Math Cheat Sheet
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Basic Multiplication Squares Cubes Powers of 2 Fractions Primes Exponents 2 3 4 5 6 7 8 9 22 = 4 23 = 8 22 = 4 1/2=.5 2, 3, 5, 7, xz*xy=xz+y 3 6 9 12 15 18 21 24 27 32 =9 33 = 27 23 = 8 1/3= .33 11, 13, 17, z y z-‐y 4 8 12 16 20 24 28 32 36 42 =16 43 = 64 24 = 16 1/4=.25 19, 23, 29, x /x =x 5 10 15 20 25 30 35 40 45 52 =25 53 = 125 25 = 32 1/5=.2 31, 37, 41, x-‐z=1/xz 6 12 24 24 30 36 42 48 54 62 =36 63 = 216 26 = 64 1/6=.166 43, 47, 53, (xz)y=xz*y 7 14 21 28 35 42 49 56 63 72 = 49 73 = 343 27 = 128 1/7=.142 59, 61, 67, z/y y z 8 16 24 32 40 48 56 64 72 82 = 64 83 = 512 28 = 256 1/8=.125 71, 73, 79, x = √x 9 18 27 36 45 54 63 72 81 92 = 81 93 = 729 29 = 512 1/9=.111 83, 89, 97 Slope intercept equation Standard Deviation Liner growth: Quadratic F ormula y=mx+b small SD means numbers are clustered y=ax+c ! large SD numbers spread out Exponential growth: 𝑥 = (𝑏 ± 𝑏 − 4𝑎𝑐) m=rise/run t ÷ 2𝑎 b=y intercept y(t)=y0 (k ) Properties of triangles sum of angles=180 Properties of evenly spaced sets Areas sum of any2 sides>the third side -‐mean=median=average of first Triangle-‐ base*height/2 common right triangles: 3-‐4-‐5, and last terms Rectangle-‐length*width 5-‐12-‐13, 8-‐15-‐17 -‐sum=mean*count Trapezoid-‐(base1+base2)h/2 isosceles right triangles -‐for a set of an odd # of Parallelogram-‐base*h sides: x-‐x-‐x√2 consecutive integers the sum is Rhombus-‐(diagonal1*diag2)/2 angles:45-‐45-‐90 a multiple of the number 30-‐60-‐90 triangles Quadrants sides: x-‐x√3-‐2x Diagonals Circles and Arcs 2 Equilateral triangles: square-‐d=side√2 area of a circle: πr II I Area=(side2√3)/4 cube-‐d= side√3 arc length: (angle/360)2πr Similar triangles (angles equal) arc area: (angle/360) πr2 III IV -‐corresponding sides ratio a:b inscribed angles=1/2 central Angles -‐areas ratio a2:b2 angle of the same arc Cylinders Combinatorics b b=d a=c # of ways of arranging groups of n terms SA=2πr2 + 2πrh a c 2 -‐no restrictions no repeats = n! d V= πr h -‐no restrictions 1 repeat =n!/r! Distance and rate r=the number of repeats Parallel lines -‐rate*time=distance -‐no restrictions multiple repeats=n!/(r1!r2!) a b -‐average speed= total distance/total # of ways a group of x people can be arranged from b a time y people: y!/(x!(y-‐x)!) a b -‐2 people moving towards or away # of ways x people can be arranged around a b a from each other at speeds of x and y, circular table= (x-‐1)! respectively are decreasing or Remainders increasing the distance between them What is left over at a speed of x+y Probability after a number Quadratics Work and rate Interest # s uccessful is divided by 2 2 2 (a+b) =a +2ab+b rate*time=work P=principal, r=rate, (a-‐b) 2=a2-‐2ab+b2 outcomes/#possible another. -‐a and b working t=number of years outcomes Remainder is (a+b) 2+(a-‐b) 2= together, the total rate Simple: P(1+rt) OR-‐add probabilities always less than 2a2+2b2 is brate+arate Compound: P(1+r)t the divisor (a+b) 2-‐(a-‐b) 2=4ab AND-‐multiply -‐if a is undoing the x=# of times (a-‐b) 2-‐(a+b) 2=-‐4ab P(A)=1-‐P(notA) work of b, the total compounded per year rate is brate-‐arate P(1+r/x)xt
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