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258 Cards in this Set
- Front
- Back
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Positive X Negative = ?
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Negative
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Negative X Negative = ?
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Positive
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Positive / Negative =
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Negative
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Negative / Negative =
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Positive
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Odd + Odd =
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Even
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Even + Even =
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Even
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Odd - Odd =
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Even
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Even - Even =
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Even
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Odd + Even =
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Odd
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Odd - Even =
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Odd
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Even x Odd =
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Even
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Even x Even =
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Even
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Odd x odd x odd x ... =
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Odd
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Odd / Even =
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Not an Integer
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Even / Odd =
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Even (or a fraction)
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Odd / Odd =
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Odd (or a fraction)
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Final Value [given X percent change) =
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(1 + X%/100)Initial Value
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% change [given Final and Initial values] =
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(F-I)/I x 100
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Simple Interest: R =
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R = P X (1 + rt)
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Compound Interest: R =
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R = P X (1+ r/n)^nt
(^nt indicates nt is an exponent) |
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X^a * X^b =
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X^(a+b)
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x^a / x^b =
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x^(a-b)
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x^a * y^a =
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(xy)^a
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(x/y)^a =
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x^a / y^a
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(x^a)^b
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x^(ab)
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0! = ?
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1
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1! = ?
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1
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2! = ?
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2
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3! =
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6
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4! =
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24
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5! =
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120
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6! =
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720
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7! =
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5040
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x^-a
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1 / x^a
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x^0 =
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1, unless x = 0
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nPk =
Permutations (order matters) with n options for k slots |
n! / (n-k)!
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nCk =
Combinations (order does not matter) with n options for k slots |
n! / (n-k)!k!
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nPk =
Permutations (order matters) with identical objects k sub i n is the total number of objects and ki is the number of objects of the ith kind |
n! / k1!k2!...kn!
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Arrangements in a circle of non-identical things =
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(n-1)!
With two different types of things (men & women) it is (m-1)!w! (only one "anchor" needed) |
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Probability is?
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number of ways the particular something can happen divided by the number of ways that anything can happen
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x^(a/b) =
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b√(x^a)
[b root of x to the a power] |
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n√x =
[nth root of x] |
x^(1/n)
[x to the 1/n power] |
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Quadratic Formula ?
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x = (-b+/-√(b^2-4ac))/2a
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Area of a triangle?
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A = 1/2 bh
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Sum of the angles of a triangle?
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180 deg
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The sum of the lengths of any two sides of a triangle is _____ than the length of the third?
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longer
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45-45-90 triangle has what relationship between its sides?
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1-1-√2
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30-60-90 triangle has what relationship among its sides?
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1-√3-2
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Right triangle: 3-4-___
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5
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Right triangle: ___ -8-10
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6
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Right triangle: 5-___-13
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12
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Right triangle: 10-24-____
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26
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Right triangle: ___-24-25
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7
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Right triangle: 8-__-17
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15
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Equation of a line:
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y=mx+b
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slope of a line equals?
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m=(y2-y1)/(x2-x1)
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x-intercept of a line =
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-b/m
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Area of a rhombus (all sides equal, opposite angles equal, perpendicular diagonals)?
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A=1/2(d x d)
d = diagonal |
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Area of a trapezoid (one pair of sides parallel [sides a and c])
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A=1/2(a+c)h
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Area of a parallelogram (opposite sides equal and parallel, opposite angles equal)?
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A=bh
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Measure of all angles of a regular polygon?
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(n-2)180
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Measure of any interior angle of a regular polygon?
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(n-2)/n ∗ 180
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pi ≈ ? (fraction)
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22/7
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Area of a circle?
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A=πr^2
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Relationship between central angle and arc?
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L/(2πr) = α /360 deg
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Area of a sector of a circle?
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A = (α/360) πr^2
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Inscribed angle = ?
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1/2 central angle
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Definition of Central Angle?
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An angle in a circle which uses the center of the circle as its vertex.
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Definition of Inscribed Angle?
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An angle formed by two chords within a circle. Its vertex is on the circle. The measure of an inscribed angle equals 1/2 the measure of its arc.
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Diagonal of a cube =
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√3 * length
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Diagonal of a rectangular solid?
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D = √(l^2 + w^2 + h^2)
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Volume of a cylinder?
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V = π(r^2)h
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Surface area of a cylinder?
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A = 2πrh +nπr^2, n= 0,1, or 2
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Volume of a sphere?
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V = 4/3 πr^3
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Surface area of a sphere?
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A = 4πr^2
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Exponential growth formula?
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F = Ia^n
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Compound interest formula?
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Earnings = Investment x (1+rate)^t
t= no. of periods |
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Average?
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Add 'em all up and divide by the number of things added.
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Standard Deviation formula?
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σ = square root of the sum of the differences between each number and the mean, squared, divided by the number of numbers.
√((∑(xi-mean)^2)/n) |
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Permutation formula (order matters)?
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nPk = n!/(n-k)!
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Combination formula?
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nCk = n! / (n-k)!k!
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Possible circular arrangements of n items?
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(n-1)!
