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Review for the Algebra EOC

The test is Thursday, January 26th, 2017

The answer key for this review booklet can be found at: www.mrshicklin.pbworks.com

1. A 1,500-gallon tank contains 200 gallons of water. Water begins to run into the tank at the rate of

75 gallons per hour. After 2 hours, the rate increases to 80 gallons per hour. What is the total number of hours that the water can flow before the tank is full, but not overflowing?

O A. 14 hours, 22.5 minutes

O B. 16 hours, 22.5 minutes

O C. 17 hours, 20 minutes

O D. 18 hours, 45 minutes 2. Which statement best describes the difference(s) between the graphs of :

𝑓(𝑥) = 3𝑥 − 10 and 𝑔(𝑥) = 6𝑥 − 5

O A. The graph of 𝑓(𝑥) is twice as steep as the graph of 𝑔(𝑥)

O B. The graph of 𝑓(𝑥) is half as steep as the graph of 𝑔(𝑥)

O C. The graph of 𝑓(𝑥) has a y-intercept of –5 while 𝑔(𝑥) has a y-intercept of –10.

O D. The graph of 𝑓(𝑥) has a lower y-intercept than the graph of 𝑔(𝑥)

3. Solve the equation for 𝑥 :

7 − 3(2𝑥 − 4) = 5𝑥 − 2

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4. Solve for 𝑥: 22

𝑥 − 3+ 4 = 7

O A. 𝑥 =31

3

O B. 𝑥 =47

7

O C. 𝑥 =55

3

O D. 𝑥 =29

7

5. Mr. Shaw begins traveling east on the freeway with a full tank of gasoline. His car has an 18-gallon

gas tank and gets 25 miles per gallon during highway travel.

Let m = the number of miles Mr. Shindler has driven Let g = the number of gallons of gas remaining in his tank

Select which equation describes the relationship between the number of miles Mr. Shaw has traveled and the number of gallons remaining in his gas tank:

O A. 𝑔 = 18 − 25𝑚

O B. 𝑚 = 25𝑔 − 18

O C. 𝑔 = 18 −𝑚

25

O D. 𝑚 =25

𝑔− 18

Justify your choice in the answer box below. Support your answer using words, numbers, &/or diagrams.

6. Choose the correct solution to the equation

3𝑥 − 1

2= 4𝑥 + 3

O A. 𝑥 = 2

O B. 𝑥 = −7

5

O C. 𝑥 = −4

O D. 𝑥 =5

7

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7. Given the inequality: −5 < 2𝑥 + 7 ≤ 12 .

Solve for 𝑥:

Represent the set of solutions on a number line: 8. One worker at a gadget assembly factory can assemble 10 gadgets each hour. After working for 3

hours, the worker’s supervisor starts to assemble gadgets also. The supervisor can assemble 12 gadgets each hour. Together, they assemble 140 gadgets.

How many hours did the worker assemble gadgets in order to have 140, total? Support your answer using words, numbers, and/or pictures.

How many hours will the worker assemble gadgets? __________

9. Solve the system of linear equations.

{ 3𝑥 + 𝑦 = 13 𝑥 + 5𝑦 = −5

O A. (-5, 28)

O B. (-2, 19)

O C. (7, 2)

O D. (5, -2)

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10. An ice cream store is keeping track of the number of chocolate and vanilla ice cream cones sold. One day, the number of chocolate cones sold was 10 less than twice the number of vanilla cones sold. A total of 140 cones were sold that day.

Write equations to determine the number of chocolate cones sold that day.

Be sure to define your variables.

Use the equations to determine the number of chocolate cones sold that day.

Show your work using words, numbers, and/or diagrams.

11. After solving the following system of equations:. {𝑦 = 2𝑥 − 5

4𝑥 − 2𝑦 = 10

Sarah claimed that the system has no solution. Carl disagreed and said that the system has an infinite number of solutions. Who is correct and why?

