Math 3 EOC Formulas Review
Area of a Sector
(degree / 360) · pi · r^2
Standard Form of a Circle
(x - h)^2 + (y - k)^2 = r^2 - where r is the radius & (h, k) is the center
5 # Summary in Calculator
* Go to STAT * Edit * Clear list of L1 if needed * Enter data in List 1 * Go back to STAT * Calculate 1-Var Stats * Use Sx for the sample standard deviation
Centroid
- A median is created by a vertex connected to the midpoint of the opposite side. - Center of Mass: Balance Point ~ AM (longer portion) = 2/3 AY (shorter portion) ~ AM (longer) = 2 MY (shorter) ~ MY (shorter) = 1/2 AM (longer) ~ MY (shorter) = 1/3 AY (longer)
Point of Discontinuity
- Holes - Vertical Asymptotes - (den = 0)
Remainder Theorem
- If P(x) is divided by (x - r), then the remainder is equal to P(r). Ex: (4x^2 + 6x -7) / (x - 5) 5// 4 6 -7 20 130 ______________________ 4 26 123 4(5)^2 + 6(5) - 7 100 + 30 - 7 123 *REMAINDER OF 123
Circumcenters
- The circumcenter is equidistant from each vertex of the triangle AM = BM = CM
Incenter
- The incenter is equidistant from each side of the triangle XM = YM = ZM
Margin of Error for a Sample Proportion
2 square root p hat (1-p hat) over n - n = # of sample items
Centroid Segment Relationship
2x = y
Area of a Triangle
A = 1/2bh
Area of a Cone
A = pi * r^2
Area of Trapezoids
A=1/2h(b1+b2)
Tolerance Formula
Absolute Value of x - desired is less than or equal to tolerance
Orthocenter
An altitude is created by a vertex connected to the opposite side so that it is perpendicular to that side.
Expo Form
Base^power/exponent = answer
Degree to Radian
Degree * pi/180 degrees
Dividing Fractions (Functions)
Keep Change Flip a/b/c/d = a/b * d/c = ad/bc
Margin of Error
ME = 2 (s/square root n) - ME = Margin of Error - n = # of terms (sample size) - s = standard deviation - sx = sample standard deviation
Segments Outside Circle
Outside * Whole = Outside * Whole
Fundamental Theorem of Algebra
The degree shows the # of solutions
Incenter
The incenter is equidistant from each side of the triangle.
Volume of a Cone
V(cone) = 1/3 Bh *B = area of the circular base *h = height of the cone
Volume of a Prism
V(prism) = Bh *B = Area of the base *h = height of the prism
Volume of Cylinder
Volume(cylinder) = Bh *B = Area of the cylinder base *h = height of the cylinder
Sphere Volume
Volume(sphere) = 4/3 * pi * r^3
Segments Inside Circle
a * b = c * d (multiply measures on the same line)
Arc Length
a/360 * (2πr)
Pythagorean Theorem
a^2 + b^2 = c^2 OR c^2 - a^2 = b^2
Difference of Squares
a^2 -b^2 = (a+b)(a-b)
Central Angle
an angle with its vertex at the center of a circle
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²] (x1, y1), (x2, y2)
P hat
desired #/total # OR small #/large #
Confidence Interval
line measure x + or - ME - line measure x = sample mean
Log Form
logb(answer) = exponent
Angle Outside Circle
m angle k = 1/2 (large arc - small arc)
Inscribed Angle
measure of angle x = 1/2 measure of arc length n
Angle Inside Circle
measure of angle x = measure of arc length n
Radian to Degrees
radian * 180/pi
Secant Tangent
whole * outside = tangent^2
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
45 - 45 - 90 Triangle
x, x, x√2 the measure of the hypotenuse is (√2) times the measure of a leg
30 - 60 - 90 Triangle
x, x√3, 2x a right triangle that consists of a right angle, a 30 degree angle, and a 60 degree angle
Cos
x-coordinate
Negative Exponents
x^-3/y^-2 = y^2/x^3 (Flip exponents and bases to get positive exponents)
Interests
y = P(1 + r)^t P = Principle Original R = Rate T = Time in Years
Vertex Form
y = a(xx - h)^2 + k - vertex = (h, k)
Sin
y-coordinate
