UGA Math Placement Test

x=5 (lin equation)

1 solution

4=5 (lin equation)

0 solutions

5=5 (lin equation)

infinite solutions

distance formula

d squared= delta x squared plus delta y squared

Slope Intercept Formula

y=mx+b

Point Slope Formula

y-y1=m(x-x1)

Two Point Formula

y-y1=(y2-y1)/(x2-x1) x (x-x1)

Standard Form of a Line

ax plus by equals c

if dividing an inequality by a negative number

flip the sign

Interval notation

Bracket= definite, parentheses = indefinite

Quadratic Formula

x equals -b plus or minus the square root of b squared minus four ac over 2a

the rule that generates a function is

y=f(x)

rational expression

a fraction where the numerator and denominator are polynomials

x to the -n

1 divided by x to the n

x to the 1/n

n root x

x to the p/n

(n square root) to p

x to the a times x to the b

x to the a plus b

(xy) to the a

x to the a times x to the b

x to the a / x to the b

x to the a minus b

(x/y) to the a

x to the a divided by x to the b

x to zero

one

standard form of quadratic equation

ax^2 + bx +c = 0

vertex form of a quadratic

y= a(x-h)^2 + k

h equals

-b/2a

k equals

f(h)

in quadratics, (x,y) are equal to what in standard form

(h,k)

axis of symmetry equals

-b/2a

if an object strikes the ground that means

s(t)=0

the maximum of a negative quadratic is located at

the vertex

velocity equals what when units are in feet

16

velocity equals what when units are in meters

4.9

if slopes are equal

lines are parallel

if slopes are opposite reciprocals

lines are perpendicular

k equals

the constant of variation

a^b=c

log base a C = b

logbA + logbC

logb(A x C)

logbA - logbC

logb(A/C)

logb(A x C)

logbA + logbC

logb(A/C)

logbA - logbC

logb(A^C)

ClogbA

logb(1)

0

logb(B)

1

logb(B^A)

A

b^logb(A)

A

Rational Function Formula

f(x)=a/b(x-h) +k

an increase in a

moves function outward

an increase in b

moves function inward

an increase in h

moves function left/right

a change in k

moves function up/down

f(x) + or - b

up/down

f(x + or - b)

left/right

-f(x)

reflects over x axis

f(-x)

reflects over y axis

sin

1/cos

cos

1/sin

tan

1/cot

sec

1/cos

csc

1/sin

cot

1/cot

tan(x) =

sin/cos

cot(x) =

cos/sin

sin squared plus cos squared

1

tan squared plus 1

sec squared

1 plus cot squared

csc squared

sin(-t), cos(-t), tan(-t)

-sin(t), -cos(t), -tan(t)

sin(a + b)

sin(a)cos(b) + cos(a)sin(b)

cos(a + b)

cos(A)cos(B) + sin(a)sin(b)

tan(a +b)

tan(a) + tan(b)/ 1-tan(a)tan(b)

sin(2x)

2sin(x)cos(x)

cos(2x)

2cos squared x minus 1

tan(2x)

2tan(x)/ 1-tan^2(x)

sin (x/2)

plus or minus square root 1-cos(x)/2

cos (x/2)

plus or minus square root 1+cos(x)/2

tan (x/2)

sin(x)/ 1-cos(x)