Trigonometry
Log/Exp Equations
Polar
Functions
Miscellaneous
100

What is equivalent to 1 + tan2x

sec2x

100

Write the logarithmic form of: 43 = 64

log464 = 3

100

List three additional polar coordinates for the same location in the polar coordinate system: 

(-2, -2pi/3)


( 2, pi/3 ), ( -2, 4pi/3 ), ( 2, 7pi/3 )

100

Determine whether the function is even , odd or neither. 

f(x) = 3x4 - x2 + 2

Even

100

What is the solution to the system: 

x - y - 2z = -6

3x + 2y = -25

-4x + y - z = 12

(-5, -5 , 3)

200

What is the reference angle of -215 degrees. 

35 degrees

200

Solve for the positive value of x: 

logx(27) = 3

x = 3

200

Convert (1, pi/3) into a rectangular coordinate point.

(1/2, rad3/2)

200

If f(x) = -x - 5 and g(x) = x2 - 6x + 13 find (f o g)(x)

-x2 + 6x -18

200

Apply the difference quotient to the following function. Express your answer in simplest form. 

f(x) = x2 - 3

2x + h

300

If cos D = 1/2, then what are the possible angle measure of D? 

60 or 300

300

Solve for the exact value of x: 

logx(7x - 12) = 2

x = 3, x = 4

300

Convert the point (1,1) from rectangular coordinates to polar coordinates. 

( rad2, pi/4 )

300

Given the function f(x) = 1 - 18x2, find the value of f(1/3) in simplest form.

-1

300

Factor completely x4 - 16

(x + 2)(x - 2) (x2 + 4) 

400

Find all solutions to the equation in the interval [0,2pi).

2cos2(theta)+ cos(theta) - 1 = 0

theta= pi, theta = pi/3, 5pi/3

400

$1200 is invested at a rate of 12% compounded quarterly. After how many years will the principle reach $3500? 

9 years

400

Convert the equation from rectangular form to polar form. 

x2 + y2 - 8y = 0

r = 8sin(theta)

400

Find the horizontal or slant asymptote of: 

f(x) = 7x/x2 - 4

y = 0

400

Expand the binomial 

(2x - 5)4

16x4 - 160x3 + 600x2 - 1000x + 625

500

Find all solutions to the equation in the interval [0,360)

sin2x- 6 sin x + 3 = 0

x=33.4 degrees or x = 146.6 degrees 


500

At what rate is a strand of bacteria growing if the population triples every 36 hours?

0.03 or 3%

500

Convert the polar equation from rectangular to polar: (x - 1)2 + (y + 1)2 = 2 

r = 2 cos(theta)-2sin(theta) 

500

Write a 4th degree polynomial with a lead coefficient of 1 and the following zeros: 

2, -4, i

x4+2x3-7x2+2x-8

500

Factor the polynomial into linear factors:

9x4-18x3-71x2-2x-8

(x+2)(x-4)(3x+i)(3x-i)

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