ANSWER KEY

Algebra I

EOC Review Booklet

1. Find the difference between the polynomials. ID: 263217 — Standard: GSE A-APR.1

(−5𝑥2 + 𝑥 − 5) − (−3𝑥2 − 8𝑥 − 3)

A. − 2𝑥2 + 9𝑥 + 5

B. − 2𝑥2 + 9𝑥 − 2

C. − 2𝑥2 + 9𝑥 − 8

D. − 2𝑥2 − 7𝑥 − 2

2. Which equation corresponds to the graph shown?

A. y = x + 1 B. y = 2x + 1 C. y = x - 2 D. y = 3x – 1

3. Which set of numbers is ordered from least to greatest?

A. 3 1

; ; ; 2 ; 48 2

B. 3 1

; ; 2 ;1; 48 2

C. 1 3

4 ; 2 ;1; ;2 8

D. 1 3

; ;1; 4 ; 22 8

4. Andrew purchased some drinks and some chips. Each bag of chips cost $2.00 and each drink cost $2.50. The expression 2x + 2.5y gives the total amount of money spent by Andrew on

chips and drinks. What is the meaning of the term 2.5y? ID: 262964 — Standard: GSE A-SSE.1a

A. The number of chips purchased by Andrew

B. The cost of one drink

C. The total amount spent on drinks by Andrew

D. The number of drinks purchased by Andrew

5. What are the zeros of the function? ID: 276120 — Standard: GSE A-REI.4b

3𝑥2 − 40 = 7𝑥

A. 𝑥 = −5,8

3

B. 𝑥 = 5, −8

3

C. x = −15, 8

D. x = −8, 15

6. Use the table to answer the questions

What is the average rate of change of f(x) over the interval 2 ( ) 0f x ?

A. -10

B. -5

C. 5

D. 10

7. How would you shift the parent function y = x2 to graph the function y = (x - 4)2+ 5? ID: 274705 — Standard: GSE F-IF.7

A. The parent function would be shifted 4 units to the right and 5 units down.

B. The parent function would be shifted 4 units to the right and 5 units up.

C. The parent function would be shifted 5 units to the right and 4 units down.

D. The parent function would be shifted 5 units to the left and 4 units up.

8. Then length of a rectangle is 6 inches. The width is 𝑤 inches. If the coefficient of the width increases by 2, what could be an expression for the area of the rectangle?

ID: 278497 — Standard: GSE A-SSE.1b

A. 12w sq in.

B. 18w sq in.

C. 4w + 12 sq in.

D. 6w + 12 sq in.

9. Which graph would represent a system of linear equations that has multiple common coordinate pairs?

A. B. C. D.

10. Find the solutions to the following equation: 𝑥2 − 2𝑥 − 4 = 0.

A. 𝑥 = 1 ± √3

B. 𝑥 =2 ± √3

2

C. 𝑥 =2 ± 2√5

2

D. 𝑥 = 1 ± √5

11. Based on the tables, what common point do the equations y = –x+5 and y = 2x–1 share?

A. (1, 1)

B. (3, 5)

C. (2, 3)

D. (3, 2)

12. The points (0, 1), (1, 5), (2, 25), and (3, 125) are on the graph of a function. Which equation represents

that function?

A. f(x)=2x

B. f(x)=3x

C. f(x)=4x

D. f(x)=5x

13. Find the product to the following expression. ID: 263221 — Standard: GSE A-APR.1

(𝑥 − 15)(𝑥 − 3)

A. 𝑥2 − 18𝑥 − 18

B. 𝑥2 − 18𝑥 − 45

C. 𝑥2 − 18𝑥 + 45

D. 𝑥2 − 12𝑥 + 45

14. Determine the area of the shaded region.

12x2+20x-8

15. Which function is modeled with this table?

A. f(x) = x + 7

B. f(x) = x + 9

C. f(x) = 2x + 5

D. f(x) = 3x + 5

16. Which of the following does not correctly illustrate a property of radical expressions?

A. √19 ⋅ √19 = 19

B. √7 ⋅ √11 = √77

C. √10 + √13 = √23

D. √105

√3= √35

17. The height h in feet of a rocket launched vertically upward from the top of a 96-foot tall bridge is given

by 𝒉(𝒕) = −𝟏𝟔𝒕𝟐 + 𝟏𝟔𝒕 + 𝟑𝟖, where t is time in seconds.

