Download Topics in Math Spring Exam Review

Topics in Math
Spring Exam Review
1. A polling company conducted a survey of voters to obtain data for a political campaign. They
selected 3500 voters randomly from the 168,000 names on the voter registration lists of the
county and found that 1372 intended to vote for candidate Doe. The 3500 voters represent:
2. A polling company conducted a survey of voters to obtain data for a political campaign. They
selected 3500 voters randomly from the 168,000 names on the voter registration lists of the
county and found that 1372 intended to vote for candidate Doe. The 168,000 names
represent:
3. A marketing company conducted a survey of college students to obtain data for an advertising
campaign. They selected 1421 students randomly from campus directories of 132 colleges and
universities. The 1421 students represent:
4. A marketing company conducted a survey of college students to obtain data for an advertising
campaign. They selected 1421 students randomly from campus directories of 132 colleges and
universities. The students in the directories at the 132 colleges and universities represent:
5. To determine the proportion of voters who favor a certain candidate for governor, the
campaign staff phones 2500 residents of the state chosen from the state property tax rolls.
The 2500 residents represent:
6. To determine the proportion of voters who favor a certain candidate for governor, the
campaign staff phones 2500 residents of the state chosen from the state property tax rolls. All
property owners in the state represent:
7. In order to determine the mean weight of bags of chips filled by its packing machines, a
company inspects 50 bags per day and weighs them. In this example, the population is:
8. To estimate the proportion of voters in a town likely to favor a tax increase for road repair, a
random sample of people chosen from the voter registration list is surveyed and the
proportion who favor the increase is found to be 43%. The actual proportion in the town is
40%. This difference is most likely an example of sampling:
9. To determine the proportion of students at a university who favor the construction of a
parking garage, a sample of people driving through the student center parking lot is surveyed
and it is found that 45% favor the garage. The actual proportion of the student body who favor
the garage is 40%. This difference is most likely an example of sampling:
10. To determine the proportion of students at a university who favor the construction of a
parking garage, a sample of people on the current enrollment list is surveyed and it is found
that 45% favor the garage. The actual proportion of the student body who favor the garage is
40%. This difference is most likely an example of sampling:
11. To estimate the mean income of all residents in a town, a sample of people chosen from the
telephone directory is surveyed and the mean is found to be $43,000. The actual mean income
in the town is $40,000. This difference is most likely an example of sampling:
12. A polling company surveys 200 people outside a county courthouse concerning tighter
restrictions on smoking in public buildings. Their results indicate that 34% of those surveyed
favor tighter restrictions. The actual proportion of county residents who favor tighter
restrictions is 65%. The difference is most likely due to:
13. To determine the proportion of students at a university who favor the construction of a
parking garage, a student senate member surveys students as they leave the student union.
This type of sample is a:
14. In order to determine the proportion of voters in a small town who favor a candidate for
mayor, the campaign staff takes out an ad in the paper asking voters to call in their preference
for mayor. This type of sample is a:
15. A marketing company conducts a survey of college students to obtain data for a marketing
campaign. They randomly select five in-state colleges and then randomly choose 100 students
from the registration lists of these colleges. This type of sample is a:
16. To estimate the number of motorists likely to favor a tax increase for road repair, a polling
company chooses 1000 names at random from a list of registered car owners provided by the
county license office. This type of sample is a:
17. A die is rolled and a coin is flipped simultaneously. The number rolled on the die and whether
the coin lands heads or tails is recorded. How many outcomes are in the sample space?
18. Two coins are flipped at the same time and it is recorded whether each coin lands heads or
tails. The sample space for this is:
19. A spinner numbered 1 through 10 is spun and one die is tossed simultaneously. The number
spun and the number rolled are recorded. How many outcomes are in the sample space?
20. A spinner numbered 1 through 10 is spun and one die is rolled simultaneously. The sum of the
number spun and the number rolled is recorded. How many outcomes are in the sample
space?
21. Three dice are tossed. The number rolled on each die is recorded. How many outcomes are in
the sample space?
22. Three dice are tossed. The sum of the numbers rolled is recorded. How many outcomes are in
the sample space?
23. Three dice are rolled and the number rolled on each die is recorded. The outcomes in the
sample space are all equally likely. (T or F)
24. Three dice are rolled and the sum of the numbers rolled is recorded. The outcomes in the
sample space are all equally likely. (T or F)
25. Two coins are flipped and the number that landed on heads is recorded. The outcomes in the
sample space are all equally likely. (T or F)
26. Two coins are flipped and whether each one landed heads or tails is recorded. The outcomes
in the sample space are all equally likely. (T or F)
27. There are seven blue and six black socks in a drawer. One is pulled out at random. Find the
probability that it is black.
28. Two fair dice are rolled and the sum rolled is recorded. Find the probability that the sum is 4.
29. A fair coin is tossed three times. Find the probability of getting exactly 2 heads.
30. If a fair die is rolled once, what is the probability of getting a number less than five?
31. A computer is programmed to randomly print two letters in a row without repeating a letter.
What is the probability that the first combination printed is the word "DO"?
32. We need to create three-digit code numbers that must begin with a 7. How many such codes
can be made?
33. We need to create serial numbers that start with one of the letters a, b, c, d, or f followed by
three non-repeating digits. How many serial numbers can be created?
34. We need to create code words that use three letters of the alphabet. Repeating of letters is
allowed. How many code words can be created?
35. A computer system requires users to have an access code that consists of a three-digit number
that is not allowed to start with zero and cannot repeat digits. How many such codes are
possible?
36. The Olympic flag consists of five intertwined circles, one in each of the colors black, blue,
green, red, and yellow. What is the probability that a random coloring of the five circles using
these colors will produce the exact match of the Olympic symbol?
37. Either Terry, Chris, or Kim will attend a party. The probability Terry attends is 0.31 and the
probability Chris attends is 0.5. What is the probability that Kim attends?
38. If there is a 0.8 probability of rain today, what is the probability it will not rain?
39. A sample space has three outcomes, A, B, and C. The probability of outcome A is 0.39 and the
probability of outcome B is 0.25. What is the probability of outcome C?
Simplify the rational expression.
40.
41.
Multiply or divide. State any restrictions on the variables.
42.
43.
44.
45.
Add or subtract. Simplify if possible.
46.
47.
Simplify the complex fraction.
48.
49.
Solve the equation. Check the solution.
50.
51.
52.
Find the period of the graph shown below.
2 y
1
O

