Free Printable Math 1 - EOC Review (Mixed)

1.

Which choice is the graph of y = (4 – x)(x + 2)?

a)

b)

c)

d)

2.

In which graph does the shaded region represent the solution set for the inequality shown below? 2x – y < 4

a)

b)

c)

d)

3.

a)

A

b)

B

c)

C

d)

D

4.

b = (a)

5.

The largest integer value of x would be (a) .

6.

In order for the net income to equal $0, the company needs to sell (a) units of its product.

7.

a)

A

b)

B

c)

C

d)

D

8.

a)

A

b)

B

c)

C

d)

D

9.

$ (a)

10.

(a) ft.

11.

a)

b)

c)

d)

12.

a)

A

b)

B

c)

C

d)

D

13.

The value of the positive zero of the function is (a) .

14.

x = (a)

15.

The value of the smaller zero of the function is (a) .

16.

a)

b)

c)

d)

17.

a)

A

b)

B

c)

C

d)

D

18.

What is the distance, in units, between the y-intercept of f(x) = x² + 7x – 18 and the y-intercept of the linear function that passes through the points shown in the table below?

distance = (a) units

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

The distance from the ground to where the ladder is touching the wall is 7 feet. The distance from the wall to the base of the ladder is 4 feet. What is the length of the ladder?

a)

√65

b)

9

c)

√49

d)

65

22.

The dimensions of a flatscreen television are 15 in and 20 in. What is the length of the diagonal across the TV?

a)

√144in

b)

√125 in

c)

25in

d)

35in

23.

What is the distance from the tee box to the hole?

a)

275 yd

b)

75625 yd

c)

385yd

d)

√385 yd

24.

Find the distance between the points (-3, 5) and (7, -1) using the distance formula.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

25.

Find the distance between the points (4, 3) and (0, 6).

a)

3

b)

4

c)

5

d)

7

26.

Find the distance between J and K.

a)

8.2

b)

7.7

c)

9

d)

10.2

27.

Find the distance between the points (5, 7) and (-2, -2).

a)

5.7

b)

5.8

c)

8.6

d)

11.4

28.

Find the midpoint of the line segment with the given endpoints (3,9) and (5,9).

a)

(-1,0)

b)

(4,9)

c)

(6,7)

d)

(7,9)

29.

What is the midpoint between (-4,4) and (-2,2)?

a)

(3,2)

b)

(-3,3)

c)

(4,5)

d)

(6,7)

30.

Find the endpoint of the segment with the endpoint of (-4, 5) and midpoint of (7, -9).

a)

(18, -23)

b)

(13, 18)

c)

(11,4)

d)

(1.5, -2)

31.

Find the endpoint of the segment with the endpoint of (-4, 5) and midpoint of (7, -9).

a)

(18, -23)

b)

(13, 18)

c)

(11,4)

d)

(1.5, -2)

32.

Find the missing endpoint if the midpoint is at (2, -5) and one endpoint is at (12, -5).

a)

(2, -5)

b)

(10, -8)

c)

(-8, -5)

d)

(12, -5)

33.

Slopes of parallel lines are...

a)

opposite reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

34.

Slopes of perpendicular lines are...

a)

opposite reciprocals.

b)

opposites.

c)

identical.

d)

always 7.

35.

Write an equation in point-slope form for a line perpendicular to $y=-5x+3$ and that passes through the point (-5, -4).

a)

$y+4=-5\left(x+5\right)$

b)

$y-4=\frac{1}{5}\left(x-5\right)$

c)

$y+4=\frac{1}{5}\left(x+5\right)$

36.

Write an equation of a line in point-slope form that passes through the point (3, 4) and is parallel to the line $y=6x+2$ .

a)

$y+4=6\left(x+3\right)$

b)

$y-4=6\left(x-3\right)$

c)

$y-4=-\frac{1}{6}\left(x-3\right)$

d)

$y-4=-6\left(x-3\right)$

37.

Are the two linear equations parallel, perpendicular, or neither?