Part 1: How long will it take the rocket to strike the ground?

2.12 Seconds

Part 2: At how many seconds will the rocket be 30 ft?

1.36 Seconds

18. A manager is comparing the cost of buying ball caps with the company emblem from two different companies.

Company X charges a $50 fee plus $7 per cap. Company Y charges a $30 fee plus $9 per cap.

For what number of ball caps will the manager’s cost be the same for both companies?

A. 10 caps

B. 20 caps

C. 40 caps

D. 100 caps

19. Which is the coefficient of the cubic term of the following polynomial?

−3𝑥6 + 𝑥5 − 2𝑥4 − 6𝑥3

A. 4 B. 3 C. -2 D. -6

20. Which statement BEST describes how the graph of g(x)=-3x2 compares to the graph of f(x)=x2?

A. The graph of g(x) is a vertical stretch of f(x) by a factor of 3.

B. The graph of g(x) is a reflection of f(x) across the x-axis.

C. The graph of g(x) is a vertical shrink of f(x) by a factor of 1/3 and a reflection across x-axis.

D. The graph of g(x) is a vertical stretch of f(x) by a factor of 3 and a reflection across the x-axis.

21. What is the value of the function 𝑓(𝑥) = 𝑥2 − 5𝑥 + 2 evaluated at 𝑥 = 2?

ID: 263594 — Standard: GSE F-IF.2

A. 𝑓(2) = 16

B. 𝑓(2) = 6

C. 𝑓(2) = 2

D. 𝑓(2) = −4

22. If the parent function is f(x) = mx + b, what is the value of the parameter m for the curve passing through the points (–2, 7) and (4, 3)?

A. -9

B. -3/2

C. -2

D. -2/3

23. What value of c would make the expression 𝑥2 + 𝑥 + 𝑐 factorable? Explain in a sentence how you

arrived at your answer.

Answers may vary

24. A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased?

A. 3

B. 6

C. 9

D. 18

25. Which function shows the function f(x) = 3x being translated 5 units to the left?

A. f(x)=3x-5

B. f(x)=3(x+5)

C. f(x)=3(x-5)

D. f(x)= 3x+5

26. What is the solution of the following system of equations?

2x – 6 = 2y 3 – 2x = y

A. x = -2, y = -3

B. x = 0, y = -3

C. x = 1, y = -2

D. x = 2, y = -1

27. Jill swam 200 meters in 2 minutes 42 seconds. If each lap is 50 meters long, which is most likely to be her time, in seconds, per lap?