2
3 
–1
–2
Sketch one cycle of y = 4 sin 4.
53.
x
y
Amp: ____ Period: _____
Increments: ________
Key
Point
54.
A particular sound wave can be graphed using the function
function.
. Find the amplitude and period of the
55.
Write the equation for the sine function shown below.
y
4
2
O

2

–2
–4
56.
Find the amplitude of the sine curve shown below.
y
4
2
O

2
3

–2
–4
Write an equation of the cosine function with amplitude 2 and period 4.
57.
Graph the function in the interval from 0 to 2.
58.
y = 4 cos
x
y
1

2
Key
Point
Amp: ____ Period: _____
Increments: ________
y
59.
Find the amplitude of the periodic function of the graph to the right.
4
2
–4
–2
2
–2
–4
Simplify the radical expression.
60.
Multiply and simplify if possible.
61.
Divide and simplify. Assume that all variables are positive.
62.
Add if possible.
63.
4
x
Subtract if possible.
64.
Simplify.
65.
66.
Solve the equation. Show your work.
67.
68.
Use the graph of the sine function
shown below for 69-70.
y
2
O

2

–2
69.
How many cycles occur in the graph?
70.
Express in simplest form without negative or zero exponents
71.
 2ab  3a 
4
2
72.
Find the period and amplitude of the graph.
 4 x y 
 2 x y 
2
4 2
2
3 3
Simplify
73.
x 2  9 x  20
2x  8
Solve
74.
12
7
2


x  5x  6 x  3 x  2
2
75.
2
7
4x  2

 2
x  6 x  2 x  4 x  12