Equation 1: 10x + 8y = 16

Equation 2: 5y = 4x - 15

a)

Parallel

b)

Perpendicular

c)

Neither

38.

What is the length of Side BD?

a)

√(10)

b)

√(90)

c)

4

d)

12

39.

What is the slope of Side AB?

a)

-4

b)

-1/4

c)

1/4

d)

4

40.

What is the length of Side AB?

a)

5

b)

10

c)

√(17)

d)

√(68)

41.

Determine the value of x that would classify this quadrilateral as a parallelogram.

a)

x = 8

b)

x = 4

c)

x = 11

d)

x = 44

42.

Adriana deposits $480 into an account that earns 2.6% annual interest. She makes no further deposits or withdrawals. Which function models the total amount, j(t), in the account after t years?

a)

j(t) = t(480)^2.6

b)

j(t) = (480)^2.6^t

c)

j(t) = 1.026(480)^t

d)

j(t) = 480(1.026)^t

43.

An arithmetic sequence has these terms.

a₅= 32

a₁₀= 52

Which explicit formula can be used to determine the nth term?

a)

a_n= 20n + 16

b)

a_n = 20n + 12

c)

a_n= 4n + 16

d)

a_n= 4n + 12

44.

Which function best represents the graph?

a)

f(x) = x² – 7x – 8

b)

f(x) = x² – 4x + 2

c)

f(x) = x² – 2x – 8

d)

f(x) = x² + 2x – 8

45.

Jacob and Heath install carpets.

Jacob charges a flat fee of $112, plus $16 for each hour he works.

Heath charges a flat fee of $200, plus $12 for each hour he works.

Which function, p(x), represents the total amount of money, in dollars, they earn when they each work x hours?

a)

p(x) = 124x + 216

b)

p(x) = 124x + 88

c)

p(x) = 28x + 312

d)

p(x) = 28x + 88

46.

Leila purchased a car for $22,000. It decreased in value by 13% each year.

Which equation represents the value of the car, V(t), after t years?

a)

$V(t)=0.87(22,000)^t$

b)

$V(t)=1.13(22,000)^t$

c)

$V(t)=22,000(0.87)^t$

d)

$V(t)=22,000(1.13)^t$

47.

The table shows the amount of mold, y, on a surface at various times, x.

Which function could be used to model the amount of mold on the surface after x minutes?

a)

$y=\frac{1}{4}\left(4\right)^x$

b)

$y=\frac{1}{4}x^4$

c)

$y=\frac{1}{16}\left(8\right)^x$

d)

$y=\frac{1}{16}x^8$

48.

Which function models the data in the table?

a)

$y=-2x+5$

b)

$y=-2x+10$

c)

$y=-\frac{1}{2}x+5$

d)

$y=-\frac{1}{2}x+10$

49.

The graph shows the number of bacteria in a petri dish over a period of time.

Which exponential function could be used to model the number of bacteria after x days?

a)

$y=1.5\left(1,266\right)^x$

b)

$y=1,266\left(1.5\right)^x$

c)

$y=1.05\left(1,266\right)^x$

d)

$y=1,266\left(1.05\right)^x$

50.

Two cellphone companies have different charges for a cell phone plan.

Caiden's provider charges $35 per month plus $0.03 per minute, x, for his phone plan.

Jonas's provider charges $0.12 per minute, x, with no monthly fee for his phone plan.

Which function represents the difference in cost between Caiden's and Jonas's plans?

a)

f(x) = ^–35x – 0.09

b)

f(x) = ^–35x + 0.09

c)

f(x) = ^–0.09x – 35

d)

f(x) = ^–0.09x + 35

51.

At the end of December, Leo and Diego both earned a one-time bonus at work, plus their hourly wages.

Leo's earnings are modeled by the function J(x) = 38.25x + 50.00.

Diego’s earnings are modeled by the function E(x) = 30.20x + 52.00.

Leo and Diego worked the same number of hours.

