Precalculus Final Exam Review Game

Trigonmetry

100

Complete the identity: ______ + 1 = cot² x

csc² x

200

Solve on [0, 2pi): sec x + 2 = 0

2pi/3, 4pi/3

300

What would you find first in this problem, and what law would you use to find it? Solve triangle ABC given that a = 8, c = 5, and B = 40

b, using law of cosines

400

State the range of y=arctan(x)

(-pi/2, pi/2)

500

Given that a = 15, b = 25, A = 85, how many triangles are possible?

no triangles possible

Evaluate

100

log₂(1/8)

-3

200

ln e⁷

7

300

csc (pi)

undefined

400

arccos (1)

0

500

arcsin (-1/2)

-pi/6

Equations

100

Solve on [0, 2pi): tanx = -1

x = 3pi/4, 7pi/4

200

Solve: 4^(x+3) = 16^(5x)

x=1/3

300

e^x + 5 = 66  (exact answer)

x = ln(61)

400

Solve: log₂ (x+3) = 5

x=29

500

Solve on [0, 2pi): 2sin² x - 3sin x +1 =0

x = pi/6, 5pi/6, pi/2

Graphing

100

Is this graph of this function increasing or decreasing? f(x)=4^(-x)

decreasing (because equivalent to f(x)=(1/4)^x

200

State the vertical asymptotes of this function: 

x / (x² -3x+2)

x=2, x=1

300

State the horizontal asymptote of this function: (3x²)/(x³ - 4x +3)

y=0

400

How may petals does the polar equation r = 3cos4u have?  

8

500

What is the name for the type of polar graph represented by the equation r²=4sin2u?  

Lemniscate

Mixed Topics

100

Find the value of r and determine if it converges or diverges:  -12, 6, -3, 1.5, ...

r = -1/2;  Converges

200

Find the point of removable discontinuity of the rational function f(x)=(x²-1) / (x² + 4x + 3)

(-1,-1)

300

Eliminate the parameter and write the equation in its appropriate conic form and identify the conic.  

3sinu = x and 2cosu = y

x²/9 + y²/4 = 1; Ellipse

400

Simplify (sec²x - 1) / (sec²x) to a single trig function (no fractions)

sin²x

500

Find the sum of the series, if possible: 

12 + 4 + 4/3 + 4/9 + ....

S=18