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Area of a triangle
1/2 (base)(height)
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Special Right Traingles
- 3-4-5 (or any multiple of); right triangle; given any 2-find 3rd side length
- 30-60-90; side ratio of X:Xsqrt(3):2X
- 5-12-13 (or any multiple of); right triangle;given any 2-find 3rd side length
- 45-45-90; side ratio of X:X:Xsqrt(2)
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Circumference of a circle
2(pi)r
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Arclength
If n is a degree measure-
- S= 1(n/360)(2pi(r))
- S=(ratio of degree part:whole)(circumference)
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Area of a circular sector
If n is the degree measue of the sector's central angle-
- A= 1(n/360)(pi(r^2))
- A=(ratio of degree of sector:degree of circle)(area of circle)
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Interior Angles of a polygon
The sum of the interior angles of a polygon= (n-2)(180), where n is the number of sides
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Surface area of a rectangular solid
2lw+2wh+2lh
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Volume of a rectangular solid
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Volume of a cylinder
(pi)(r^2)(h)
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Percent formula
Part= (perecnt)(whole)
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Probability
Favorable/Possible
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Solving an inequality
When multiplying or dividing both sides by a negative number you must reverse the sign
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Midpoint between
(x1, y1), (x2, y2)
= [(x1+x2)/2], [(y1+y2)/2]
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Divisible by 2
If last digit is divisible by 2
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Divisible by 3
If the SUM of its digits is divisible by 3
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Divisible by 4
If last two digits are divisble by 4
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Divisible by 5
Ends in 0 or 5
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Divisible by 6
If it is divisible by both 2 (last two digists divisible by 2) and 3 (SUM of its digits is divisble by 3)
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Divisible by 9
If the SUM of its digits is divisible by 9
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First 25 primes (<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
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complimentary lines
make up a right angle
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supplementary lines
make up a straight line
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Ratio of areas of two similar triangles
square of the ratio of corresponding lengths
(if triangle b is twice the size of triangle a, (2/1)^2=4; 4 times the area of triangle a)
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Special right traingle side length ratios
1:1:(sqrt)2 -isosceles right triangles
1:(sqrt)3:2 -30-60-90 triangle
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pythagorean triplets
3,4,5 (and any multiple of these e.g., 6,8,10)
5,12,13 (and any multiple of these)
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Surface area of a cylinder
- A=(circumfrence of circular base)(height)+(2area of circular bases)
- A=[(2pi(r)h)] + [2(pi)r^2)]
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The diagonal through a box
d^2=(l^2)+(w^2)+(h^2)
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Area of a trapeziod
1/2(b1+b2)(h)
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Counting Principle
-two tsks; N ways to do/choices for the first and M was to do/choices for the second
- (NM)
- Use anytime a question asks, "how many" (ways to do..., numbers between..., arrangments of...)
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Probability an experiment will replicate
- (probability of first event)(probability of second)(...)...
- [ex; coin landing heads 3x in a row; (1/2)(1/2)(1/2)=1/8]
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Probability of E and F occurring
- Independent: p(E and F) = p(E) x p(F)
- Dependent: p(E and F) = p(E) x p(FlE)
- Conditional: p(FlE) = p(E and F)/p(E)
- 0 if mutually exclusive
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Probability of E or F occurring
- p(E)+p(F) - p(E and F)
- If mutually exclusive: p(E)+p(F)
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Common factorials
- 0!=1
- 1!=1
- 2!=2
- 3!=6
- 4!=24
- 5!=120
- 6!=5040
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Permutation (without replacement) (nPr)
(ways to select officers)
- The number of ways of obtaining an ordered subset of elements from a set of elements is given by
- nPr=n!/(n-r)!
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Permutation (with replacement) (nPr)
"permutation lock"
n^r
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Combination (without order) (nCr)
- Number of combinations of n distict objects taken r at a time
- n!/[r!(n-r)!] = nPr/r!
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