If x represents hours worked, which function represents the total monthly earnings of Leo and Diego, M(x)?

a)

M(x) = 170.45x

b)

M(x) = 68.45x + 102.00

c)

M(x) = 88.25x + 82.20

d)

M(x) = 102.00x + 68.45

52.

A sample of a substance with an initial mass of 963 grams is decaying at a rate of 27% per hour.

Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.

Enter your answer in the space provided.

53.

The population of wolves in an area is represented by the function $y=800\left(0.95\right)^x$ where x is the number of years since the year 2000.

In this function, a = (a) and b = (b) . This is a (c) function. The population started at (d) and decreases (e) every year.

Choose from the below words

Initial Population

Decay Rate

Exponential

Years

54.

A shipping company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year.

Which function can be used to model the number of employees, f(x), at the shipping company after x years?

(a)

Choose from the below words

f(x) = 40(1 + 0.075)^x

f(x) = 40 + 40(0.075)x

f(x) = 40^{0.075x}

f(x) = 40(1 - 0.075)^x

55.

A sample of a substance with an initial mass of 500 grams is decaying at a rate of 32% per hour.

Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.

Enter your answer in the space provided.

56.

A store owner represents the price of a car using the function $f\left(x\right)=20\left(0.95\right)^x$ where x is the number of months the item has been for sale at the store. The initial price of the item is

(a) The price of the item is (b) .

Choose from the below words

Initial Price

Current Price

Discounted Price

Final Price

57.

The population of Kinston has decreased at a rate of 0.6% each year since 1980. In 1980, the population of Kinston was 60 thousand people. Which function could be used to model the population, p, of Kinston (in thousands) x years after 1980

a)

$p=60-0.6x$

b)

$p=60(1.006)^x$

c)

$p=60(0.94)^x$

d)

$p=60(0.994)^x$

58.

Which expression is equivalent to $2f\left(x\right)-4g\left(x\right)$ if $f\left(x\right)=8x^2+5x-7$ and $g\left(x\right)\ =\ x^2+5x\ -\ 3$ ?

a)

$10x^2-8x+1$

b)

$12x^2+5x-11$

c)

$20x^2+10x+2$

d)

$12x^2-10x-2$

59.

Which function can be used to determine the number of coins in the nth figure in the pattern?

3, 9, 27

a)

$3+3^{n-1}$

b)

$3+3^n$

c)

$3(3)^{n-1}$

d)

$3(3)^n$

60.

The function $f\left(x\right)=64\left(\frac{1}{2}\right)^x$ represents the number of teams competing in a basketball tournament after x rounds. What is the range of the function in this context?

a)

$y>0$

b)

all real numbers

c)

$\left\{1,2,4,8,16,32,64\right\}$

d)

$\left\{0,1,2,4,8,16,32,64\right\}$

61.

An ice rink can hold up to 400 skaters. The owners charge $200 to rent the rink for 6 hours, plus $4 for each person skating. The total cost to rent the rink is a function of the number of people skating, p. Which inequality best represents the domain of the function?

a)

$0\le p\le200$ , where p is an integer

b)

$0\le p\le400$ , where p is an integer

c)

$200\le p\le1,600$ where p is an integer

d)

$200\le p\le1,800$ where p is an integer

62.

The function $f\left(x\right)=16\left(\frac{1}{2}\right)^x$ represents the number of teams remaining after x rounds of a softball tournament. What is the range of the function in this context?

a)

$f\left(x\right)\ge0$

b)

all real numbers

c)

$\left\{1,2,4,8,16\right\}$

d)

$\left\{0,1,2,4,8,16\right\}$

63.

This graph shows the percent of households worldwide that had a computer, y, x years after 2005.

What is the range of this data?

a)

$o\le y\le14$

b)

$0\le y\le50$

c)

$25\le y\le50$

d)

$27\le y\le49$

64.