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P(A ∩B) =
Intersection of independent events (and) |
P(A) * P(B)
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P(A∩B) =
Intersection of dependent events (and) |
P(A)*Pa(B) or P(B)*Pb(A)
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P(A∪B) =
Union of two overlapping events (or) |
P(A) + P(B) - P(A∩B)
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P(A∪B∪C) =
Union of three overlapping events (or) |
P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C)
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12 x 6
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72
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12 x 7
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84
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12 x 8
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96
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12 x 9
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108
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12 x 12
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144
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12 x 11
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132
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13 x 4
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52
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13 x 5
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65
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13 x 6
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78
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13 x 7
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91
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13 x 8
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104
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13 x 9
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117
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13 x 11
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143
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13 x 12
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156
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13 x 13
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169
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14 x 3
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42
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14 x 4
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56
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14 x 5
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70
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14 x 6
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84
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14 x 7
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98
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14 x 8
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112
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14 x 9
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126
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14 x 11
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154
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14 x 12
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168
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14 x 13
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182
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14 x 14
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196
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15 x 5
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75
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15 x 6
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90
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15 x 7
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105
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15 x 8
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120
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15 x 9
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135
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15 x 11
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165
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15 x 12
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180
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15 x 13
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195
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15 x 14
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210
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15 x 15
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225
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1/6 =
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0.166...
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5/6 =
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0.833...
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1/8 =
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0.125
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3/8 =
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0.375
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5/8 =
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0.625
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7/8 =
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0.875
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1/9 =
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0.111...
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2/9 =
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0.222...
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17/20 =
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0.85
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1^2 =
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1
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1.4^2 ≈
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2
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1.7^2 ≈
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3
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2^2 =
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4
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3^2 =
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9
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4^2 =
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16
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5^2 =
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25
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6^2=
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36
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7^2 =
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49
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8^2 =
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64
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9^2=
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81
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11^2 =
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121
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12^2=
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144
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13^2 =
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169
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14^2=
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196
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15^2=
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225
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16^2=
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256
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17^2=
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289
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18^2=
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324
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19^2 =
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361
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21^2=
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441
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22^2=
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484
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23^2=
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529
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24^2=
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576
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25^2=
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625
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√1 =
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1
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√2 ≈
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1.4
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√3 ≈
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1.7
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√4 =
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2
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√9 =
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3
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√16 =
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4
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√25 =
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5
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√36
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6
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√49
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7
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√64 =
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8
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√81
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9
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√121
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11
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√144
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12
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√169
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13
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√196
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14
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√225
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15
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√256
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16
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√289
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17
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√324
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18
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√361
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19
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√441
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21
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√400
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20
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√441
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21
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√484
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22
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√529
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23
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√576
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24
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√625
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25
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2^(-3)
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1/8
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2^(-2)
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1/4
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2^(-1)
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1/2
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2^0
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1
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2^2
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4
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2^3
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8
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2^4
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16
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2^5
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32
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2^6
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64
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2^7
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128
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2^8
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256
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2^9
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512
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2^10
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1024
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3^(-3)
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1/27
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3^(-2)
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1/9
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3^(-1)
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1/3
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3^0
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1
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3^1
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3
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3^2
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9
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3^3
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27
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3^4
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81
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3^5
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243
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3^6
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729
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3^7
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2187
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3^8
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6561
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3^9
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19,683
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3^10
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59,049
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1^3
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1
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2^3
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8
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3^3
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27
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4^3
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64
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5^3
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125
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3√1
(cubed root of 1) |
1
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3√8
(cubed root of 8) |
2
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3√27
(cubed root of 27) |
3
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3√64
(cubed root of 64) |
4
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3√125
(cubed root of 125 |
5
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0!
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1
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1!
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1
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2!
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2
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3!
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6
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4!
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24
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5!
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120
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6!
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720
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7!
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5,040
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Shortcut for the sum of consecutive integers?
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1. Average the first and last term to find the middle point or term
2. Derive the total # of terms 3. The sum = middle point * # of terms |
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Positive x Negative =
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Negative
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Negative x Negative =
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Positive
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Positive ÷ Negative =
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Negative
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Negative ÷ Negative =
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Positive
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Odd + Odd =
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Even
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Even + Even =
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Even
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Odd - Odd =
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Even
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Even - Even =
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Even
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Odd + Even =
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Odd
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Odd - Even =
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Odd
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Even x Odd =
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Even
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Even x Even =
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Even
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Product of an even integer with any other integer is ?
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Even
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Product of ALL odd integers is?
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Odd
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Odd ÷ Even ≠
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Integer
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Even ÷ Odd =
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Even (or Fraction)
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Odd ÷ Odd =
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Odd (or Fraction)
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Divisibility test for 2:
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last digit divisible by 2
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Divisibility test for 3:
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sum of digits
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Divisibility test for 4:
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last two digits
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Divisibility test for 5:
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Last digit 0 or 5
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Divisibility test for 6:
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test for 2 AND 3
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Divisibility test for 8:
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last three digits
(remember powers of 2 -> 64, 128, 256, 512, 1024, etc.) |
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Divisibility test for 9:
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sum of digits
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Divisibility test for 12:
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test for 3 AND 4
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Divisibility test for 14:
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Test for 2 and 7
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Divisibility test for 15:
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Test for 3 and 5
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Do Not Multiply Out Intermediate Calculations
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Simplify later
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X^2-Y^2 =
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(X+Y)(X-Y)
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