Math Equations

Question 1

Exponential Form

Answer 1

a=b^x

Question 2

Log Form

Answer 2

Log(underscore b)a=x

Question 3

Addition of Logs

Answer 3

-log(underscore b) (mn)= log(underscore b)m + log(underscore b)n

Question 4

Subtraction of Logs

Answer 4

-log (underscore b) (M/n) = log (underscore b)m - log(underscore b)n

Question 5

Change of Base Formula

Answer 5

-log (underscore b)x = log (Underscore a)X / log (underscore a)b

Question 6

Exponential Growth and Decay

Answer 6

• f(X) a times b^X

- A(t)= a( 1 + or - r)^t

Question 7

Direct Variation

Answer 7

Y=kx

Question 8

Joint Variation

Answer 8

Y=kxz

Question 9

Inverse Variation

Answer 9

Y= k/x

Question 10

Combined Variation

Answer 10

Y= k (indirect)/ (direct)

Question 11

Test for Direct Variation

Answer 11

Y/X

Question 12

Test for Inverse Variation

Answer 12

Y times X

Question 13

If Degree of P is greater than the degree of Q…

Answer 13

No asymptote

Question 14

If the Degree of P is less than the degree of Q..

Answer 14

Y=0

Question 15

If degree of P is equal to degree of Q…

Answer 15

-Leading Coefficient (LC) of P/ LC of Q

Question 16

Word problem 5.5 (How long it takes someone/ a group to do something)

Answer 16

1= (rate 1) times (time done together) + (rate 2) times (time of job done together)
-Rate= work/time

Question 17

Order of Transformations

Answer 17

• Horizontal First
  
  • Reflection X Axis & Stretch/Shrink (any order)
  • Translation (after 1st 2)
• Vertical Second
  
  • Reflection (y axis) & stretch/shrink (any order)
  • Translation (last)

Question 18

Addition of Functions

Answer 18

(F+g) (X) = f(X) + g(X)

Question 19

Subtraction of Functions

Answer 19

(F-g)(X)= f(X) -g(X)

Question 20

Multiplication of Functions

Answer 20

(F times g) (X) = f(X) time g(X)

Question 21

Division of Functions

Answer 21

(F/g) (X)= f(X)/g(X)

Question 22

Composition

Answer 22

(F o G) (X)= f(g(X))

Question 23

Sine

Answer 23

Sin(0)= opposite/hypotenuse

• y/r
• Period: 2(pie)/b

Question 24

Cosine

Answer 24

Cos(0)= adjacent/hypotenuse

• X/r
• Period: 2(pie)/b

Question 25

Tangent

Answer 25

Tan(0)= opposite/ adjacent

• y/r
• Period: (pie)/b
• Asymptotes: pie/2(b) +(pie)n/b
• X intercepts: period * n

Question 26

Cosecant

Answer 26

CSC(0)= hypotenuse/opposite

• Opposite of sine
• Period: 2(Pie)/b
• Asymptotes: pie/2(b)+(pie)n/b

Question 27

Secant

Answer 27

Sec(0)= hypotenuse/opposite

• Opposite of Cosine
• period: 2(pie)/b
• Asymptotes: pie/2(b)+(pie)n/b

Question 28

Cotangent

Answer 28

Cot(0)=adjacent/opposite

• Opposite of tangent
• Period: pie/b
• Asymptotes: period *n
• X intercepts: pie/2(b) + (pie)n/b

Question 29

45-45-90 Triangles

Answer 29

Short Sides: X or 1

Hypotenuse: X Times Square root of 2, or square root of 2

Question 30

30-60-90

Answer 30

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

Question 31

Coterminal

Answer 31

X + 360 times n
Or
X -360 times n

Question 32

R Equation

Answer 32

R= square root of x^2 +y^2

Question 33

Radians to Degrees

Answer 33

180/ (pie)

Question 34

Degrees to Radians

Answer 34

(Pie)/180

Question 35

Law of Sines

Answer 35

SinC/c= SinB/b= SinA/a

Question 36

Area Equations Triangles

Answer 36

A= 1/2 (b)(c)SinA
A= 1/2 (a)(c) SinB
A= 1/2 (b)(a) Sin C

Question 37

Law of Cosines

Answer 37

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)

Question 38

Joint Relativity Frequencies & Marginal Relative Frequencies

Answer 38

• JRF: Divide numbers in the body of the graph by grand total
• MRF: add joints