one for negative and one for positive # x and y +ve and x < y 1/x > 1/y # x and y -ve and x < y 1/x > 1/y # x -ve and y +ve and x < y 1/x < 1/y # squaring inequalities Both sides -ve, flip the inequality sign when square Both sides +ve, inequality sign will remain as it is when square If both sides have different signs, you cannot square If signs are unclear, you cannot square |
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Statistics |
# weighted average: (Weight 1 * data point 1 + weight 2 * data point 2) / sum of weights Weight 1 = actual value - average value # Median: middle value for odd set Average of two mid values for even set # Standard deviation: distance of average from the data point Small SD means set is clustered around the average Large SD means set is spread out widely # changes in SD: analyse the data moving closer to mean, farther from mean or neither # Variance: square of SD |
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Consecutive Integers |
# arithmetic mean = median = average of first and last term # number of integers = last - first + 1 # number of multiples of n = (last multiple - first multiple) / n + 1 # sum = average * number (Last+first) / 2 * ( last-first+1) # average of odd number of integers = integer #average of even number of integers = never integer |
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Extra on consecutive integers |
# product of any 3 consecutive integers = always div by 3 and 2 # product of n consecutive integers = divisible by n! # sum of odd numbers = multiple of number of items |
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Triangle |
Sides= 3 Perimeter = sum of 3 sides Sum of interior angles = 180 Area = base*height /2 Sum of two sides > third side > difference b/w two sides # common right angle triangle combos 3-4-5 6-8-10 5-12-13 10-24-26 8-15-17 # Isoceles 45-45-90 triangle Ratio of sides 1:1: root2 # if diagonal of a square is given, use 45-45-90 triangle ratio to find length of square # Equilateral 30-60-90 triangle Ratio of sides = 1: root3 : 2 # Similar triangles All corresponding angles equal Corresponding sides in proportion If corresponding sides are in ratio a/b then area of similar triangles in ratio a^2/b^2 # Equilateral triangle Can be split in two 30-60-90 triangles Area = base^2 * root3 / 4 Height = base * root3 / 2 |
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Circles |
# inscribed angle of the arc = 1/2 central angle of the arc # if one of the side is diameter then the triangle inscribed in a circle is always right angle |
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Circles |
# inscribed angle of the arc = 1/2 central angle of the arc # if one of the side is diameter then the triangle inscribed in a circle is always right angle |
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Cylinder |
# surface area = 2 circles + rectangle A = 2 pi r^2 + 2 pi r*h = 2 pi r (r+h) # volume = pi * r^2 * h |
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Circles |
# inscribed angle of the arc = 1/2 central angle of the arc # if one of the side is diameter then the triangle inscribed in a circle is always right angle |
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Cylinder |
# surface area = 2 circles + rectangle A = 2 pi r^2 + 2 pi r*h = 2 pi r (r+h) # volume = pi * r^2 * h |
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Co-ordinate Geometry |
# shortest distance b/w 2 points = straight line # slope = y/x Or (y2-y1) / (x2-x1) # positive slope = line rises upwards from left to right # negative slope = line falls from left to right # zero slope = y axis # undefined slope = x axis # x intercept where y=0 Y intercept where x=0 # line equation y=mx + b # line equation when two points given (y - y1) = m ( x-x1) m = (y2 - y1)/ (x2- x1) # distance b/w two points = root [ (y2-y1)^2 + (x2-x1)^2] # of all the quadrilaterals, with a given perimeter, square has the largest area # of all the quadrilaterals, with a given area, square has the min perimeter # area of parallelogram or triangle can be maximised by keeping 2 sides perpendicular to each other # parallel lines m1 = m2 # perpendicular lines m1 * m2 = -1 # midpoint of a line = [ (x1+x2)/2 , (y1+y2)/2 ] |
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Divisibility rules |
# div by 2: int. is even # div by 3 : if sum of int. digits div by 3 # div by 4: if int. is twice div by 2 # div by 5: if int. ends in 0 or 5 # div by 6: if int. digits are both div by 2 and 3 # div by 8: if the int. is div thrice by 2 or last 3 digits are div by 8 # div by 9: if sum of int. digits are div by 9 # div by 10: if the int. ends in 0 |
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Divisibility |
# an int. is always both a factor and multiple of itself # 1 is a factor of every int. # fewer factors more multiples # factors divide into an int. Multiples multiply out from int. # if you add or subtract multiples of N, result will be multiple of N # if you add multiple of N and no-multiple of N, the result will be non-multiple of N |
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Primes |
# prime no. is any positive int. > 1 with exactly two factors 1 and itself # first prime no. = 2 # only even prime no. = 2 # first 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 # total 25 primes up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 # prime factorisation: 1. To check Divisibility 2. To find GCF 3. To find LCM 4. To reduce fractions 5. To simplify square roots 6. To solve exponents # if integer then only prime |
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GCF and LCM |
# if a is factor of b, b is factor of c, then a is also factor of c # GCF : largest divisor of two or more integers # GCF will be smaller than or equal to the starting integers # LCM: smallest multiple of two or more integers # LCM, being a multiple, will be larger than or equal to the starting integers # GCF * LCM = product of numbers # GCF cannot be > than difference of numbers # consecutive multiples of N have GCF = 1 # |
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Even / Odd |