Keylee owns a cabin that she rents to people for a maximum of 21 nights. She uses the function f(x) = 175x + 50 to calculate the rental cost for x nights. What is the domain for the function in this context?

a)

0 ≤ x ≤ 3,725, where x is an integer

b)

0 < x < 3,725, where x is an integer

c)

0 ≤ x ≤ 21, where x is an integer

d)

0 < x < 21, where x is an integer

65.

Alexa is starting a new exercise program.

Each day of the first week she will exercise 30 minutes.

Each week thereafter, she will increase her daily exercise time by 5 minutes until she is able to exercise for 60 minutes each day.

A function represents the number of minutes she will exercise in the nth week.

What is the domain of the function?

a)

{0, 1, 2, 3, 4, 5, 6, 7}

b)

{1, 2, 3, 4, 5, 6, 7}

c)

{25, 30, 35, 40, 45, 50, 55, 60}

d)

{30, 35, 40, 45, 50, 55, 60}

66.

A 150-gallon water tank is 50% filled with water. It begins leaking at a rate of 4 gallons per hour, x. The amount of water in the tank, y, is a function of time. What is the domain of the function?

a)

0 ≤ x ≤ 18.75

b)

0 ≤ y ≤ 18.75

c)

0 ≤ x ≤ 75

d)

0 ≤ y ≤ 75

67.

Nephi’s Plumbing charges a $75 diagnostic fee and $60 per hour for repairs. Sterling has a repair that could take up to 10 hours to complete. The amount of money, f(x), the company charges Sterling is a function of the number of hours, x, the job takes. What is the best range of the function?

a)

75 ≤ x ≤ 675

b)

75 ≤ f(x) ≤ 675

c)

0 ≤ x ≤ 10

d)

0 ≤ f(x) ≤ 10

68.

Asher mows yards to earn money on weekends.

He charges $25 for each yard he mows.

He has time to mow, at most, 6 yards per weekend.

The function P(x) represents the money Asher earns for mowing x yards on a weekend.

What is the domain of this function?

a)

0 ≤ x ≤ 6, where x is an integer

b)

0 ≤ x ≤ 25, where x is an integer

c)

0 ≤ x ≤ 150, where x is an integer

d)

6 ≤ x ≤ 25, where x is an integer

69.

The function f(x) = 2.5x models the amount of water, in quarts, in a bucket after x seconds. Ben needs to fill a 55-quart bucket. Which is the most appropriate domain for the function?

a)

x ≥ 0

b)

x ≤ 22

c)

0 ≤ x ≤ 22

d)

0 ≤ x ≤ 55

70.

What is the value of the larger zero?

$h\left(x\right)=-3x^2+15x+72$

71.

The function $g\left(x\right)$ is given:

$g\left(x\right)=-3x^2-6x+24$

Which statement accurately describes the function?

a)

Has a zero of -2

b)

Vertex at (1, 27)

c)

Minimum at (-1, 27)

d)

Axis of symmetry at x = -1

72.

Which choice shows a factor of $g\left(x\right)=2x^2+3x-9$

a)

$3x-2$

b)

$3x+2$

c)

$2x-3$

d)

$2x+3$

73.

$f\left(x\right)=-16x^2+16x+32$

What is the axis of symmetry for this function?

a)

$x=-1$

b)

$x=0$

c)

$x=0.5$

d)

$x=2$

74.

A function, $f\left(x\right)$ , can be defined by the equation $f\left(x\right)=\left(x-2\right)^2+5$ . Another function, $h\left(x\right)$ , is graphed in the image. Which statement is true of both functions.

a)

The parabolas have the same vertices

b)

The parabolas open downward

c)

The parabolas have the same y-intercept

d)

The parabolas have the same maximum

75.

The function $g\left(x\right)$ is graphed in the image. Which of the following has the same vertex?

a)

$q\left(x\right)=x^2-5$

b)

$h\left(x\right)=\left(x-3\right)^2+4$

c)

$p\left(x\right)=\left(x+3\right)^2+4$

d)

$f\left(x\right)=\left(x-5\right)^2+1$

76.

$f\left(x\right)=\left(x+4\right)^2-3$

$g\left(x\right)$ passes through the points shown in the table.

