Practice Math 102 Common Final Exam
1.
(4) For 
and 
, find 
. Express your answer
in interval notation.
2. (4) Simplify completely. Express your answer without negative exponents.
[those
teensy
fractional exponents are –4/5 and –1/4 ]
3. (4) Factor completely.
[those teensy fractional exponents are 3/2, 1/2, and –1/2
]
4. (5) Divide. Express your answer in the form 
.
5. (5) Solve. Express your answer in interval notation.
6. (4) Solve. Express your answer using interval notation.
7. Let A = (2,–5) and B = (–1,3) be points in the xy-plane.
a) (4) Find the length of segment AB. (simplify the answer)
b) (2) Find the midpoint of segment AB.
8.
(4) Find the center and radius of the circle
with equation: 
.
9. (4) The manager of a cheap plastic furniture factory finds that it costs $2400 to produce 200 chairs in a day, and $6200 to produce 400 chairs in a day. Assuming that the relationship between cost (y) and the number of chairs produced (x) is linear, find an equation that relates x and y.
10. (5) For 
+3, find 
. (Simplify your
answer completely.)
11. a) (2) Sketch the graph of 
b) (3) Use transformations to
sketch the graph of 
12. (4) For 
, find the formula for 
.
13. (5) Sketch the graph of 
. Label all
intercepts; describe end behavior.
14.
For 
,
a) (2) List all the theoretically possible rational zeros of P(x)..
b) (2) Use synthetic
division to show that 
is a zero of P(x).
c) (3) Find all the zeros of P(x). Simplify your answers.
15.
(5) Find a fourth degree polynomial 
with
a zero, 1 a zero of multiplicity 2, and a constant term of
10.
Express your answer in the form 
(
are integers).
16. 
a) (2) Find the x and y intercepts. (express as ordered pairs)
b) (1) Find the vertical asymptote. (write the equation)
c) (1) Find the horizontal asymptote. (write the equation)
d) (3) Sketch the graph.
17. (4) Sketch the graph of
(Label one point on the graph and the asymptote.)
18. (5) Simplify
completely: 
19. (4) Solve for x: 
(Give an exact answer.)
20. (5) Solve for x: 
21. (4) $2000 is invested in an account that pays 3% (annual percentage rate) compounded continuously. How long will it take for the balance to reach $3000?