Download Review for Final Exam (7 4-7 5 Ch 6 8

HONORS ALGEBRA II: 2ND SEMESTER
REVIEW FOR FINAL EXAM
SECTIONS 7.4-7.5: RATIONAL FUNCTIONS
Find the sum or difference.
1.
4.
12 3

5x 5x
14
6

x  7 x  18 x  9
2
2.
7
4

2
2x
3x
3.
6
5

x 4 x3
1 1

x y
6.
1 1

y x
3
2
x
5.
4
y
Solve each equation. Check for extraneous solutions.
7.
4
6

x2 x2
8.
5 1 9
 
2x 4 2x
9.
4
1 x 1
 
x 5 x x 5
10. You can clean the gutters of your house in 5 hours. Working together, you and your friend can clean
the gutters in 3 hours. Let t be the time (in hours) your friend would take to clean the gutters when
working alone. Write and solve an equation to find how long your friend would take to clean the gutters
when working alone. (2pts)
CHAPTER 6: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Rewrite the expression in exponential or logarithmic form.
2. 23  0.125
1. log3 243  5
3. Use log 4 5  1.1610 and log 4 11  1.7297 to evaluate log 4 55 .
 3x 2 
 .
3
 5
4. Expand the logarithmic expression log 
Simplify each expression without using a calculator. Show all work.
5. e
ln x
1

 16 
6. log 4 
7.
log 3 9
3 x
Graph each function (make sure to draw and label the asymptote). State the domain and range.
8.
y  2x
9. y  log 2 x
Describe the transformations of equation and sketch a graph. State the domain and range.
10. y  2 x 1  3
11. y  log 2 ( x  4)  1
Solve each equation. Check for extraneous solutions and round all decimals to the nearest
thousandth.


12. 2 2 x 3  8
13. log x 2  5 x  log 6
14. 5e 3 x  2  17
15. ln 3  ln x  1  12
16. Find the exponential equation in the form y  a  b x that goes through the points (1, 20) and (3, 5).
17. An endangered species of bird has a population that is modeled by the exponential equation
A  1600e 0.23t , where A (in hundreds) represents the current population of the birds t years from
now.
a. Tell whether your function in represents exponential growth or exponential decay.
b. Identity the annual percent increase or decrease in the bird population.
c. What will the population be 6 years from now?
18. $10,000 is put into an account earning 4% interest compounded quarterly. How long will it take for
the account to have $20,000 in it? Round the answer to the nearest hundredth.
CHAPTER 8: SEQUENCES AND SERIES
1. Write a recursive and explicit rule for the sequence 5, 10, 20, 40, 80,… .
2. Write a recursive and explicit rule for the sequence 50, 40, 30, 20,…. .
3. Given a6  37, a10  53 ; write a rule for the nth term of the arithmetic sequence.
4. Given a5  45 , a8  360 ; write a rule for the nth term of the geometric sequence.
Determine whether each sequence is arithmetic, geometric or neither. If the sequence is arithmetic
or geometric, find a10 .
5. 64, 4, 1,
1
…
4
6. 1, 5, 9, 13, …
Determine whether each series is arithmetic, geometric or neither. If the series is arithmetic or
geometric, then find the sum for the first 10 terms.
7. 1 + 1 + 2 + 3 + 5 + …
8. 20 + 15 + 10 + 5 + …
9.
1
1 1 1
   ...
243 81 9 3
Find the sum of each infinite geometric series.
10. 15  5 
5 5
  ...
3 9
11. 3  6  12  24  ...
Find the sum.
 2n
5
12.
2
5

n2

500
13.
 3n 
n 1
14.
160.5
n 1
Express the given finite series in summation notation.
15. 10 + 7 + 4 + 1 - 2 - 5
16. 81 + 27 + 9 + 3 + 1 + 1/3 + 1/9
n 1
CHAPTER 9: TRIGONOMETRY
Draw an angle with the given measure in standard position. Find its reference angle.
1. 
3.
4
3

2. 460

Convert 285 into radians.
4. Find one positive and one negative coterminal angle for
15
.
6
5. Solve for x.
Find the exact value of each trigonometric expression.

6. cos 150
 

 6
9. csc 
7. sin
3
4
8. tan( 60  )

10. sec 90
11. tan
2
3
Sketch one cycle of each trigonometric function.
12. y  4 csc 2 x
13. y  3 tan x


14. y  2 cos x 

3
4
15. Find the amplitude and period of the graph
shown to the right; then find an equation.
16. A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the
Jin Mao Building in Shanghai, China. The person estimates the angle of elevation to the top of the
building is about 80O. What is the approximate height of the building?
17. Suppose a windshield wiper arm has a length of 20 inches and rotates through an angle of
135  . What distance does the tip of the wiper travel as it moves once across the windshield?
Round answer to the nearest tenth.
18. You decide to ride the carousel at an amusement park. The carousel has a radius of 25 feet and makes
5 revolutions in one minute. If you were to sit on the very outside of the carousel, then what is the
total distance that you would travel if you ride the carousel for 5 minutes?
19. You are riding a Ferris wheel that turns for 180 seconds. Your height h (in feet) above the

t  10  90 .
ground at any time t (in seconds) can be modeled by the equation y  85 sin
20
a. What is the period of the function and what does it represent?
b. How many cycles does the Ferris wheel make in 180 seconds?
c. What is the radius of the Ferris wheel?
Simplify each expression.



