Pre Calculus B MP3 Cumulative Exam Review
Pre Calculus B MP3 Cumulative Exam Review
Pre Calculus B MP3 Cumulative Exam Review
=
x
x g 3.
6
3
) (
2
+
=
x x
x
x h
Solve the following rational equations. Check for extraneous solutions
4. 3
4
15
2
2
2
+
=
x x
x
5.
8 6
2 32
4
3
2
2
+
+
x x
x
x
x
x
x
Graph the following exponential equations. State the domain, range, y-intercept and equation of the
asymptote.
6. 2 3 ) (
1
+ =
x
x f 7. 3 ) 2 ( ) (
1
=
+ x
x g
8.
x
x h |
.
|
\
|
=
2
1
) ( 9. 1 3 ) ( =
x
x j
Name Date Pd
Evaluate the following logarithms WITHOUT A CALCULATOR
9. 32 log
2
11.
|
.
|
\
|
1000
1
log
12. 27 log
9
13.
x
e
3
ln
14.
x
7
log
7 15.
|
.
|
\
|
36
1
log
216
Evaluate the following using a calculator. Round your answer to 3 decimal places.
16. 3012 log
7
17. 7 log
3
18. 19 log
108
Condense the following expressions using the properties of logarithms
19. y z x
4 4 4
log
2
1
log log 3 + 20. ) ln 10 ln 3 ( ln 5 z y x +
Expand the following expressions using the properties of logarithms.
21.
|
|
.
|
\
|
3
2
log
x
z
22. ( )
3 2
log z x 23.
|
|
.
|
\
|
x
e
ln
Solve the following equations without a calculator.
24.
3 2 1
4 8
+
=
x x
25. 11 5 ) 3 2 ( log 3
3
= + x
26. ) 16 log( ) log( ) 6 log( = + x x 27. 4 2 ) 3 ( log 3
5
= x
28. ) 2 ln( ) 1 ln( ) ln( ) 6 2 ln( = + x x x 29. 0 ) ln( ) 3 ln( = x x
Solve the following equations with a calculator. Round your answer to 3 decimal places
30. 129 3 . 3 =
x
31. 2 ) 3 ln( = x
32. 1 ) 4 ( log log
4 4
= + x x 33. ) 20 log( ) log( 2 = x
Name Date Pd
34. Mr. Frank puts $3000 into a bank account that bears 3.2% interest that is compounded quarterly.
How long will it take for him to have $5500 in his account? Round your answer to 3 decimal places.
35. The population of Frankenville is 21,345 people and is decreasing at a continuous rate of 7%
annually.
a. Write a model (equation) to represent this situation.
b. What will the population be in 10 years?
c. How long will it take until the population is $10,000?
36. A colony of ants is growing continuously and has an initial population of 2000 ants. After t = 6 hours
the population is 3200 ants. What is the growth rate of this ant colony?