AP Precalculus Review Game

Trigonometry

100

Complete the identity: The ratio sin(x)/cos(x) = _____

Tan(x)

200

Simplify using a double angle identity:  6sinxcosx=_________

3sin2x

300

Complete the following using a sum/difference identity:

cos(35)=cos(20)_______________________

cos(35)=cos(20)cos(15)-sin(20)sin(15)

400

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

sin²x

500

What is the argument of the complex number:

z = -2+2i

135 degrees or 3pi/4

Evaluate

100

log₂(1/8)

-3

200

lne⁷

7

300

csc (3pi/2)

-1

400

cos^-1(-1/2)

2pi/3

500

arcsin(sin(11pi/6))

-pi/6

Equations

100

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

x = 3pi/4, 7pi/4

200

Solve: 4^(x+3) = 8^(2x)

Simplify, if necessary.

x = 3/2 or 1.5

300

Solve: e^x + 5 = 16  (exact answer)

x = ln(11)

400

Solve: 2log₂ (x+3) = 8

x=13

500

Solve on [0, 2pi): 

2sin² x - 3sin x +1 =0

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

Trig Graphs

100

What is the range of the function:

f(x)= -5sin(2x)-2

[-7,3]

200

State the range of y=arctan(x) using interval notation.

(-pi/2, pi/2)

300

What is the period of the function:

f(x)=3sin(x/3)-2

y=6pi

400

How many petals does the polar equation r = 5cos12u have?  

24 petals

500

What is the specific name (indicating characteristics) for the type of polar graph represented by the equation r=3-4sinx?  

Limacon with inner loop

Rational Functions

100

State the equation of the horizontal asymptote of this rational function: 

f(x) = (x³)/(3x³ - 4x +3)

y = 1/3

200

State the vertical asymptote(s) of this rational function: 

x / (x² -3x+2)

x=1 and x=2

300

Find the point of removable discontinuity of the rational function 

f(x)=(x²-1) / (x² + 4x + 3)

(-1,-1)

400

What is/are the x-intercept(s) of the following:

r(x) = (x²-4)/(3x²+5x-2)

Write your answer(s) as an ordered pair.

(2,0)

500

What is the slope of the slant asymptote of the following rational function?

h(x)=(x²-x+4)/(2x+2)

Slope is 1/2