Who is correct? __________________

Show work to justify your conclusion. Explain how your work supports your conclusion:

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12. A moving box can hold at most 40 pounds. I have at least 50 books to load into the box. On average, the hardcover books weigh 3 pounds and paperbacks weigh 1 pound.

Write a system of inequalities to represent the situation.

Define your variables. 13. Tara’s cell phone plan costs $35.00 a month, which includes 150 text messages. After she uses all

of those text messages, it will cost her $0.12 per text message.

Write an equation or inequality that could be used to determine the total cost of her

cell phone bill if she sends more than 150 text messages.

Be sure to define your variables.

Tara wants to spend no more than $48 on her cell phone bill. How many text messages can she

send, total? Support your answer with words, numbers, and/or diagrams.

Explain what your answer means:

Equation/inequality: definition of variable:

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14. Fred, Thomas, and Zachary worked at the ice cream store in the mall. Last week, Fred earned more money than Thomas, but less than Zachary. The graph shows the money earned by Zachary and Thomas.

Which area of the graph represents Fred’s possible weekly pay, and why?

O A. P because that represents more than Thomas.

O B. T because that represents more than Zachary and less than Thomas.

O C. P because that represents more than both Zachary and Thomas.

O D. T because that represents more than Thomas and less than Zachary. 15. Which is the graph of the solution set of the system of inequalities?

x 2y 10

2x y 0

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16. Look at the system of linear inequalities.

{ 𝑥 − 𝑦 < 3𝑥 + 𝑦 < 8

Which graph represents the solutions to the system of linear inequalities?

O A.

O B.

O C.

O D.

17. Graph A is the graph of 𝑦 = 2(3)𝑥 and graph B is the graph of 𝑦 = 3(2)𝑥 .

Which statement about the two graphs is true?

O A. Both graphs A and B rise at the same rate.

O B. Graph B rises at a faster rate than graph A.

O C. Graph A rises at a faster rate than graph B.

O D. The y-intercept of graph A is above the y-intercept of graph B. 18. In 2000, there were 4800 people who attended the state basketball tournament. The enrollment

has been increasing 3% annually since then.

Create an equation that would determine the total number of people who will attend after x years. (Let 𝑥 = 0 represent the year 2000.)

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19. Solve the equation 2𝑥 = 68 .

O A. 𝑥 = 5

O B. 𝑥 = 6

O C. 𝑥 = 34

O D. 𝑥 = 64

20. In the laboratory, a bacteria population grows in size every hour, as shown in the table. A new

bacteria culture is started with 20 bacteria.

Hour 1 2 3 4 # bacteria 40 80 160 320

Create a function that describes the size of the bacteria population, 𝑃(𝑡), in terms of the number of hours, t.

Predict the number of bacteria in 7 days.

After how many hours will the population first exceed 10,000?

a) 7 hours

b) 8 hours

c) 9 hours

d) 10 hours

21. The student population at a high school has been decreasing each year, as shown in the table.

Years 1 2 3 4 5 # students 1230 1205 1180 1155 1130

Write a function, for 𝑡 ≥ 1 to represent the number of students, 𝑆(𝑡), based on the number of students from the previous year, 𝑆(𝑡 − 1).

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22. Consider a sequence given by the formula: 𝑓(𝑛) = 5 − 8(𝑛 − 1) Which of the following is an equivalent sequence?

e) 𝑓(𝑛) = 5𝑛 − 1 𝑤𝑖𝑡ℎ 𝑓(1) = 8

f) 𝑓(𝑛) = 𝑓(𝑛 − 1) + 5 𝑤𝑖𝑡ℎ 𝑓(1) = 8

g) 𝑓(𝑛) = 𝑓(𝑛 − 1) − 8 𝑤𝑖𝑡ℎ 𝑓(1) = 5

h) 𝑓(𝑛) = 𝑓(𝑛 − 1) − 8𝑛 𝑤𝑖𝑡ℎ 𝑓(1) = 5

23. Given the functions: 𝑓(𝑥) =1

3𝑥 + 5 and 𝑔(𝑥) = 5 (

1

3)

𝑥

Select all the statements that apply to the functions: (4 pts)

a) 𝑓(𝑥) and 𝑔(𝑥) have the same y-intercept;

b) 𝑓(𝑥) and 𝑔(𝑥) are linear functions;

c) 𝑓(𝑥) and 𝑔(𝑥) are decreasing functions;

d) 𝑓(𝑥) is an increasing function, 𝑔(𝑥) is a decreasing function.

