Notes Flashcards
Union symbol + word
U + or
Intersection symbol + word
∩ + and
Equation of a circle & center point.
(x - h)^2 + (y - k)^2 = r^2, center at (h,k)
Quadratic formula standard form + vertex
f(x) = a(x - h)^2 + k, vertex: (h,k)
Slant Asymptote: how to find & how to know if there is one
- Find through polynomial long division (not including remainder)
- Present when degree of numerator leading coefficient is greater than degree of denominator leading coefficient
Horizontal Asymptote: how to find & how to know if there is one
- Look at degree of leading coefficient in numerator (n) and denominator (m).
- Asymptote at y=0 if m > n
- Asymptote = leading coefficient of n divided by leading coefficient of m if m = n
n < m (slant asymptote)
Vertical Asymptote: how to find
-Present at x = ? when x causes denominator to equal 0.
Distance Formula
distance = rate * time
Vertex: how to find without standard quadratic formula
x-coord: -b/2a, y-coord: plug in x
Exponential Growth Formulas (2)
y = Initial(1 + rate)^time
y = Initial * e^(rate*time)
Exponential Decay Formulas (2)
y = Initial(1 - rate)^time
y = Initial * e^(-rate*time)
Point Slope Form
y - y1 = m(x - x1)
Direct Variation
y = kx
Indirect Variation
y = k/x
Distance Formula (between two points on a plane)
distance = √( (x2 - x1)^2 + (y2 -y1)^2 )
Rectangular Prism: Volume + SA
- Volume: lwh
- SA: 2lw + 2wh + 2lh
Cube: Volume + SA
- Volume: a^3
- SA: 6a^2
Cone: Volume + SA
- Volume: 1/3πr^2*h
- SA: πrs + πr^2 (s = slant)
Cylinder: Volume + SA
- Volume: πr^2*h
- SA: 2πr^2 + 2πrh
Sphere: Volume + SA
- Volume: 4/3πr^3
- SA: 4πr^2
Circle: Area + Circumference
- Area: πr^2
- Circumference: 2πr
Radians - > Degrees
Degrees - > Radians
- Multiply by 180/π
- Multiply by π/180
Quadratic Formula
x = ( -b ±√(b^2 - 4ac) )/2a
Rectangle: Area + Perimeter
- Area: l*w
- Perimeter: 2l + 2w
Triangle: Area + Perimeter
- Area: 1/2b*h
- Perimeter: a + b + c
6 Trig Functions
- Sinx = O/H
- Cosx = A/H
- Tanx = O/A or Sinx/Cosx
- Cscx = 1/Sinx or H/O
- Secx = 1/Cosx or H/A
- Cotx = 1/Tanx or A/O or Cosx/Sinx
Pythagorean Thereom
H^2 = A^2 + O^2
What are inverse ratios/arcratios used for?
To find angles using sides
Magic Hex + Functions
- Quotient Identities: Target identity = Next Identity/Identity After (Clockwise or Counter-clockwise) (Ex. Tanx = Sinx/Cosx)
- Product Identities: Identity Between Two Identities = The Two Multiplied + Identity Multiplied by Identity Directly Across = 1. (Ex. Tanx*Cosx = Sinx)
- Reciprocal Identities: Target identity = 1/Identity Across (Go Through 1) (Ex. Sinx = 1/Cscx)
- Pythagorean Identities: Clockwise In Upside Down Triangles Squared. Target + Next = Next (Ex. Tan^2(x)+ 1 = Sec^2(x).
- Angle Bonus: Left to Right Only: Target(x) = Next(90-x) (Ex. Sec(40) = Csc(90 - 40) = Csc(50)
Sin^2θ vs. Sinθ^2
Sin squared vs. Theta squared
Law of Sines
a/SinA = b/SinB = c/SinC
Law of Cosines
c^2 = a^2 + b^2 - 2ab*CosC
Arc: Definition + Length Formula + Theta Formula
- Arc = s, 2 points intersect on a circle make major (3 points) & minor arcs. Minor = Arc AB, Major = Arc ACB
- Length Formula: s = rθ
- Theta Formula: θ = s/r
Trig Not on Unit Circle (Where x^2 + y^2 ≠ 1): Radius Formula, 6 Functions, Terminal Side
- Radius Formula: r^2 = x^2 + y^2 OR r = √(x^2 + y^2)
- Terminal Side: ( x, y )
- 6 Functions:
- Sinx = y/r
- Cosx = x/r
- Tanx = y/x, x ≠ 0
- Cscx = r/y, y ≠ 0
- Secx = r/x, x ≠ 0
- Cotx = x/y, y ≠ 0
Loga(x) = s in Exponential Form
a^s = x
a^s = x in Logarithmic Form
Loga(x) = s
Logarithm Properties (3)
- Logarithm of a Product: Loga(MN) = Loga(M) + Loga(N)
- Logarithm of a Quotient: Loga(M/N) = Loga(M) - Loga(N)
- Logarithm of a Power: Loga(M)^p = pLoga(M)
Change of Base Formula
Loga(b) = Logc(b)/Logc(a), where C is any number (with few exceptions)
