Download Math 111 practice final exam:

Math 111 practice final exam:
(From Fall 1999 final exam)
General test instructions: Show all your work on this test paper! If you solve a problem algebraically
show all your steps. If you solve a problem by graphing on your calculator, show a sketch of the graph,
with the solution labeled. Where appropriate, round answers to 3 decimal places.
Solve the following equations:
1. x 2  10 x  5  8
2.
3.
4 x  17  2 x  1
Solve this system of equations:
3 x  y  15
 x  2y  2
4. Solve this system of equations, find all points
of intersection.
x 2  y 2  169
x 2  8 y  104
5. .A store has $30,000 of inventory in 12-inch
and 19-inch color televisions. The profit on a
12-inch set is 22 % and the profit on a 19inch set is 40 %. The profit for the entire
stock is $10,500. What is the $ value of the
inventory for each type of television?
Solve the following inequalities:
6. 2 x  3  6
7. x 2  x  2
8. Evaluate:
a. log 6 39 =
b. log e 5 =
Solve for x:
9. e( 6 x 1)  4  7
11. a. Determine the interest rate if $600 grew
to $800 in 5 years assuming interest was
compounded continuously.
b. At that interest rate, when would the
account balance be 1200?
12. a. Graph f ( x)  log 3 x and
g ( x)  log 3 ( x  1)  2
(Label intercepts and asymptotes.)
b. Describe how the graph of g(x) differs
from that of f(x) in terms of transformations
such as shifts up or down, left or right.
c. What is the domain
of g ( x)  log 3 ( x  1)  2 ?
13. Sketch a graph of a 3rd degree polynomial
with a leading coefficient that is negative.
14. a. Graph f ( x)  x 4  2 x 2  10 . Clearly label
all important aspects such as intercepts and
maximum or minimum points.
b. Over what intervals is this graph
increasing?
15. Find the number of units, x, that would have
to be sold to produce a maximum revenue, R,
where R   01
. x2  70x  25000 .
b. What is the maximum revenue?
2x  1
16. Analyze the function f(x) =
x
(a) y-intercept
(b) x-intercept
(c) vertical asymptotes
(d) horizontal asymptote
10 log 4 ( x  1)  log 4 ( x  2)  1
(e) graph y = f(x); include x and y-intercepts and
all asymptotes.
17. Multiply these complex numbers, simplify
the
answer and write it in the standard a+bi form.
(3 + 2 i)(6 – 5 i)
18.Find all the zeros of the polynomial function
f ( x)  4 x3  20 x 2  25x
19. f ( x ) is sketched on the axes below.
Translate it to sketch a graph of f ( x  2)  1
23. The approximate number of new AIDS
cases reported in each of the years 1983-1986
is given in the table, with year 3 corresponding
to 1983.
Year(3=1983)
3
New AIDS Cases 2100
4
5
6
4400 8200 13100
a. Use your graphing calculator to fit a linear
model to the data. Write the equation and
correlation coefficient here.
b. Use your graphing calculator to fit an
exponential model to the data. Write
the equation and correlation coefficient
here.
20.Given the function g ( x)  2  x , what is
it’s
a. domain?
b. range?
c. inverse function?
d. Graph g ( x) and g 1 ( x)
c. Which equation is a better model of the
data?
Explain.
21. Given
f ( x ) = x  2 and g ( x ) = 4  x 2 find:
a. f (5)
b. g (-2)
c. ( g  f )( x ).
22. Find an equation of the line that passes
through the point (1, 2) and is perpendicular
to the line 3x - 2y = 5.
d. Using the better equation, estimate how
many new cases of aids there were in
1987.