21. sin  x   tan   x 
2


20. cos 2 x sec 2 x  1
Verify each identity.
22. tan x  cot x  sec x  csc x
23.
sin 2 x
 1  cos x
1  cos x
24. Use the sum or difference formulas to find the exact value of cos 105  .
25. Evaluate sin a  b given that sin a  12 13 with 0  a   / 2 and
cos b  8 17 with 3 / 2  b  2 .
Solve each equation for 0  x  2 .
26. 2 sin 2 x  1  0
27. 2 cos x  1  0
28. tan x   3
CHAPTER 10: PROBABILITY
1. A fair coin is flipped 3 times. List the possible outcomes for this situation and find the
probability that it lands on tails at least twice.
2. A bag contains 5 red marbles, 11 blue marbles, and 14 green marbles.
A marble is drawn, its color is recorded, and then the marble is put
back into the bag. This process was repeated 60 times and the results
are shown to the right. For which color marble is the experimental
probability the same as the theoretical probability?
3. Tell whether the following pair of events is considered independent or dependent.
Explain your reasoning.
You pull a card from a standard deck of 52-playing cards, put the card back into the deck,
and then select a second card.
Event A: The first card you pull out is a diamond.
Event B: The second card you pull out is a diamond.
4. The following is a breakdown of the
200 members of a health club.
a. What is the probability that a randomly selected member is divorced?
b. What is the probability that a randomly selected member is a divorced man?
c. What is the probability that a randomly selected member is divorced or a man?
d. What is the probability that a randomly selected man is divorced?
5. A menu has 3 appetizers, 6 main courses, and 5 desserts to choose from. How many
different meals are there possible if a person orders 1 appetizer, 1 main course, and 1 desert?
6. Twenty people are running in a race. In how many different ways can they come in first, second and
third?
7. To win the lottery you must correctly select 6 numbers from 1 to 50. What is the probability
of you winning the lottery?
8. Using a standard deck of 52-cards, find each of the following:
a.
b.
c.
d.
The probability that you pull out a red card.
The probability that you pull out a red face card.
The probability that you pull out a red or a face card.
The probability that you pull out a face card given that the card is red.
9. A bag contains 3 red marbles and 7 white marbles. A marble is drawn from the bag and a
marble of the other color is put into the bag. A second marble is then drawn from the bag.
Find the probability that the two marbles selected are a different color.
10. Find the coefficient of x 4 in the expansion of the binomial 3 x  2  .
10
CHAPTER 11: STATISTICS
1. The table shows the lengths of 9 songs.
Song Length (min) 3.2 3.5 3.2 7.2 3.8 4.2 3.4 3.5 3.5
a.
b.
c.
d.
Find the mean, median, and mode of the lengths.
Which measure of center best represents the data? Explain.
Identify the outlier. How does the outlier affect the mean, median, and mode?
Describe one possible explanation for the outlier.
2. The heights of a boys and girls track team are shown.
a.
b.
c.
d.
Find the range of the heights for each team. Compare your results.
Find the standard deviation of the heights of the boys track team. Interpret your result.
Find the standard deviation of the heights of the girls track team. Interpret your result.
Compare the standard deviations for the boys and the girls track teams. What can you
conclude?
3. A normal distribution has mean  and standard deviation  . Find P  3  x      for a
randomly selected x-value.
4. A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a
randomly selected x-value from the distribution is in the given interval.
a. between 25 and 37
b. at most 29
c. at least 33
5. In the United States, a survey of 1777 adults ages 18 and over found that 1279 of them do some kind
of spring cleaning every year. Identify the population and sample of this survey. Describe the
sample.
6. A survey of U.S. adults found that 10% believe a cleaning product they use is not safe for the
environment. Determine whether the numerical value is a parameter or a statistic. Explain your
reasoning.
7. You spin a five-color spinner, which is divided into equal parts,
five times and every time the spinner lands on red. You suspect
that the spinner favors red. The maker of the spinner claims that
the spinner does not favor any color. You simulate spinning the
spinner 50 times by repeatedly drawing 200 random samples of
size 50. The histogram shows the results.
a. Does the histogram have a normal distribution? Explain.
Use the histogram to determine what you should conclude when you spin the actual spinner 50 times
and the spinner land on red (b) 19 times
and
(c) 9 times.
8. Identify each type of sample described and explain why the survey is biased or not.
a. A sportswriter wants to determine whether baseball coaches think wooden bats should be
mandatory in collegiate baseball. The sportswriter mails surveys to all collegiate coaches and
uses the surveys that are returned.
b. A governor wants to know whether voters in the state support building a highway that will pass
through a state forest. Business owners in a town near the proposed highway are randomly
surveyed.
9. Identify the method of data collection each situation describes.
a. The effects of wind sheer on airplanes during both landing and takeoff are studied by using
complex computer programs that mimic actual flight.
b. An Australian study included 588 men and women who already had some precancerous skin lesions.
Half got a skin cream containing a sunscreen with a sun protection factor of 17; half got an inactive
cream. After 7 months, those using the sunscreen with the sun protection had fewer new precancerous
skin lesions. (New England Journal of Medicine).
c. A teacher records how many students enter the classroom and turn in their homework before
sitting down at their desks.
10. Determine whether the survey question may be biased or otherwise introduce bias into the survey. Explain.
“Do you think that renovating the old town hall would be a mistake?”