North Seattle Community College
Spring 2012
PRECALCULUS II
Practice Final 1
MATH 142, Section 03
STUDENT NAME: __________________________
SCORE: __________________________________
1. Find the all exact solutions for on the interval 3 tan 2x = -3 on the interval 0<x<2
2. Verify the identity ln(sec θ + tan θ) + ln(sec θ – tan θ) = 0
3. If cot x = -4/3, and
o sin 2x
3π
2
< 𝑥 < 2𝜋 , find exact values for the following:
x
o
cos 2
o
cos (2 + 𝑥)
𝜋
4𝑡
4. For y = 6sin ( 3 + 6) + 10 find the amplitude, period, phase shift and vertical
shift.
5. Iodine 131 is a radioactive material that decays according to the function A(t) =
A0e-0.087t, where A0 is the initial amount present and A is the amount present at
time t (in years). Determine how long it takes for 250 grams of iodine 131 to
decay to 50 grams.
6. Melody has $45,000 to invest and wishes to receive an annual income of $4290
from this money. She has chosen investments that pay 5%, 8%, and 12% simple
interest. Melody wants to have the amount invested at 12% to be double the
amount invested at 8%. How much should she invest at each rate?
7. The perimeter of a rectangle is 24 inches and its area is 27 square inches. What
are its dimensions?
8. Find the equation of a hyperbola with center at (0, 0), focus at (53, 0), vertex at (2,
0). Find the equations for its asymptotes.
9. Analyze the parabola and write it’s equation in standard form: Opening to the left
with the vertex at (−6, 3) and passing through (−14,−9).
10. An arch in the form of a semi-ellipse is 52 ft wide at the base and has a height of
20 ft. How wide is the arch at a height of 12 ft above the base?
11. A new piece of equipment cost a company $53,000. Each year, for tax purposes
the company depreciates the value by 25%. What value should the company give
the equipment after 6 years?
12. Letitia borrows $3750 at a rate of 11% per annum compounded semiannually.
Find how much does Letitia owes at the end of 5 years.
13. Solve the equation:
o 2-x=16
o log3(x2 + 1)=2
𝑥
14. Find the domain of each function: f(x) = 3-2log4(2 − 5)
15. Show that loga(𝑥 + √𝑥 2 − 1) + loga(𝑥 − √𝑥 2 − 1) =0
16. Write the trigonometric expression cos (cos-1 u + sin-1 v) as an algebraic
expression in u and v. Use it to find: cos(cos-1 ½ + sin-11).