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