Free Printable EOC Review

1.

What is the product of the following expression?

$\left(3x+6\right)^2$

a)

$6x^2+12$

b)

$9x^2+36$

c)

$9x^2+18x+36$

d)

$9x^2+36x+36$

2.

Which is the simplified form of this expression?

$\left(2x+3\right)\left(x-6\right)-2x^2+3x+30$

a)

$4x^2-6x+12$

b)

$-2x^2+6x+27$

c)

$-6x-12$

d)

$-6x+12$

3.

In the diagram, the dimensions of the large rectangle are $\left(3x-1\right)$ and $\left(3x+7\right)$ units. The dimensions of the cut-out rectangle are $x$ by $\left(2x+5\right)$ units. Which choice expresses the area of the shaded region, in square units?

a)

$x^2+23x-7$

b)

$x^2+13x-7$

c)

$7x^2+23x-7$

d)

$7x^2+13x-7$

4.

There are 60 students going on a field trip to the chocolate factory. The students are from three different classes. Mrs. Hooper's class has 24 students and Mr. Gomez's class has 18 students. Which of the equalities correctly describes the students and could be used to solve for how many students are from Mr. Anderson's class? (Let A = the number of students in Mr. Anderson's class.

a)

$A+18=24$

b)

$A+A+A=60$

c)

$60-18=A-24$

d)

$24+18+A=60$

5.

The ages of three friends are consecutively one year apart. Together, their ages total 48 years. Which equation can be used to find the age of each friend (where a represents the age of the youngest friend)?

a)

$3a=48$

b)

$a\left(a+1\right)\left(a+2\right)=48$

c)

$a+\left(a-1\right)+\left(a-2\right)=48$

d)

$a+\left(a+1\right)+\left(a+2\right)=48$

6.

The ages of three friends are consecutively one year apart. Together, their ages total 48 years. Using the equation you came up with before (where a represents the age of the youngest friend), what are the ages of the friends?

a)

16, 17, 18

b)

15, 16, 17

c)

14, 15, 16

d)

17, 18, 19

7.

Student council is renting a tent for $350 for an upcoming student fair. Each student attending the fair will pay $0.50. All other attendees will pay $2.25 each. If 200 students attend the fair, which inequality can be used to determine the number of "other" attendees, a, needed to cover the cost of the tent?

a)

$\left(0.50\right)\left(200\right)-2.25a\ge350.00$

b)

$\left(0.50\right)\left(200\right)+2.25a\ge350.00$

c)

$0.50a-\left(2.25\right)\left(200\right)\ge350.00$

d)

$0.50a+\left(2.25\right)\left(200\right)\ge350.00$

8.

A heart shaped chocolate box is composed of one square and two half circles. The total number of chocolates in the box is calculated by adding the area of a square given by $4x^2$ and the area of the circle approximated by $3x^2$ . The company plans to add a small additional box for a promotional campaign containing one row $\left(2x\right)$ of chocolates. If the total combined heart shape and small box contain 69 chocolates, which of these equations could be utilized to solve for the number of chocolates in the small box (2x)?

a)

$4x^2+3x^2+2x=69$

b)

$4x^2-3x^2+2x=69$

c)

$4x^2+3x^2-2x=69$

d)

$4x^2-3x^2-2x=69$

9.

A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by 20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the area of the new field?

a)

$\left(100+2x\right)\left(150+x\right)=18,000$

b)

$2\left(100+x\right)+2\left(150+x\right)=15,000$

c)

$\left(100+x\right)\left(150+x\right)=18,000$

d)

$\left(100+x\right)\left(150+x\right)=15,000$

10.

Solve for x: $4\left(x+5\right)=3\left(x-2\right)-2\left(x+2\right)$

a)

$x=-1$

b)

$x=-4$

c)

$x=-6$

d)

$x=-10$

11.

Solve the following inequality for b, showing all of your work carefully and completely.

$4b-12-5b<9b+8$

(a)

12.

What is the value of x in the equation $\frac{3}{4}x+2=\frac{5}{4}x-6$ ?

a)

-16

b)

16

c)

-4

d)

4

13.

The formula for simple interest plus starting principal, where A = amount, P = principal, r = interest rate per period, and t = time, is given below.

$A=P+\Pr t$

a)

$A-P-\Pr=t$

b)

$\frac{A-P}{\Pr}=t$

c)

$\frac{A-\Pr}{P}=t$

d)

$\frac{A}{P+rt}=t$

14.

A line is represented by the equation $3x+2y=4$

a)

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

b)

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

c)

$y=\frac{3}{2}x+4$

d)

$y=-\frac{3}{2}x+4$

15.

Tim was asked to solve the equation for x. His solution is shown below.

Start: $kx=my-mx$

Step 1: $kx+mx=my$

Step 2: $x\left(k+m\right)=my$

Step 3: $x=\frac{my}{k+m}$

a)

Step 1

b)

Step 2

c)

Step 3

d)

Tim did not make a mistake.

16.