A. 32 seconds

B. 40 seconds C. 48 seconds

D. 60 seconds

28. Which equation corresponds to the points in the coordinate plane?

A. y = 2x – 1 B. y = x – 3 C. y = x + 1 D. y = x – 1

29. If f (12)=100(0.50)12, which expression gives f(x)?

A. f(x)=12x B. f(x)=100x C. f(x)=100(x)12 D. f(x)=100(12)x

Answer Unavailable: f(x)=100(0.5)x

30. Which is the solution of the following system of equations:

2x + y = 4 3x – y = -14

A. (-2, 8) B. (-2, 0) C. (2, 0) D. (0, -2)

31. The axis of symmetry of a parabola does not always contain which point? ID: 274719 — Standard: GSE F-IF.4

A. Maximum or minimum

B. Vertex

C. Midpoint of the x-intercepts

D. y-intercept

32. Which equation represents the graph?

A. y = 2(x+1) -2 B. y = 2(x-1) +2 C. y = 2(x+2) -1 D. y = 2(x-2) + 1

33. A model of a house is shown. What is the perimeter of the model? ID: 263275 —Standard: GSE A-APR.1

A. 32𝑥 + 12

B. 46𝑥 + 25

C. 50𝑥 + 11 D. 64𝑥 + 24

34. The sum of two numbers is 25. One number is twice the second plus seven. What are the two numbers?

A. 2, 23

B. 5, 7

C. 6, 19

D. 12, 13

35. Does the function f (x) = x2 - 10x + 18 have a maximum or a minimum and what is its value?

ID: 274721 — Standard: GSE A-SSE.3b

A. Maximum at y = 93 B. Minimum at y = 93 C. Maximum at y = -7 D. Minimum at y = -7

36. Find the mode, median, mean, lower quartile, upper quartile, interquartile range, and population

standard deviation for each data set.

Test Scores:

37 42 48 51 52 53 54 62 54

Mode: _____54____

Mean: _____50.3______

Median: _____52______

Lower quartile: ___45_______

Upper quartile: ____54______

Interquartile range: ___9______

Population standard deviation: _____6.88________

37. Calculate the average rate of change of 𝑓(𝑥) = 4𝑥2 + 3𝑥 + 5 on the interval[2,5].

ID: 274725 — Standard: GSE F-IF.6

A. 93 B. 31

C. 7

D. 10

38. Given the following functions, determine which statement is true. ID: 276018 — Standard: GSE F-IF.9

Function 1: 𝑓(𝑥) = 𝑥2 + 14𝑥 − 32

Function 2: g (x) has a vertex of (-7, 9) and a leading coefficient of 1.

A. f (x) has the zeros x = 2 and x = -16.

B. g (x) has the zeros x = 2 and x = -16.

C. Both functions have the zeros x = 2 and x = -16.

D. f (x) and g (x) have no real roots.

39. The length of a rectangle is 2 cm longer than its width. The perimeter is 16 cm. What are the length and

width of the rectangle?

A. 7 cm, 5 cm B. 6 cm, 4 cm C. 5 cm, 3 cm D. 4 cm, 2 cm

40. Michelle lives 4.5 miles from work. Kelly lives 5.6 kilometers from work. Staci lives 4,200 meters from

work. Kyle lives 670,000 centimeters from work. (1 mile = 1,609 meters) ID: 325710 — Standard: GSE N-Q.1b

Part B: Put all of the employees in order from closest distance to furthest distance from work. Justify

your answer.

Staci=2.61 miles, Kelly=3.48 miles, Kyle=4.164 miles; Michelle 4.5 miles

41. Which is the solution of the following system of equations?

-3x + 7y = 3 y =6

A. (3, 6) B. (13, 6) C. (-6, 6) D. (-15, 6)

42.

43. Use the function below to identify the following.

1322 xy

Vertex: ___(3,1)__________

Axis of symmetry: ____x=3______

Zeros: __2

32

ix ____________

Interval of increase: __[3, )_____________

Interval of decrease: ___(-__,3]___________

Average rate of change on 0 < x < 4: ______-4_____________

-4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

44. To rent a canoe, the cost is $3 for the oars and life preserver, plus $5 an hour for the canoe. Which graph models the cost of renting a canoe?

A. B. C. D

45. Which answer choice is equivalent to the expression? ID: 263225 — Standard: GSE A-APR.1

(𝑥 + 6)2

A. 𝑥2 + 12𝑥 + 12 B. 𝑥2 + 12𝑥 + 36 C. 𝑥2 + 6𝑥 + 36 D. 𝑥2 + 36

46. Juan and Patti decided to see who could read the most books in a month. They began to keep track after

Patti had already read 5 books that month. This graph shows the number of books Patti read for the next 10 days.

If Juan has read no books before the fourth day of the month and he reads at the same rate as Patti, how many books will he have read by day 12?

A. 5

B. 10

C. 15

D. 20

47. Which is the solution of the following system of equations?

y = -x 2x – y = 6

A. (6, -6)

B. (2, -2)

C. (0, 0)

D. (-2, 2)

48. Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in

costs in order to turn a profit.

It costs $10 in labor and materials to make each of his widgets. His rent each month for his factory is $4000. He sells each widget for $25.

