Pre-Calculus Final Review

Algebra Review

100

Write an equation in point slope form of a line that goes through (-1,2) with slope 3

y-2=3(x+1)

200

f(x) = x²-2x+1

g(x) = 4x-7

Find f(g(3))

16

300

What is f^-1(x) for the function f(x)=x²+2

f^-1(x) = sqrt(x-2)

400

What is the test to determine if a relation is a function?

Vertical line test

500

What is the location of the vertex of this quadratic?

y = -3(2x-4)²-8

(2,-8)

Trigonometry

100

cos(3pi/4) 

-sqrt(2)/2

200

(calc active) A 25 ft ladder leans against the top of a 23 foot building, what angle does the ladder make with the ground? 

67 degrees

300

(calc active) A helicopter at an altitude of 1000 ft spots a boat at an angle of depression of 11 degrees. How far away is the boat (through the air)? 

5241 ft

400

 Find the exact value of csc(315)

-sqrt(2)

500

Solve for x on 0 < x < 360.

Find x in degrees

2sin(x) - 1 = 0

30,150

Exponents/Logs

100

log₃(1/9)

-2

200

Simplify completely:

(3x³)²*x^-4 / (27x⁵*x³)

1/3x⁶

300

What is the asymptotes of the following graph?

y = 2log(x-3) + 1

x = 3

400

calc active) Solve for x:

7*8^(x-2)+5 = 26

2.528

500

Solve for x:

log₃(x-5)+log₃(x+3)=2

x = 6

Random Pre-Calc

100

Condense and simplify:

log(5) + log(200) - log(10)

2

200

Factor:

6x²−31x+5

(6x−1)(x−5)

300

Factor: 

2x²−3x−35

(2x+7)(x−5)

400

Use the quadratic formula to solve. Express your answer in simplest form. (no decimal answers)

6w²−26w+5=w²

w=5 or w=1/5

500

Use the quadratic formula to solve. Express your answer in simplest form. (no decimal answers)

14b²+b−6=2b²

b=2/3,b=−3/4

Misc

100

Who wrote Hamlet?

William Shakespeare

200

What is a group of crows called?

a murder

300

Which country gifted the Statue of Liberty to the US?

France

400

What are the four states of matter?

Solid, liquid, gas, plasma

500

What is 12*11=

132