Kesha is planning to rent a van for her trip to Mt. Rainier. Two of her friends each rented the same type of van from the same car rental company last week. This is what they told her:

John: "The cost of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for five days and I drove it 200 miles."

Katie: "The cost of my rental was only $100. I drove it for 100 miles and had it for two days."

Kesha plans to get the same type of van that John and Katie had from the same car rental company. Kesha estimated her trip would be 250 miles, and she would have the vehicle for four days.

Let C = cost, M = miles, and D = Days.

Which equation could Kesha use to figure out how much her rental would cost?

a)

$C=40.00M+0.20D$

b)

$C=40.00D+0.20M$

c)

$C=20.00M+0.40D$

d)

$C=20.00D+0.04M$

17.

A shipping company charges $1.20 times the sum, s, of the length, width, and height of a package to be shipped. All dimensions are measured in inches. The company also charges $3.00 for processing the package to be shipped. On the line below, write an equation that the shipping company can use for determining the cost, C, for shipping any package.

(a)

18.

Which system of equations has the same solution as the system below?

$2x+2y=16$

$3x-y=4$

a)

$2x+2y=16$

$6x-2y=4$

b)

$x+y=16$

$3x-y=4$

c)

$2x+2y=16$

$6x-2y=8$

d)

$6x+6y=48$

$6x+2y=8$

19.

The enrollment at High School R has been increasing by 20 students per year. Currently High School R has 200 students attending. High School T currently has 400 students, but its enrollment is decreasing in size by an average of 30 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment?

a)

4 years

b)

5 years

c)

10 years

d)

20 years

20.

What is the solution for the system of equations?

$y=2x-3$

$4x-3y=31$

a)

$\left(-11,\ -25\right)$

b)

$\left(-11,\ -19\right)$

c)

$\left(11,\ 19\right)$

d)

$\left(14,\ 25\right)$

21.

Which system of inequalities describes the graph?

a)

$y>2x-3$

$y\ge-\frac{1}{3}x+2$

b)

$y\le2x-3$

$y>-\frac{1}{3}x+2$

c)

$y>2x-3$

$y\le-\frac{1}{3}x+2$

d)

$y\ge2x-3$

$y<-\frac{1}{3}x+2$

22.

Which quadrant will be completely shaded by the graph of the inequality $y<3x$ ?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

23.

Justin plans to spend $20 on sports cards. Regular cards cost $3.50 per pack and foil cards cost $4.50 per pack. Which inequality shows the relationship between the number of packs of regular cards (r) and the number of packs of foil cards(f) Justin can afford to buy?

a)

$3.5f+4.5r\le20$

b)

$3.5r+4.5f\le20$

c)

$3.5f+4.5r\ge20$

d)

$3.5r+4.5f\ge20$

24.

John's solution to an equation is shown below.

Given: $x^2+5x+6=0$

Step 1: $\left(x+2\right)\left(x+3\right)=0$

Step 2: $x+2=0\ or\ x+3=0$

Step 3: $x=-2\ or\ x=-3$

Which property of real numbers did John use for Step 2?

a)

multiplication property of equality

b)

zero product property of multiplication

c)

commutative property of multiplication

d)

distributive property of multiplication over addition

25.

Use the solution to the equation $3\left(x-9\right)=12$ below to answer this question.

Start: $3\left(x-9\right)=12$

Step 1: $3x-27=12$

Step 2: $3x-27+27=12+27$

Step 3: $3x=39$

Step 4: $x=13$

In Step 3, the addition property of equality was applied.

a)

True

b)

False

26.

The system $5y=8x+8\ and\ 7y=-8x+16$ is graphed as shown. Which choice is the point of intersection?

a)

$\left(\frac{1}{2},\ 2\right)$

b)

$\left(\frac{1}{3},\ 2\right)$

c)

$\left(\frac{1}{4},\ 2\right)$

d)

$\left(\frac{1}{8},\ 2\right)$

27.

At which point do the two equations $3x+5=y+4x\ and\ y=x^2$ intersect?

a)

$\left(1.8,\ 3.2\right)$

b)

$\left(-2.8,\ 7.8\right)$

c)

$\left(0,\ 5\right)$

d)

Both (A) and (B)

28.

4) $f\left(x\right)=g\left(x\right)\ at\ \left(0,-7\right)$

5) $f\left(x\right)=g\left(x\right)$ somewhere on the interval $-3<x<-2$

a)

4) True

b)

4) False

c)

5) True

d)

5) False

29.

Dr. Math thinks he knows more than you about what is true and false about the world just because he's a doctor. He says that the equation $y=17x+1$ also includes the point (1, 8). Is Dr. Math right or wrong?

a)

He's right

b)

He's wrong

c)

We need more information before we can say if he's right or wrong

d)

None of the above

30.