# Even + / - Even = Even Even + / - Odd = Odd Odd + / - Odd = Even Even * Even = Even ( div by 4) Even * Odd = Even Odd * Odd = Odd Even / Even = Even or Odd or Non Int Even / Odd = Even or Non Int Odd / Even = Non Int Odd / Odd = Odd or Non Int # all primes are odd except 2 # sum of 2 primes ( when not 2) = even # if sum of primes is odd then one of the prime is 2 |
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Positives and Negatives |
# absolute value of any number is always positive # if two numbers are opposite to each other then they have the same absolute value # signs same, product and division are positive #signs different, product and division are negative |
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Factors |
# total number of factors of a^x * b^y * c^z = (x+1) * (y+1)* (z+1) # total number of different factors = 3 i.e a,b,c #total number of prime factors = x*y*z # all perfect squares have odd no. of total factors and vice versa # all perfect squares contains only even power of primes # when you divide an int. by a positive int. N, possible remainders range from 0 to (N-1) Means total N possible remainders # Remainder must be smaller than divisor # |
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Circles |
# inscribed angle of the arc = 1/2 central angle of the arc # if one of the side is diameter then the triangle inscribed in a circle is always right angle |
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Cylinder |
# surface area = 2 circles + rectangle A = 2 pi r^2 + 2 pi r*h = 2 pi r (r+h) # volume = pi * r^2 * h |
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Co-ordinate Geometry |
# shortest distance b/w 2 points = straight line # slope = y/x Or (y2-y1) / (x2-x1) # positive slope = line rises upwards from left to right # negative slope = line falls from left to right # zero slope = y axis # undefined slope = x axis # x intercept where y=0 Y intercept where x=0 # line equation y=mx + b # line equation when two points given (y - y1) = m ( x-x1) m = (y2 - y1)/ (x2- x1) # distance b/w two points = root [ (y2-y1)^2 + (x2-x1)^2] # of all the quadrilaterals, with a given perimeter, square has the largest area # of all the quadrilaterals, with a given area, square has the min perimeter # area of parallelogram or triangle can be maximised by keeping 2 sides perpendicular to each other # parallel lines m1 = m2 # perpendicular lines m1 * m2 = -1 # midpoint of a line = [ (x1+x2)/2 , (y1+y2)/2 ] |
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Divisibility rules |
# div by 2: int. is even # div by 3 : if sum of int. digits div by 3 # div by 4: if int. is twice div by 2 # div by 5: if int. ends in 0 or 5 # div by 6: if int. digits are both div by 2 and 3 # div by 8: if the int. is div thrice by 2 or last 3 digits are div by 8 # div by 9: if sum of int. digits are div by 9 # div by 10: if the int. ends in 0 |
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Divisibility |
# an int. is always both a factor and multiple of itself # 1 is a factor of every int. # fewer factors more multiples # factors divide into an int. Multiples multiply out from int. # if you add or subtract multiples of N, result will be multiple of N # if you add multiple of N and no-multiple of N, the result will be non-multiple of N |
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Primes |
# prime no. is any positive int. > 1 with exactly two factors 1 and itself # first prime no. = 2 # only even prime no. = 2 # first 10 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 # total 25 primes up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 # prime factorisation: 1. To check Divisibility 2. To find GCF 3. To find LCM 4. To reduce fractions 5. To simplify square roots 6. To solve exponents # if integer then only prime |
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GCF and LCM |
# if a is factor of b, b is factor of c, then a is also factor of c # GCF : largest divisor of two or more integers # GCF will be smaller than or equal to the starting integers # LCM: smallest multiple of two or more integers # LCM, being a multiple, will be larger than or equal to the starting integers # GCF * LCM = product of numbers # GCF cannot be > than difference of numbers # consecutive multiples of N have GCF = 1 # |
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Even / Odd |
# Even + / - Even = Even Even + / - Odd = Odd Odd + / - Odd = Even Even * Even = Even ( div by 4) Even * Odd = Even Odd * Odd = Odd Even / Even = Even or Odd or Non Int Even / Odd = Even or Non Int Odd / Even = Non Int Odd / Odd = Odd or Non Int # all primes are odd except 2 # sum of 2 primes ( when not 2) = even # if sum of primes is odd then one of the prime is 2 |
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Positives and Negatives |
# absolute value of any number is always positive # if two numbers are opposite to each other then they have the same absolute value # signs same, product and division are positive #signs different, product and division are negative |
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Factors |
# total number of factors of a^x * b^y * c^z = (x+1) * (y+1)* (z+1) # total number of different factors = 3 i.e a,b,c #total number of prime factors = x*y*z # all perfect squares have odd no. of total factors and vice versa # all perfect squares contains only even power of primes # when you divide an int. by a positive int. N, possible remainders range from 0 to (N-1) Means total N possible remainders # Remainder must be smaller than divisor # you can add or subtract remainders directly to correct excess or negative remainders # you can multiply remainders, to correct excess remainders at the end # if a prime factor has power N, then it’s factors can be N+1 |
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Combinatorics |
# OR means ADD # AND means MULTIPLY # no. of ways of arranging n distinct objects, when no restrictions = n! # no. of ways of arranging n objects, when m objects are identical = n! / m! |
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