Math 238_Practice Exam 1: Show work to receive full credits
Name:________________________________________________
1) Find the slope-intercept form and standard form of the equation of the line that passes through
(-3,5 ) and (-6,1)
2) Describe how the graph of h( x)  3 
1
x  2 is related to the graph of one of the basic
2
functions
3) Given f ( x)  ( x  3) 2 
1
. Find each of the following
4
a) Intercepts
b) Vertex
c) Maximum or minimum
c) Range.
4) Find the equation of horizontal and vertical asymptotes of f ( x) 
3x 3  x
6 x 3  12 x
5) Solve each equation
a)
b) 3xe x  x 2 e  x  0
45 x x  4 6
2
6) Solve the equation:
1
1
( x  18)  ( x  7)  x  9 (Answer: 756/65)
9
7
7) Solve and graph the inequality:
x 2 x 3 3 x


3
3
6
2
8) You have $500,000 in an IRA at the time you retire. You have the option of investing this money
into 2 funds. Fund A pays 5.2% a nnually and fund B pays 7.7% annually. How should you divide
your money between Fund A and Fund B to produce an annual interest income of $34,000?
(Answer: $180,000 in Fund A and $320,000 in Fund B)
9) A sporting goods store sells tennis rackets that cost $130 for $208 and court shoes that cost
$50 for $80.
a) If the markup policy of the store over $10 is linear and is reflected in the pricing of these two
items, write an equation the expresses retail price R in terms of cost C.
(Answer: R=1.6C )
b) What would be the retail price of a pair of in-line skates that cost $120?
(Answer: $192)
c) What would be the cost of a pair of cross-country skis that had a retail price of $176?
(Answer: $110)
d) What is the slope of the graph of the equation found in part a? Interpret the slope relative
to the problem.
10) Bank of America recently offered a certificate of deposit that paid 1.25% compounded quarterly.
If a $20,000 CD earns this rate for 18 months, how much will it worth? (Answer: $20377.94)
11) The research department in a company that manufactures AM/FM clock radio established the
follow price-demand, cost and revenue functions:
p(x)=50 - 1.25 x
price-demand function
C(x)=160 + 10x
Cost function
R(x)=xp(x) = x(50-1.25x)
Revenue function
Where x is in thousands of units, and C(x) and R(x) are in thousands of dollars. All three
functions have domain 1  x  40
a) Find the value of x that will produce the maximum revenue. What is the maximum revenue
to the nearest thousand dollars? (Answers: x= 20 thousand units; max revenue= $500,000)
b) What is the whole sale price per unit that produces the max revenue? (Answer: $25)
c) Find the break-even points to the nearest thousandth units. (Answer: x=4.686 thousands
units and x=27.314 thousands units
d) For what values of x will a loss occur? A Profit? (Answers: loss: 1  x  4.868 or
27.314  x  40 ; profit: 4.686  x  27.314 )
12) In 2008, the estimate population in Ethiopia was 83 million people with a relative growth rate of
3. 2%
a) Write an equation that models the population growth in Ethiopia, letting 2008 be year 0
b) Based on the model, what is the expected population in Ethiopia (to the nearest million) in
2020?
13) A donut shop has a fixed cost of $124 per day and a variable cost of $0.12 per donut.
a) Find the total daily cost of producing x donuts.
b) How many donuts can be produced for a total daily cost of $250?
14) Retail prices in a department store are obtained by marking up the wholesale price by 40%. That
is, retail price is obtained by adding 40% of the wholesale price to the wholesale price.
a) Write a linear equation that expresses the retail prices R in terms of wholesale price.
b) What is the retail price of a suit if the wholesale price is $300? (Answer: $420)
c) What is the wholesale price of a pair of jeans if the retail price is $77? (Answer: $55)
15) A person wishes to have $15,000 cash for a new car 5 years from now. How much should be
placed in an account now, if the account pays 4.75% compounded monthly? (Answer: $11834.5)
16) Review your lecture notes sections 1.1,1.2, 2.1-2.5