## ACT math

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Artbon Plus on September 23, 2010

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# ACT math

 quadratic formula[-b ± √(b² - 4ac)] / (2a)
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#### Definitions

quadratic formula [-b ± √(b² - 4ac)] / (2a)
slope formula (y₂- y₁) / (x₂- x₁)
integers ..., -3, -2, -1, 0, 1, 2, 3, ...
rationals fractions (anything expessable as a ratio of integers)
reals integers, rationals, plus special #s (like √2 or pi)
order of opperations PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
Arithmetic Sequences t₁, t₁+ d, t₁+2d, ...
Geometric Sequences t₁, t₁· r, t₁· r², ...
Factors ex. factors of 52 are 2, 4, 13, and 26
Multiples ex. multiples of 20 are 40, 60, 80, 100, ...
percentages part = (percent / 100) x whole
average average = sum of terms / number of terms
average speed average speed = total distance / total time
sum sum = average x (number of terms)
mode mode = value in the list that appears most often
median median = middle value in the list
fundamental counting principle if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.
probability probability = number of desired outcomes / number of total outcomes
adding exponents x^a · x^b = x^(a+b)
subtracting exponents x^a / x^b = x^(a-b)
negative exponents 1 / x^b = x^(-b)
multiplying exponents (x^a)^b = x^(a·b)
x^0 1
roots √(xy) = √x · √y
FOIL (x+a)(x+b) = x^2 + (b+a)x + ab
difference of squares a^2 -b^2 = (a+b)(a-b)
a^2 + 2ab + b^2 (a+b)^2
a^2 - 2ab + b^2(a-b)(a-b)
distance formula √[(x₂- x₁)^2 + (y₂- y₁)^2)]
mid-point formula [(x₁+ x₂)/2 , (y₁+ y₂)/2]
intersecting lines opposite angles are equal (each pair of angles along the same line add to 180 degrees)
area of triangle area = (1/2)bh
angles of triangle add up to 180 degrees
length of triangle sides length of 1 side is always less than the sum of the other 2
equilateral three equal sides, all angles = 60 degrees
isosceles 2 equal sides, 2 equal angles
similar same shape, corresponding angles are equal, corresponding sides are in proportion
circle area pi · r^2
circle circumference 2 · pi · r
full circle = 360 degrees
length of arc (n degree / 360 degrees) · 2 · pi · r
area of sector (n degree / 360 degrees) · pi · r^2
rectangle area area = lw
parallelogram area area = lh
rectangular solid volume volume = lwh
right cylinder volume volume = pi · r^2 · h
prime factors 2, 3, 5, 7, 11, ...
Greatest Common Factor ex. GCF of 200 and 60 is 20
Least Common Multiple ex. LCM of 200 and 60 is 600
equation of circle with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2
logarithms y = log(little b)x asks b^y = x
complex numbers i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i
sin of an angle opp / hyp
cos of an angle adj / hyp
tan of an angle opp / adj
special sin cos relationship sin^2(angle) + cos^2(angle) = 1
degree to radian degree# · (pi / 180 degrees)
trapezoid area area = [(base1 + base2) / 2] · h
Direct Variation y=kx
Inverse Variation y=k/x
Slope intercept form y=mx+b
Point-Slope form y - y₁= m(x - x₁)
standard form Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
Dividing by a negative number in an inequality You must flip the sign
Graphing < or > on a coordinate plane dotted line
Graphing ≥ or ≤ on a coordinate plane solid line
Graphing ≥ or > on a coordinate plane shade upwards or to the right
Graphing ≤ or < on a coordinate plane shade downwards or to the left
circle perimeter 2 pi r
Chord The distance from one point on the circle to another point on the circle.
Sector The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
arc Part of a circle connecting two points on the circle.
Central Angle An angle whose vertex is the center of the circle

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