1a. Solve for x (Hint: simplify first)
1b. Simplify (Hint: factor first ) 
1c Solve for x: 
2a. A librarian is shipping boxes of books. The cost, C, of shipping is directly
proportional to the
weight (in pounds), W, of the books. The company advertises that 18,000 pounds
of books
can be shipped for $810.
i. How much does it cost to ship 51,000 pounds of books?
ii. How many pounds of books can be shipped for $2, 430?
2b. Here is the graph of a linear function. Find the
function in the form y = mx + b.
3. The sketches be low show the graph of a piecewise linear
function y = f(x).
i) What is the value of f(−1) =
ii) Find the average rate of change from x = −7 to x = 1.
iii) Add to the graph the sketch of y = f(x − 4) − 3
iv) Add to the graph the sketch of  |
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4a. Sketch the graph of  . Indicate
the
points found below on the graph.
b. Find the y-intercept.
c. Find the vertex .
d. Find the x-intercepts (if any). |
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5. A project in a business class involves building and
selling picture frames. The students are
selling 160 a week at $12 each. The materials for each cost $10 a piece. A
carefully done survey
indicates that for every dollar increase in price the number of sales per week
will decrease by
four.
a. What is their current weekly profit?
b. Find a (quadratic) formula (in the form ax2 +bx+c) for the profit as a
function of the price.
c. Find that price that maximizes the profit and determine the maximum profit.
6a. Do the following calculations and put the answer in the form a + bi (and put
fractions into
reduced form.)
6b. Find all ( real and complex ) solutions of x 3 − 10x2 + 61x = 0.
6c. Find a polynomial with integer coefficients (in standard polynomial form
)
such that P has degree three, and zeros 12 and 6 − 5i
7. A bio logist is developing a new strain of fruit flies. Careful examination
reveals that 1,500
fruit flies grows to 3,250 in nine weeks. As suming that the growth rate follows
the exponential
law 
, where t denotes time measured in weeks, answer the following.
a. Find the value of the constant k.
b. Starting from 1500 fruit flies, how many will there be in twelve weeks?
c. How many weeks does it take for 1, 500 fruit flies to grow to 6, 000?
8a. A research ship from Woods Hole is tracking an errant
iceberg in the Atlantic ocean. At 6:50
PM on July 18 the iceberg was at latitude 35 degrees, 25 minutes. The ship was
due south
of it at latitude 30 degrees, 45 minutes. Using r = 3960 miles for the radius of
the Earth
determine how far the ship is from the iceberg.
8b. Solve the triangle by finding the values of
i. c = 
ii. (in degrees) α =
iii. (in degrees) β = . |
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8ci. From the graph, find 
ii. What is the amplitude?
iii. What is the vertical shift?
iv. What is the wavelength? .
v. What is the phase shift (starting x-value)?
i. y = |
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9a. Solve the following system of equations. (Use any
method, but show your work.)
9b. A laboratory is supplied with two containers of salt solutions. The first is
a 60 percent solution
and the second is a 10 percent solution. For an experiment you need 1,000
milliliters of a 50
percent salt solution. How much of each should you mix in order to get the
required salt
solution?
10. Solve the following system of linear equations for x , y and z. (You may use
your calculator to
check your answer-but you still must show the computational work to receive
credit.)
Some Formulas you may need
Quadratic Formula: 
Exponential/Logarithmic Relation:
, and
.
Exponential Rules : 
, and
.
Logarithmic Rules : 
, and
.
Exponential Growth/Decay: . Compound
Interest : 
Degree/Radians: 360° = 2π radians. Deg/Min/Sec: 1° = 60', 1' = 60''.
Arclength:
, ( θ must be in radians).
Sinusoidal Function: 
Trignometric Definitions:
.