What is the absolute value of the difference of the y-intercepts of the $f\left(x\right)$ and $g\left(x\right)$ ?

77.

A rectangle has a perimeter of 74 centimeters. The length of the rectangle is 5 centimeters less than twice the width. What is the area of the rectangle, in square centimeters?

a)

294

b)

322

c)

336

d)

368

78.

Matthew and Kevin each begin filling pools at the same time.

Matthew fills his pool at a rate of 6 gallons per minute.

Kevin’s pool already contains 200 gallons, and he fills it at a rate of 2 gallons per minute.

How many minutes pass before both pools have the same amount of water?

a)

300

b)

100

c)

50

d)

33

79.

The equation of a line is $f\left(x\right)=\frac{1}{2}x-3$ . A second line passes through the points (^–1, 1) and (4, ^–4). At what point do the lines intersect?

a)

$\left(-2,-4\right)$

b)

$\left(-1,1\right)$

c)

$\left(0,0\right)$

d)

$\left(2,-2\right)$

80.

Mrs. Williams bought cans of pears and cans of mixed fruit.

She bought a total of 7 cans at a cost of $21.50.

Each can of pears cost $3.20, and each can of mixed fruit cost $2.90.

How many cans of mixed fruit did Mrs. Williams purchase?

(a)

81.

Halle traveled 20 miles in 3 hours.

Halle walked part of the distance at a speed of 4 miles per hour.

Halle rode her bicycle for the remaining distance at a speed of 12 miles per hour.

How many hours did Halle spend walking?

(a)

82.

Which system of equations would have no solution?

a)

$y=\frac{1}{3}x-2$

$x+3y=6$

b)

$y=3x+2$

$x+3y=-6$

c)

$y=3x+2$

$x+3y=6$

d)

$y=\frac{1}{3}x-2$

$x-3y=-6$

83.

Danna is considering two car rental plans. Plan A can be modeled with the equation $C=30d$ and Plan B can be modeled with the equation $C=25d+15$ where C represents the cost in dollars and d represents the number of days a car is rented. Which statement would justify selecting Plan B instead of Plan A?

a)

Danna rents a car for 1 day.

b)

Danna rents a car for 2 days.

c)

Danna rents a car for 3 days.

d)

Danna rents a car for 5 days.

84.

A club will create T-shirts for a fundraiser. The club members need to compare the cost of creating the T-shirts between two companies. Company A charges $30 for setup, plus $5 per T-shirt. Company B charges $15 for setup, plus $7 per T-shirt.

Which option below best interprets the results from the graphic solution of these paired equations?

a)

For orders less than or equal to 7 shirts, the cost using Company A is less.

b)

For orders less than or equal to 8 shirts, the cost using Company A is less.

c)

For orders less than or equal to 7 shirts, the cost using Company B is less.

d)

For orders less than or equal to 8 shirts, the cost using Company B is less.

85.

Farmer Darien has 300 acres of land and $117,335 available to produce corn and soybeans. Each of these acres is used to produce one of these two crops. It costs the farmer $349 per acre to produce soybeans and $444 per acre to produce corn. If all the money is used for these two crops, how many acres of soybeans are produced by Farmer Darien?

a)

133

b)

148

c)

150

d)

167

86.

An apartment building contains 100 units. The one-bedroom units rent for $495 per month and the two-bedroom units rent for $600 per month. When all the units are rented out, the total monthly rent paid by the tenants is $55,275. How many two-bedroom apartments are there?

a)

45

b)

50

c)

55

d)

66

87.

Sports Warehouse had a sale on two models of baseball gloves. Model A sold for $30.00, and model B sold for $45.25. A total of 52 gloves was sold. The total amount of sales earned on the gloves, excluding tax, was $2,078.50. How many model B baseball gloves were sold?

a)

18

b)

22

c)

29

d)

34

88.