You talk on the phone y minutes on day x of every month according to the equation $y=2x+1$ . The cell phone company claims you talked 12 minutes on the phone on the fourth day of the month. Are they right?

a)

Yes, you did talk on the phone for 12 minutes on the fourth of the month

b)

No, you talked on the phone for 7 minutes on the fourth of the month

c)

No, you talked on the phone for 9 minutes on the fourth of the month

d)

No, you talked on the phone for 15 minutes on the fourth of the month

31.

Which point is NOT on the graph represented by $y=-x^2-2x+8$ ?

a)

$\left(-4,\ 0\right)$

b)

$\left(-1,\ 9\right)$

c)

$\left(2,\ 0\right)$

d)

$\left(4,\ 0\right)$

32.

Which of these shows the following expression factored completely?

$6x^2+15x-36$

a)

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

b)

$\left(6x+9\right)\left(x-4\right)$

c)

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

d)

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

33.

If $f\left(x\right)=2x^2-8x+9$ , which statement regarding the vertex form of $f\left(x\right)$ is true?

a)

In vertex form, $f\left(x\right)=2\left(x-2\right)^2+1$ and therefore has a minimum value of 1.

b)

In vertex form, $f\left(x\right)=2\left(x-2\right)^2+1$ and therefore has a minimum value of 2.

c)

In vertex form, $f\left(x\right)=2\left(x-2\right)^2+4.5$ and therefore has a minimum value of 4.5

d)

In vertex form, $f\left(x\right)=2\left(x-2\right)^2+4.5$ and therefore has a minimum value of 2.

34.

Which expression is equivalent to $x^4-12x^2+36$ ?

a)

$\left(x^2-6\right)\left(x^2-6\right)$

b)

$\left(6-x^2\right)\left(6+x^2\right)$

c)

$\left(x^2+6\right)\left(x^2+6\right)$

d)

$\left(x^2+6\right)\left(x^2-6\right)$

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

a)

A

b)

B

c)

C

d)

D

39.

a)

A

b)

B

c)

C

d)

D

40.

a)

A

b)

B

c)

C

d)

D

41.

a)

A

b)

B

c)

C

d)

D

42.

a)

A

b)

B

c)

C

d)

D

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

a)

A

b)

B

c)

C

d)

D

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

-12

b)

0

c)

7

d)

9

e)

12

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

-5 feet

b)

0 feet

c)

60 feet

d)

200 feet

e)

220 feet

52.

4 lines

53.

a)

A

b)

B

c)

C

d)

D

54.

a)

A

b)

B

c)

C

d)

D

55.

a)

T, F, F, T

b)

T, T, F, F

c)

T, F, T, T

d)

F, T, F, F

56.

a)

A

b)

B

c)

C

d)

D

e)

E

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

A

b)

B

c)

C

d)

D

60.

(a)

61.

a)

A

b)

B

c)

C

d)

D

62.

a)

A

b)

B

c)

C

d)

D

63.

a)

A

b)

B

c)

C

d)

D

64.

a)

A

b)

B

c)

C

d)

D

65.

a)

A

b)

B

c)

C

d)

D

66.

Write the function $-3=2\left(x-4\right)$ in the equivalent form most appropriate for identifying the slope and y-intercept of the function.

(a)

67.

a)

A

b)

B

c)

C

d)

D

68.

a)

T, T, T

b)

F, F, F

c)

T, T, F

d)

F, F, T

69.

a)

A

b)

B

c)

C

d)

D

70.

a)

A

b)

B

c)

C

d)

D

71.

a)

A

b)

B

c)

C

d)

D

72.

a)

A

b)

B

c)

C

d)

D

73.

a)

A

b)

B

c)

C

d)

D

74.

a)

A

b)

B

c)

C

d)

D

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

77.

a)

A

b)

B

c)

C

d)

D

78.

a)

A

b)

B

c)

C

d)

D

79.

a)

A

b)

B

c)

C

d)

D

80.

a)

A

b)

B

c)

C

d)

D

81.

a)

A

b)

B

c)

C

d)

D

82.

a)

A

b)

B

c)

C

d)

D

83.

4 lines

84.

a)

A

b)

B

c)

C

d)

D

85.

a)

A

b)

B

c)

C

d)

D

86.

a)

A

b)

B

c)

C

d)

D

87.

a)

A

b)

B

c)

C

d)

D

88.

a)

A

b)

B

c)

C

d)

D

89.

a)

A

b)

B

c)

C

d)

D

90.

a)

A

b)

B

c)

C

d)

D

91.

a)

A

b)

B

c)

C

d)

D

92.

a)

A

b)

B

c)

C

d)

D

93.

a)

A

b)

B

c)

C

d)

D

94.

a)

A

b)

B

c)

C

d)

D

e)

E

95.

a)

B,B,B

b)

A,B,C

c)

C,B,B

d)

D,B,C

96.

4 lines

97.

(a)

98.

a)

A

b)

B

c)

C

d)

D

99.

a)

A

b)

B

c)

C

d)

D

100.

a)

A

b)

B

c)

C

d)

D

EOC Review

Total questions: 100

Worksheet time: 3hrs 23mins

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