24. The graph of a function is shown.

Which of the following equations is represented by the graph? (1 pt)

a. 𝑓(𝑥) = 2 (1

2)

𝑥

b. 𝑓(𝑥) = 1

2(2)𝑥

c. 𝑓(𝑥) = 1

2𝑥 + 2

d. 𝑓(𝑥) = 2𝑥 +1

2

25. Given the functions: 𝑔(𝑥) = −(𝑥 − 3)2 + 2 and 𝑓(𝑥) = 𝑥2 ,

describe the graph shifts needed to create the graph of 𝑔(𝑥) from the graph of 𝑓(𝑥).

x

y

(0, 2)

(2, 0.5)

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26. A group of functions are shown.

𝑎(𝑥) = |𝑥 + 5| 𝑏(𝑥) = 3|𝑥| 𝑐(𝑥) = |𝑥| + 5

𝑑(𝑥) = −|𝑥| − 3 𝑒(𝑥) = |𝑥 − 3| + 4 𝑓(𝑥) = |𝑥| − 4

Sort the functions based on the graph shifts compared to the parent function. Write the function’s letter in the correct category below. You may need to write a letter in more than one box.

left right down up stretched reflected

27. Given the function 𝑓(𝑥) = |𝑥| + 3 , for what values of 𝑥 is the function positive?

O A. always

O B. when 𝑥 < −3

O C. when 𝑥 > 3

O D. never 28. Graph A is the graph of 𝑦 = |𝑥 + 3| − 4 and graph B is the graph of 𝑦 = 3|𝑥| − 8 .

Which statement about the two graphs is true?

O A. Graph A and B have the same slope.

O B. Graph A is less steep than graph B.

O C. Graph B has a y-intercept that is 4 units above the y-intercept of Graph A.

O D. Graph B has a vertex that is 8 units below the vertex of Graph A.

29. Choose the equation that matches the graph:

a. 𝑦 = −|𝑥 − 2| + 8

b. 𝑦 = −|𝑥 + 2| − 8

c. 𝑦 = −(𝑥 + 2)2 + 8

d. 𝑦 = −(𝑥 − 2)2 + 8

x

y

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30. Select ALL of the following that are not functions:

O A.

O B.

O C.

O D.

31. Look at the function.

Identify the domain and range:

O A. Domain: −5 ≤ 𝑥 ≤ 8, Range: −3 ≤ 𝑦 ≤ 3

O B. Domain: −5 ≤ 𝑥 ≤ 8, Range: −4 ≤ 𝑦 ≤ 4

O C. Domain: −3 ≤ 𝑥 ≤ 2.5, Range: −4 ≤ 𝑦 ≤ 3

O D. Domain: −4 ≤ 𝑥 ≤ 4, Range: −5 ≤ 𝑦 ≤ 8

32. Given the same graph as the previous problem, fill out the following table:

For the interval: 𝑥 < −1 −1 ≤ 𝑥 < 2 2 ≤ 𝑥 < 8

Is 𝑓(𝑥) increasing?

Is 𝑓(𝑥) decreasing?

Is 𝑓(𝑥) staying constant?

Is 𝑓(𝑥) both increasing and decreasing?

33. Given that 𝑓(𝑥) = 3(5𝑥 − 2), find 𝑥 when 𝑓(𝑥) = −18.

{(4,1), (7, -2), (-2,4), (1, 2)}

x

y

x

y

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34. Given the function: 𝑓(𝑥) = −𝑥2 − 6𝑥 + 1 evaluate 𝑓(−2).