Jamison plays basketball for the Varsity team. Last season, he scored a total of 1489 points consisting of 2-point and 3-point baskets. If Jamison made a total of 640 baskets, how many of the baskets counted 3 points?

a)

209

b)

431

c)

1227

d)

1489

89.

Layla rented a scooter for $15 per hour plus a $25 gas fee. She spent a total of $75 to rent the scooter. Which equation represents the number of hours, h, Lexi rented the scooter?

a)

$25h+15=75$

b)

$15h+25=75$

c)

$15h-25=75$

d)

$25h-15=75$

90.

The initial value of a car is $26,000. Its value decreases 12% each year. Which equation can be used to determine the number of years, t, for its value to reach 81% of the initial value?

a)

$26,000=21,060\left(0.88\right)^t$

b)

$26,000=21,060\left(0.81\right)^t$

c)

$26,000=29,545\left(0.12\right)^t$

d)

$21,060=26,000\left(0.88\right)^t$

91.

John purchases a car for $18,500. The value of the car depreciates by 11% per year. What is the approximate value of the car after 8 years?

a)

$2,035

b)

$2,313

c)

$7,283

d)

$16,465

92.

James weighs 42 pounds less than his older brother. Together they weigh 238 pounds. How many pounds does James’s older brother weigh?

(a)

93.

A used bookstore sells hardback books and paperback books.

A hardback book costs $18, including tax.

A paperback book costs $8, including tax.

Cameron bought 3 more paperback books than hardback books.

Cameron spent $154.

How many paperback books did Cam buy?

a)

5

b)

6

c)

7

d)

8

94.

Jamison works at a car dealership where he earns $600 each week plus a commission equal to 1% of his total sales. This week his goal is to earn at least $1,000. What is the minimum amount of total sales Jamison must have to reach his goal?

a)

$80,000

b)

$50,000

c)

$35,000

d)

$40,000

95.

Jersey needs a test average of 85 or higher to make the honor roll.

There are four tests in the term.

Her first three test grades were 74, 83, and 88.

Which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll?

a)

$\frac{74+83+88}{3}+x\le85$

b)

$\frac{74+83+88}{3}+x\ge85$

c)

$\frac{74+83+88+x}{4}\le85$

d)

$\frac{74+83+88+x}{4}\ge85$

96.

Leah’s coin collection has a total of 80 coins. Halle’s coin collection has two less than three times Leah’s collection. Which equation models the number of coins in Halle’s collection, x?

a)

$\frac{x}{2}-3=80$

b)

$\frac{x+2}{3}=80$

c)

$\frac{x}{2}+3=80$

d)

$\frac{x-3}{2}=80$

97.

Two students, Abby and Destiny, go for a walk. Abby begins walking 30 seconds earlier than Destiny.

Abby walks at a speed of 6 feet per second.

Destiny walks at a speed of 9 feet per second.

How long had Abby been walking when Destiny and she had walked the same distance?

a)

60 seconds

b)

540 seconds

c)

120 seconds

d)

30 seconds

e)

54 seconds

98.

Two boys, Kevin and Holden, go for a walk. Kevin begins walking 30 seconds earlier than Holden.

Kevin walks at a speed of 8 feet per second.

Holden walks at a speed of 10 feet per second.

How many minutes would pass before Holden catches up to Kevin?

a)

2 minutes

b)

30 minutes

c)

120 minutes

d)

12 minutes

e)

5 minutes

99.

Jason has a rectangular garden with a length of 10 meters and a width of 3 meters. He will double the area of the garden by adding the same number of meters to both the length and the width. What will be the length, in meters, of the garden after Jason enlarges it?

100.

A salesperson earns $350 per week, plus a 35% commission on each sale made. How much would the salesperson earn if he sold $750 worth of merch?

101.

Blake has a job selling souvenirs at the baseball stadium. He earns $10 per game plus $0.25 for each souvenir he sells. How many souvenirs does Blake need to sell to earn a total of $35 for working at one game?

102.

$-\frac{5}{6}\left(8+5b\right)=75+\frac{5}{3}b$