Math Equations Flashcards
Exponential Form
a=b^x
Log Form
Log(underscore b)a=x
Addition of Logs
-log(underscore b) (mn)= log(underscore b)m + log(underscore b)n
Subtraction of Logs
-log (underscore b) (M/n) = log (underscore b)m - log(underscore b)n
Change of Base Formula
-log (underscore b)x = log (Underscore a)X / log (underscore a)b
Exponential Growth and Decay
- f(X) a times b^X
- A(t)= a( 1 + or - r)^t
Direct Variation
Y=kx
Joint Variation
Y=kxz
Inverse Variation
Y= k/x
Combined Variation
Y= k (indirect)/ (direct)
Test for Direct Variation
Y/X
Test for Inverse Variation
Y times X
If Degree of P is greater than the degree of Q…
No asymptote
If the Degree of P is less than the degree of Q..
Y=0
If degree of P is equal to degree of Q…
-Leading Coefficient (LC) of P/ LC of Q
Word problem 5.5 (How long it takes someone/ a group to do something)
1= (rate 1) times (time done together) + (rate 2) times (time of job done together) -Rate= work/time
Order of Transformations
- Horizontal First
- Reflection X Axis & Stretch/Shrink (any order)
- Translation (after 1st 2)
- Vertical Second
- Reflection (y axis) & stretch/shrink (any order)
- Translation (last)
Addition of Functions
(F+g) (X) = f(X) + g(X)
Subtraction of Functions
(F-g)(X)= f(X) -g(X)
Multiplication of Functions
(F times g) (X) = f(X) time g(X)
Division of Functions
(F/g) (X)= f(X)/g(X)
Composition
(F o G) (X)= f(g(X))
Sine
Sin(0)= opposite/hypotenuse
- y/r
- Period: 2(pie)/b
Cosine
Cos(0)= adjacent/hypotenuse
- X/r
- Period: 2(pie)/b
Tangent
Tan(0)= opposite/ adjacent
- y/r
- Period: (pie)/b
- Asymptotes: pie/2(b) +(pie)n/b
- X intercepts: period * n
Cosecant
CSC(0)= hypotenuse/opposite
- Opposite of sine
- Period: 2(Pie)/b
- Asymptotes: pie/2(b)+(pie)n/b
Secant
Sec(0)= hypotenuse/opposite
- Opposite of Cosine
- period: 2(pie)/b
- Asymptotes: pie/2(b)+(pie)n/b
Cotangent
Cot(0)=adjacent/opposite
- Opposite of tangent
- Period: pie/b
- Asymptotes: period *n
- X intercepts: pie/2(b) + (pie)n/b
45-45-90 Triangles
Short Sides: X or 1
Hypotenuse: X Times Square root of 2, or square root of 2
30-60-90
Long leg (across from 60): X time square root of 3 or square root of 3 Short leg (across from 30 degrees): X or 1 Hypotenuse: 2x or 2
Coterminal
X + 360 times n
Or
X -360 times n
R Equation
R= square root of x^2 +y^2
Radians to Degrees
180/ (pie)
Degrees to Radians
(Pie)/180
Law of Sines
SinC/c= SinB/b= SinA/a
Area Equations Triangles
A= 1/2 (b)(c)SinA A= 1/2 (a)(c) SinB A= 1/2 (b)(a) Sin C
Law of Cosines
A^2= b^2+c^2-2(b)(c)(cosA)
B^2=c^2+a^2-2(a)(c)(cosB)
C^2=a^2+b^2-2(b)(a)(cosC)
Joint Relativity Frequencies & Marginal Relative Frequencies
- JRF: Divide numbers in the body of the graph by grand total
- MRF: add joints