35. You are a full time employee at a marketing firm. In order to maintain full-time status you must

work a minimum of 25 hours a week, and you cannot work more than 45 hours in a week. You make $20 per hour.

Define the domain and range variables in the context of the problem.

Express the domain and range as inequalities.

The graph shows the functions 𝑓(𝑥) = (𝑥 − 1)2 − 4 and 𝑔(𝑥) = −𝑥 + 3 .

36. Identify the value(s) of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥)

37. Fill out the following table:

at the value: Is 𝑓(𝑥) > 𝑔(𝑥) ? Is 𝑓(𝑥) < 𝑔(𝑥)?

𝑥 = −1

𝑥 = 4

x

y

𝑔(𝑥)

𝑓(𝑥)

Define domain Define range

variable: variable:

Domain inequality: _________________ Range inequality: ________________

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38. At a particular company, every employee receives a 4% cost-of-living increase to their salary. What impact does this have on the mean and on the range of salaries at the company?

O A. The mean increases but the range stays the same.

O B. The mean stays the same but the range increases.

O C. The mean and range both increase.

O D. The mean and range do not change. 39. A company decides to give every one of its employees a $1000 raise. What happens to the mean

and median of the salaries as a result?

O A. Mean stays the same, median increases by $1000

O B. Mean increases by $1000, median stays the same

O C. Mean and median stay the same

O D. Mean and median both increase by $1000. 40. A company decides to pay its employees the following salaries: $200 per week $250 per week $350 per week $8000 per week

Which statistical measure best describes the typical salary, and why?

O A. The mean, because it is not affected by extreme values.

O B. The mean, because it is the average of everyone’s salary.

O C. The median, because it is not affected by extreme values.

O D. The median, because it is the average of everyone’s salary.

41. The box plot below shows the ages of football players on a school’s football team. Select all of the statements that are supported by the box plot:

a) The youngest player on the team is 15.

b) The median age of the players is 17.

c) 25% of the players are between 17 and 18 years old.

d) 50% of the players are between 15 and 17 years old.

e) The mean age of the players is 16.5 years old.

f) Only one player is 14.5 years old.

14 15 16 17 18

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42. The two-way frequency table below shows the results of a survey regarding transportation to school at a high school:

Ride the bus Walk or ride bike Drive a car total

Freshmen 130 20 0 150

Sophomores 70 25 25 120

Juniors 55 15 60 130

Seniors 10 10 80 100

Total 265 70 165 500

Select ALL of the statements that are supported by this data:

a) The relative frequency of freshmen riding the bus is 130

500 .

b) The relative frequency of sophomores driving is lower than the relative frequency of freshmen

walking or riding their bikes.

c) The conditional frequency for a senior who drives is 80

100 .

d) The conditional frequency for a junior who rides the bus is lower than the conditional

frequency for a sophomore who rides the bus.

The graph shows the stock value for a company. 43. Which equation represents a line to fit the

data?

a) 𝑦 =1

2𝑥 + 20

b) 𝑦 = 8𝑥 + 20

c) 𝑦 = 0.125𝑥 + 20

d) 𝑦 = 10𝑥 + 20

44. What will be the most likely value of the

stock in year 10?

O A. $60

O B. $65

O C. $70

O D. $75

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8 9 10 11 12

Val

ue

(d

olla

rs)

years since 1999

Stock Value

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45. Lucy did a study on the number of hours students spend studying and their grades. She found that there was a strong positive correlation between the two.

Which scatterplot shows the strong, positive correlation of her data?

O A.

O B.

O C.

O D.

46. Samantha is gathering data to see if a vehicle’s weight is

related to its gas mileage. Her results are in this graph:

The line of best fit for this graph is: 𝑦 = −15𝑥 + 63

a) Use the equation to predict the gas mileage of a car that weighs 3 tons.

b) If the gas mileage of a car was 25 miles per gallon, how heavy would you expect the car to be?