College Algebra Final Review

Polynomials

100

State the coordinates of the vertex:

f(x)=-(x+1)²+7

(-1, 7)

200

This point is where a function changes concavity.

What is a point of inflection?

300

Solve.

x⁴+x³-x²-56=x³

x=+/-sqrt8

x=+/- sqrt(-7)

400

State the equation of the axis of symmetry.

f(x)=x²+14x+53

x=-7

500

Write a possible equation a polynomial with the following zeroes:

x=0

x=sqrt(-4)

x=sqrt(3)

f(x)=x(x²+4)(x²-3)

Rationals

100

Simplify:

(5x²-27x+10)/(3x²-22x+35)

(5x-2)/(3x-7)

200

State the equation of the vertical asymptote:

f(x)=-6/(x+8) - 2

x=-8

300

State the equation of the horizontal asymptote:

f(x)=(4x-11)/(-x+2)

y=-4

400

Solve:

(2x+80)/(x²+18x+80) = (5x)/(x+10) - (4x)/(x+8)

x=10

500

Simplify:

5/(2x-4) - 6

(-12x+29)/(2x-4)

Right Triangle Trig

100

What quadrant(s) is cosine positive?

1 and 4

200

Evaluate:

sin(45)

1/sqrt2

300

Solve in degrees.

sec x=2

x = 60, 300

400

Evaluate:

tan(3pi/2)

undefined

500

Solve in degrees:

-4cot²x-2=5cot²x-29

x= 30, 150, 210, 330

Non-Right Triangle Trig

100

mangA=108, mangC=49, b=14

mangB=?

23 degrees

200

mangA=108, mangC=49, b=14

a=?

a=34.08

300

mangC=82, b=18, c=19

mangB=?

mangB=69.7

400

a=35, b=75, c=55

mangC=?

43.2

500

During a figure skating routine, Tamara and Stephanie skate apart with an angle of 15 degrees between them. Tamara skates for 5 meters and Stephanie skates for 7 meters. How far apart are the skaters?

2.53 m

Semester 1

100

Factor completely.

3x³+7x²-27x-63

(3x+7)(x+3)(x-3)

200

Evaluate.

log4(16)

2

300

Simplify

(2x⁶)^3 * x⁸

8x²⁶

400

Write the equation of the inverse:

y=4x-5

y=1/4 x+5/4

500

State the equation of the vertical asymptote:

f(x)=ln(x+7)-1

x=-7