Notes

Question 1

Union symbol + word

Answer 1

U + or

Question 2

Intersection symbol + word

Answer 2

∩ + and

Question 3

Equation of a circle & center point.

Answer 3

(x - h)^2 + (y - k)^2 = r^2, center at (h,k)

Question 4

Quadratic formula standard form + vertex

Answer 4

f(x) = a(x - h)^2 + k, vertex: (h,k)

Question 5

Slant Asymptote: how to find & how to know if there is one

Answer 5

• Find through polynomial long division (not including remainder)
• Present when degree of numerator leading coefficient is greater than degree of denominator leading coefficient

Question 6

Horizontal Asymptote: how to find & how to know if there is one

Answer 6

• 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)

Question 7

Vertical Asymptote: how to find

Answer 7

-Present at x = ? when x causes denominator to equal 0.

Question 8

Distance Formula

Answer 8

distance = rate * time

Question 9

Vertex: how to find without standard quadratic formula

Answer 9

x-coord: -b/2a, y-coord: plug in x

Question 10

Exponential Growth Formulas (2)

Answer 10

y = Initial(1 + rate)^time

y = Initial * e^(rate*time)

Question 11

Exponential Decay Formulas (2)

Answer 11

y = Initial(1 - rate)^time

y = Initial * e^(-rate*time)

Question 12

Point Slope Form

Answer 12

y - y1 = m(x - x1)

Question 13

Direct Variation

Answer 13

y = kx

Question 14

Indirect Variation

Answer 14

y = k/x

Question 15

Distance Formula (between two points on a plane)

Answer 15

distance = √( (x2 - x1)^2 + (y2 -y1)^2 )

Question 16

Rectangular Prism: Volume + SA

Answer 16

• Volume: lwh

- SA: 2lw + 2wh + 2lh

Question 17

Cube: Volume + SA

Answer 17

• Volume: a^3

- SA: 6a^2

Question 18

Cone: Volume + SA

Answer 18

• Volume: 1/3πr^2*h

- SA: πrs + πr^2 (s = slant)

Question 19

Cylinder: Volume + SA

Answer 19

• Volume: πr^2*h

- SA: 2πr^2 + 2πrh

Question 20

Sphere: Volume + SA

Answer 20

• Volume: 4/3πr^3

- SA: 4πr^2

Question 21

Circle: Area + Circumference

Answer 21

• Area: πr^2

- Circumference: 2πr

Question 22

Radians - > Degrees

Degrees - > Radians

Answer 22

• Multiply by 180/π

- Multiply by π/180

Question 23

Quadratic Formula

Answer 23

x = ( -b ±√(b^2 - 4ac) )/2a

Question 24

Rectangle: Area + Perimeter

Answer 24

• Area: l*w

- Perimeter: 2l + 2w

Question 25

Triangle: Area + Perimeter

Answer 25

- Area: 1/2b*h | - Perimeter: a + b + c

Question 26

6 Trig Functions

Answer 26

- 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

Question 27

Pythagorean Thereom

Answer 27

H^2 = A^2 + O^2

Question 28

What are inverse ratios/arcratios used for?

Answer 28

To find angles using sides

Question 29

Magic Hex + Functions

Answer 29

- 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)

Question 30

Sin^2θ vs. Sinθ^2

Answer 30

Sin squared vs. Theta squared

Question 31

Law of Sines

Answer 31

a/SinA = b/SinB = c/SinC

Question 32

Law of Cosines

Answer 32

c^2 = a^2 + b^2 - 2ab*CosC

Question 33

Arc: Definition + Length Formula + Theta Formula

Answer 33

- 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

Question 34

Trig Not on Unit Circle (Where x^2 + y^2 ≠ 1): Radius Formula, 6 Functions, Terminal Side

Answer 34

- 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

Question 35

Loga(x) = s in Exponential Form

Answer 35

a^s = x

Question 36

a^s = x in Logarithmic Form

Answer 36

Loga(x) = s

Question 37

Logarithm Properties (3)

Answer 37

- 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)

Question 38

Change of Base Formula

Answer 38

Loga(b) = Logc(b)/Logc(a), where C is any number (with few exceptions)