Free Printable Alg Optional EOC Review

1.

Is the result rational or irrational? Explain.

a)

Rational; The sum of two rationals is always rational.

b)

Irrational; The sum of a rational and an irrational is always irrational.

c)

Rational; The product of two rationals is always rational.

d)

Irrational; The product of a nonzero rational and an irrational is always irrational.

2.

Is the result rational or irrational? Explain.

a)

Rational; The sum of two rationals is always rational.

b)

Irrational; The sum of a rational and an irrational is always irrational.

c)

Rational; The product of two rationals is always rational.

d)

Irrational; The product of a nonzero rational and an irrational is always irrational.

3.

$\sqrt{400}\div\sqrt{4}$

a)

rational

b)

irrational

4.

$\frac{1}{2}+\frac{3}{4}$

a)

rational

b)

irrational

5.

$\frac{1}{2}\cdot\frac{3}{4}\cdot\ \sqrt{2}\ simplifies\ to\ a\$

a)

Rational Number

b)

Irrational Number

6.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

7.

Tommy's ice cream shop makes sundaes by adding x ice cream scoops at $1.25 each and 2 toppings at $0.50 each. They want to make a sundae that averages $1.15 per ingredient. Choose the equation that best models the situation.

a)

1.25x-0.5=1.15(x + 2)

b)

1.25x+0.5=1.15(x+2)

c)

1.25x-0.5=1.15(x - 2)

d)

1.25x+0.5=1.15(x - 2)

8.

Solve for p

-6|-8p - 7| + 5= -10

a)

-19/16, -9/16

b)

1/4, -3.5

c)

9/16, -9/16

d)

-19/16

9.

Solve:
V = πr²h , for h

a)

V/(πr²) = h

b)

V - πr² = h

c)

V + πr² = h

d)

V/π = h

10.

a)

T = PV/K

b)

T = PK/V

c)

T=KV/P

d)

Greenland

11.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

12.

Find the equation of the line that passes through the points:

(-3, 3) and (3, -1)

a)

y = -⅔ x + 1

b)

y = -⅔ x

c)

y = ⅔ x + 1

d)

y = -⅔ x +3

13.

Identify the x-intercept of the following linear equation written in standard form.

-8x - 4y = 8

a)

(-1, 0)

b)

(0, -1)

c)

(-2, 0)

d)

(0, -2)

14.

Identify the y-intercept of the following linear equation written in standard form.

9x + 3y = -18

a)

(0, -6)

b)

(-6, 0)

c)

(-2, 0)

d)

(0, -2)

15.

Which equation below changes

9x - 6y = 18

into slope intercept form?

a)

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

b)

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

c)

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

d)

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

16.

Write the equation of a line perpendicular to y = 3x - 8 and that passes through the point (-3, -9)

a)

y + 9 = -1/3(x + 3)

b)

y - 9 = -1/3(x - 3)

c)

y + 9 = -3(x + 3)

d)

y - 9 = 3(x - 3)

17.

What slope is perpendicular to:
m = 5/8

a)

-5/8

b)

5/8

c)

-8/5

d)

8/5

18.

What slope is perpendicular to:
m = 3

a)

-3

b)

-1/3

c)

1/3

d)

3

19.

What slope is parallel to:
m = 4

a)

4

b)

-1/4

c)

-4

d)

1/4

20.

a)

Function

b)

Not a Function

21.

a)

Function

b)

Not a Function

22.

a)

Function

b)

Not a Function

23.

a)

Function

b)

Not a Function

24.

Which relation is NOT a function?

a)

{(1,-5), (3,1), (-5,4), (4,-2)}

b)

{(2,7), (3,7), (4,7), (5,8)}

c)

{(1,-5), (-1,6), (1,5), (6,-3)}

d)

{(3,-2), (5,-6), (7,7), (8,8)}

25.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

26.

Maddie plants a tree that is 6 feet tall outside her house. The label on the tree says it should grow $\frac{3}{4}$ of a foot every year. Write an equation to model y the height of the tree after x years.

27.

This table represents some points on the graph of a linear function. Write a function that would represent the same relationship.

28.

What is the solution to $15x+8=3\left(5x-4\right)-10x$ ?

29.

Sue walks dogs after school each day and earns a set amount per dog plus an hourly wage. What is a reasonable domain for this situation?

a)

$-3\ <\ x\ <\ 3$

b)

$0\ <\ x\ <\ 6$

c)

$0\ <\ x\ <\ 24$

d)

$0\ <\ x\ <\ 120$

30.

Kali sells bracelets and makes a profit, p, based on the equation $p\left(x\right)=6x-19$ where x is the number of bracelets sold. What is Kali's profit if she sells 25 bracelets?

a)

130

b)

131

c)

119

d)

answer not here

31.

