Algebra 2 Semester B EOS Final Exam Review

Question 1

Are these lines parallel, coincident or intersecting?

x- 2y =1

-2x+4y =9

Question 2

Solve and graph the following inequality: 3x + 4 < 10.

Question 3

Solve the linear system graphically

Question 4

Graph the following system:

3x + 2y < 12

x - 2y > -4

Answer: Start by solving both for y:

3x + 2y < 12 x - 2y > -4

2y < -3x + 12 -2y > -x - 4

y < (-3/2)x + 6 y < (1/2)x + 2 (Remember, we divided by a negative.)

Now, graph the lines y = (-3/2)x + 6 and y = (1/2)x + 2:

Now, in both cases, we shade below the line because the inequality is less than, so the solution is the common shaded area (dark green):

Question 5

Solve the equation for x and round your answer to the nearest hundredth.
5x+14=26

Question 6

Solve this system of equations

4x + y =24

Y = -4x +24

Answer:
(5,4)

Question 7

Make sure you know about transformations of graphs. For example, how would the following graph change if I added 2 to it? See below.

You would move the graph of by 2 units up to obtain the graph of .

Question 8

The advertising and sales model of a company is given by the functionS= 2t2+ 100, wheretis time in months andt≥ 0. If advertising is delayed by a month, which type of transformation will occur to this model?

shift along thex–axis

shift along they–axis

reflection through they–axis

reflection through the origin

Answer is A.

Question 9

What is the arc length of the subtending arc for an angle of 60° on a circle of radius 3?

Answer: π

Question 10

What is 7π / 3 in degrees?

Question 11

Find the reference to angle A = - 15 π / 4

Solution :
The given angle is not positive and less than 2Pi. We can use the positive and less than 2Pi coterminal Ac to angle A.
Ac = - 15 Pi / 4 + 2 (2 Pi) = Pi / 4
Angle A and Ac are coterminal and have the same reference angle. Ac is in quadrant I, therefore
A r = A c = Pi / 4

Question 12

If sin@ = 9/ 15 and cos@ < 0 then what is tan @?

Question 13

If the point (3/5,4/5)corresponds to an angleθ in the unit circle, what is tanθ ?

Answer: 4/3

Question 14

What are the correct definitions for cot , tan , csc, sec?

Question 15

Make sure you know these trigonometric identities:

sin2(t) + cos2(t) = 1 tan2(t) + 1 = sec2(t) 1 + cot2(t) = csc2(t)

1 – cos2x =sin2 x

Question 16

What is the range of the function y = 1 + 2sin(x- )?

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-1 to 1

-2 to 2

0 to 3

-1 to 3

-3 to 3

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Question 17

Which expression is equivalent to (cos x + 1)(cos x − 1)?

Question 18

In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for the true proportion of all individuals who are fans of the New York Yankees?

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Answer:116

Question 19

The mean and standard deviation of a population being sampled are 64 and 6, respectively. If the sample size is 50, what is the standard error of the mean?

Answer: .85

Question 20

A dealer dealt the following cards from a shuffled deck:
3 , 2 , 2, A, K, Q, K , 5 , 2, 6
4 , 5, K, 2, 7, 6, A , J , J, A
What was the experimental probability of dealing a black card?

Question 21

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data?

About 160 people weigh more than 165 pounds.

About 320 people weigh more than 165 pounds.

About 320 people weigh less than 165 pounds.

About 640 people weigh less than 165 pounds.

Answer:about 160

Question 22

The difference of sample means of two populations is 108.7, and the standard deviation of the difference in sample means is 32. Which statement is true if we are testing the null hypothesis at the 68% confidence level?

The difference of the two means is significant at the 68% confidence level, so the null hypothesis must be rejected.

The difference of the two means is significant at the 68% confidence level, so the null hypothesis must be accepted.

The difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be rejected.

The difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be accepted.

Answer: A

Question 23

The difference of the two means is significant at the 68% confidence level, so the null hypothesis must be rejected.

The difference of the two means is significant at the 68% confidence level, so the null hypothesis must be accepted.

The difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be rejected.

The difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be accepted

Answer:A

Question 24

Dana and Martin are working for the meteorological department Wyoming. They have to record snowfall that 50 sites across Wyomingreceive through the year. What type of statistical study is this?

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theoretical study
experiment
observational study
survey
investigative report

Question 25

Why would a pharmaceutical company opt for experimental studies to conducting surveys or observational studies?

Question 26

Suppose two drugs are routinely used for treatment of a particular kidney disorder. Drug 1 is known to cure the disease 85% of the time and costs $90. Drug 2 is known to cure the disease 70% of the time and costs $65. The two drugs work independent of each other (that is, administration of one has no effect on the efficacy of the other). The two treatment plans are as follows:
Plan A: Treatment with Drug 1—if not effective, treatment with Drug 2.
Plan B: Treatment with Drug 2—if not effective, treatment with Drug 1.
Which statement is most correct in this situation?

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Based on the overall probability of a cure, plan 1 should be selected over plan 2.

Based on the overall probability of a cure, plan 2 should be selected over plan 1.

Based on the overall cost of treatment, plan 1 should be selected over plan 2.

Based on the overall cost of treatment, plan 2 should be selected over plan 1.

Based on the probability of a cure and the cost of treatment, both plans are equivalent, so either can be selected.

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Question 27

passage 18223

A businessman bought a car dealership that is incurring a loss of $500,000 a year. He decided to strategize in order to turn the business around. In addition to the $500,000 annual loss, his fixed cost for running the dealership on a monthly basis is $5,000. The number of cars sold per week and their probabilities mimic the outcomes of three coins being flipped. The number of cars sold in a week was observed to be the same as the number of tails that appear when three coins are flipped. See the distribution:

Number of Tails / 0 / 1 / 2 / 3
Probability / 1

8 / 3

8 / 3

8 / 1

8

Question 28

Read passage 18223 to answer this question

What is the expected number of cars sold in one week?

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Question 29

Read passage 18223 to answer this question

Given that there are 52 weeks in a year, what is the expected revenue per car (rounded to the nearest dollar) that has to be made in order to break even in the first year?

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Question 30

A survey was taken of randomly-selected Palm Beach county students. 1,000 students where asked if they preferred math to science. The sample proportion was found to be 79%. Which statement is true?

790 students must prefer math to science.
Less than 790 students must prefer math to science.
More than 790 students must prefer math to science.
The sample proportion must precisely represent the entire population’s choice.
The population proportion is not necessarily equal to the sample proportion.

Question 31 What is the standard error of the proportion if 80% of the 1,200 respondents in a yes/no survey answered "no"?

Question 32

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data?

About 160 people weigh more than 165 pounds.

About 320 people weigh more than 165 pounds.

About 320 people weigh less than 165 pounds.

About 640 people weigh less than 165 pounds

Answer:A

Question 33

Alice has measured the hemoglobin levels of 200 people. If the data follows a normal distribution with a mean of 10 and a standard deviation of 1, what can you conclude?

About 64 people have hemoglobin levels less than 9.

About 32 people have hemoglobin levels less than 9.

About 64 people have hemoglobin levels less than 8.

About 32 people have hemoglobin levels less than 8

Answer:B

Question 34

The table shows the total number of student applications to universities in a particular state over a period of 12 semesters.States base their decisions on data like this. Suppose they decide that if fewer than 200,000 students applyduring 6 or more semesters, the state will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?

Answer: 42%

A certain survey conducted had a population proportion of at most 22% for people who agreed. What is the confidence level if 20% of the people sampled agreed, and the standard error of the proportion is ±1%?

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Question 35

f(x) = (x + 9)2 and g(x) = x2 − (x + 9)2. Find f(x) − g(x).

Question 36

and . Find f(x) g(x).

Question 37

A report on Americans' attitudes toward teachers' pay found that 82% of the respondents to the survey upon which the report is based think that teachers don't make enough money. Which factor is most relevant when evaluating this report?

49% of the respondents were women.

78% of the respondents were married.

51% of the respondents were men.

62% of the respondents were educators

Question 38

Be sure that you can summarize the information if you are given the mean and the standard deviation. (What does that tell you?).

Also, Make sure you know the difference between experimental and observational studies.