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42 Cards in this Set
- Front
- Back
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Natural numbers
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counting numbers (1, 2, 3, 4, etc)
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whole numbers
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natural numbers plus zero
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integers
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whole numbers plus negatives (-1, -2, -3, etc)
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rational numbers
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any number that can be expressed as a fraction a/b (where a and b are both integers)
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Irrational numbers
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numbers that aren't rational and which are non-repeating, nonterminating decimals
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real numbers
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all the rational and irrational numbers
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complex numbers
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a + bi where a and b are real numbers and i = √-1
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associative property of addition and multiplication
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grouping of numbers does not affect the result
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commutative property of addition and multiplication
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can alter the order of the numbers involved without affecting the result
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identity properties of addition and multiplication
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a + 0=a
a x 1=a |
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inverse properties
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a + (-a) = 0
b x 1/b = 1 |
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symmetric property
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if x=y, then y=x
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transitive property
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if a=b and b=c, then a=c
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distributive property
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a(b + c) = ab + ac
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substitution property
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if two expressions are equal, one expression can be replaced with the other
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exponential rules--
x^ax^b = |
x^ax^b = x^a+b
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(x^a)/(x^b) =
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(x^a)/(x^b) = x^a--b
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(x^a)^b =
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(x^a)^b = x^a*b
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(xy)^a =
(x/y)^a = |
(xy)^a = x^ay^a
(x/y)^a = (x^a)/(y^a) |
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x^1 =
x^0 = |
x^1 = x
x^0 = 1 |
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x^-a =
1/x^-a = |
x^-a = 1/x^a
1/x^-a = x^a |
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point-slope formula
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y -- y₁ = m(x -- x₁)
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standard form
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Ax + By = C where A, B are both integers
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slope-intercept form
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y = mx + b where m=slope and b= y-intercept
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difference of perfect squares
a^2 -- b^2 = |
a^2 -- b^2 = (a+b)(a--b)
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sum of perfect cubes
a^3 + b^3 = |
a^3 + b^3 = (a+b)(a^2 --ab+b^2)
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difference of perfect cubes
a^3 -- b^3 = |
a^3 -- b^3 = (a--b)(a^2 +ab + b^2)
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fundamental theorem of algebra
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a polynomial function with degree n will always have exactly n roots. the roots may repeat and they may be irrational or complex
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Descartes' rule of signs
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1. put the function in standard form from the highest exponent to the lowest.
2. count the sign changes 3. take the number of sign changes and subtract multiples of 2 until you get a negative number. if a function has 7 sign changes, it must have 7, 5, 3, or 1 positive root(s). 4. go back to the original function and substitute -x for x. count the sign changes again and subtract multiples of 2 to calculate the number of possible negative roots. |
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rational root test
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1. identify the leading coefficient and constant in the function, a and c
2. list all the factors of a and c separately 3. write every possible combination of c's factors divided by a's factors 4. include the opposite of every item in the list to produce a final list of possible roots. |
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logₐx = y translates to
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logₐx = y translates to a^y = x
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change of base formula
logₐx = |
logₐx = (log x)/(log a)
OR logₐx = (ln x)/(ln a) |
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log a + log b =
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log a + log b = log ab
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log a -- log b =
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log a -- log b = log a/b
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log a^b =
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log a^b = b log a
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radians to degrees
degrees to radians |
180/π
π/180 |
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coterminal angles
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any two angles that have the same terminal side when drawn in standard position
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calculating a reference angle (β) for an angle ϴ
quadrant I quadrant II quadrant III quadrant IV |
quadrant I --no reference angle needed
quadrant II -- β= π -- ϴ quadrant III -- β= ϴ -- π quadrant IV -- β= 2π -- ϴ |
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Law of Cosines
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a^2 = b^2 + c^2 -- 2bc cosA
b^2 = a^2 + c^2 -- 2ac cos B c^2 = a^2 + b^2 -- 2ab cos C use for SSS or SAS triangles |
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Law of Sines
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sinA/a = sinB/b = sinC/c
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area of SAS triangles
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if a triangle has sides a and b that form an angle C, the area of that triangle is:
1/2ab * sinC |
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area of SSS triangles
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a triangle with sides a, b, c has an area of:
√[s(s--a)(s--b)(s--c)] if s = (a+b+c)/2 |
