Studied by 41 peoplequadratic 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, ...
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
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 degrees / 360 degrees) · 2 · pi · r
area of sector
(n degree / 360 degrees) · pi · r^2 (fraction of circle’s area)
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
trapezoid area
area = [(base1 + base2) / 2] · h
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
Percent Change
old(1 +/- %) = new
<
less than
fewer than
greater than
exceeds
more than
≤
at most
less than or equal to
no more than
≥
greater than or equal to
no less than
at least
Exponential growth
y = a(1 +/- r)^t
a = initial value
r = growth rate
t = time
Vertex Form
y = a(x-h)^2 + k
(h,k) = A vertex
Distance =
rt
Sine and Cosine
sin(x) = cos(90-x)
Sum of solutions
-b/a
The discriminant
b^2 - 4ac
-3 < 0 = NO SOL
0 = 0 = 1 REAL SOL
7 > 0 = 2 REAL SOL
Area of equilateral triangle
s^2√3/4
Sum of angles in polygon
(n-2)180
Circle Equation
(x-h)^2 + (y-k)^2 = r^2
Weighted average
sum of terms/number of terms
Part
Percent x whole
Odd num + even num =
Odd num
Percent Increase
100 + (asked percent increase)/100 x whole number
Interior Angles
180 (n - 2)
30-60-90 Triangle
Short Leg: x
Second Leg: x√3
Hypotenuse: 2x
45-45-90 Triangle
Short Leg: x
Second Leg: x
Hypotenuse: x√5
3-4-5 Triangle
Short Leg: 3x
Second Leg: 4x
Hypotenuse: 5x
Note
Flashcard