How many widgets does Bruce need to sell each month to make the minimum profit?

A. 160

B. 260

C. 267

D. 400

49. Mrs. Chu owns a used car dealership. For the past 2 years, she has kept track of the number of cars sold

in each quarter. She needs to create a bar graph for the following information.

What variable should go on each axis? What scale should she use?

X= Quarter; scale =1

Y= # of Cars sold; start scale @ 80 and increase by 10’s

50. The concession stand sells pizza and drinks during football games. Jack bought 4 drinks and 6 slices of pizza and paid $6.70. Amy bought 4 slices of pizza and 3 drinks and paid $4.65. What price is each drink and each slice of pizza?

A. drink: $1.00 each, pizza: $1.50 each B. drink: $0.75 each, pizza: $1.00 each C. drink: $0.55 each, pizza: $0.70 each D. drink: $0.55 each, pizza: $0.75 each

51. An electrician charges a flat fee for each job, plus an hourly rate for the number of hours the job takes to complete. The total cost of the job, in dollars, can be modeled by the equation y = 55 + 72x.

What does y represent? ____Total cost of job______________________________________________

What does 55 represent? ___Flat fee for each job__________________________________

What does 72 represent? __Hourly Rate_________________________________________________

What does x represent? ____Number of hours job takes______________________________________

52. A manufacturer of jet engine harnesses has weekly production costs of C = 0.25x2 - 10x + 800 where

C is the total cost (in dollars) and x is the number of units produced. What is the average rate of change

in the cost per unit as the manufacturer increases the weekly production from 500 to 600 units? ID: 274710 — Standard: GSE F-IF.6

A. $583 per unit

B. $265 per unit

C. $848 per unit

D. $274 per unit

53. Which is the solution of the following system of equations:

y = 4 x = 6x – 3

A. (7,4) B. B. (4,7) C. C. (4,21) D. D. (7,4)

Answer unavailable: (3/5, 4)

54. The entrance to an athletic field is in the shape of a parabola. The archway is modeled by the

equation 𝒅 = −𝒙𝟐 + 𝟏𝟐𝒙, where d represents the distance, in feet, that the arc is above the ground and x is the distance between the archway.

Part 1: For what values of x will the arch be 20 feet above the ground?

x=10 and x=2

Part 2: How many feet wide is the base of the arch?

8 feet

55. What are the solutions to the equation 2𝑥2 − 2𝑥 − 12 = 0? ID: 274716 — Standard: GSE A-REI.4b

A. x = -4, x = 3

B. x = -3, x = 4

C. x = -2, x = 3

D. x = -6, x = 2

56. The quadratic function f (x) = - 45x2 + 350x + 1,590 models the population of a city where x

represents the number of years since 2005 and f (x) is the population of the city in thousands

of people. What is the estimated population of the city in 2010?

ID: 294336 — Standard: GSE F-IF.2

A. 2,215,000

B. 1,095,000

C. 2,070,000

D. 590,000

57. A certain population of bacteria has an average growth rate of 2%. The formula for the growth of the

bacteria’s population is 0 01.02 ,

tA P where P is the original population and t is the time in hours.

If you begin with 200 bacteria, about how many bacteria will there be after 100 hours?

A. 7

B. 272

C. 1,478

D. 20,000

Answer unavailable: 1,448.92

58. Which is the solution of the following system of equations:

2x + y = 5 3x – 2y = 4

A. (-1, 2) B. (0, 9) C. (1, 2) D. (2, 1)

59. The function graphed on this coordinate grid shows f(x), the height of a dropped ball in feet after its xth

bounce. On which bounce was the height of the ball 10 feet?

A. Bounce 1

B. Bounce 2

C. Bounce 3

D. Bounce 4

60. State if there appears to be a positive correlation, negative correlation, or no correlation. When

there is a correlation, identify the relationship as linear, quadratic, or exponential.

No Correlation linear negative Correlation

Quadratic positive correlation Exponential negative correlation

1)

2)

3)

4)