Which of the following is an arithmetic sequence?

a)

2,3,5,8

b)

2,7,12,17

c)

1,1,2,3,5

d)

2,4,8,16

32.

What type of association does this graph have?

a)

positive

b)

negative

c)

none

d)

all of the above

33.

What is the equation of the line of best fit?

a)

y = -25x + 170

b)

$y\ =\ -\frac{5}{8}+170$

c)

y = 25x + 170

d)

$y=\frac{5}{8}+170$

e)

y = 170x + 6

34.

What type of association is there between the variables shown on this scatter plot?

a)

Linear, Negative Association

b)

Non-Linear, Negative Association

c)

Linear, Positive Association

d)

Non-Linear Positive Association

e)

No Association

35.

Click on Image. Orange points are NOT necessarily data from the set.

a)

y = 5/6 x + 1

b)

y = x + 5/6

c)

y = x + 1

d)

y = 6/5 x + 1

36.

Find the solution using the elimination method. (Write your answer as an ordered pair, i.e. (1,1)

(a)

37.

Which of the following inequalities matches the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

38.

Check ALL points that are solutions of the graph.

a)

(1,3)

b)

(4,0)

c)

(-2,2)

d)

(2,2)

e)

(1,2)

39.

Which of the following graphs has the largest average rate of change over the interval $-1\ \le\ x\ \le2$ ?

a)

b)

c)

d)

40.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

41.

Please find

f\left(-1\right)

a)

-2

b)

-3

c)

11

d)

undefined

42.

Evaluate f(1)

(a)

43.

Simplify the expression

a)

$\frac{-1}{3x^5y^7}$

b)

$3x^5y^7$

c)

$16x^{13}y^9$

d)

$\frac{1}{16x^{13}y^9}$

44.

$\left(\frac{3m^2n^7}{m}\right)^5$

a)

$15m^7n^{12}$

b)

$243m^5n^{35}$

c)

$15m^{15}n^{35}$

d)

$243m^7n^{12}$

45.

Simplify:

a)

x¹²/y²²

b)

x⁸y¹⁴

c)

x¹²y²²

d)

y²²/x¹²

46.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

47.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

48.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

49.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

50.

Ms. Aldinger has 2 pet ants and will double the amount each week.

a)

arithmetic

b)

geometric

51.

Ms. Aldinger has $600 and will give a student $5 each week

a)

arithmetic

b)

geometric

52.

What is the common ratio or common difference of the sequence below:

196,-28, 4,.....

a)

d=-7

b)

d=-1/7

c)

r=-7

d)

r=-1/7

53.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

54.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

55.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

56.

Zach's parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semi-annually, what will be the balance after 18 years?

$A\ =\ P\left(1+\frac{r}{n}\right)^{nt}$

a)

$6,273.50

b)

$6,314.08

c)

$6,385.72

d)

$6,427.94

57.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

a)

Vertically stretched by a factor of 2, right 3, and up 1

b)

Vertically compressed by a factor of 1/2, left 3 and down 1

c)

Vertically compressed by a factor of 1/2, right 3, and down 1

d)

Vertically stretched by a factor of 2, left 3, and up 1

58.

4a² - 25

a)

(2a + 5) (2a - 5)

b)

(2a - 5) (2a - 5)

c)

(x + 5) (x - 5)

d)

Can't factor using Diff. of Squares

59.

Multiply the following binomials:

(3x − 4)(4x + 3)

a)

12x² − 7x − 7

b)

7x² − 7x − 12

c)

12x² − 7x − 12

60.

A rectangular garden has a length 3 times its width, w. A 1.5 ft. path is built along the garden's perimeter. What is an expression for the area of the garden including the path?

a)

$2.25w^2$

b)

$3w^2+3$

c)

$3w^2+12w+9$

d)

$3w^2+1.5w+4.5$

61.

The quadratic function shown below is used to model vertical motion.
$h\left(t\right)=-16t^2+v_ot+h_o$

If a soccer ball is kicked from ground level with an initial velocity of 64 feet per second, how high will it go?

a)

100 feet

b)

64 feet

c)

140 feet

d)

88 feet

62.

The quadratic function shown below is used to model vertical motion. $h\left(t\right)=-16t^2+v_ot+h_o$

If a soccer ball is kicked from ground level in a vertical trajectory with an initial velocity of 64 feet per second, how long will it take to get to its maximum height?

a)

t = 3 seconds

b)

t = 10 second

c)

t = 4 seconds

d)

t = 2 seconds

63.

An acrobat springs from a trampoline that is 2 feet off the floor with an initial upward velocity of 24 feet per second. What is the model of this function?

a)

h=-16t²+2t+24

b)

h=-16t²+24t+2

c)

h=24t²+2t-16

d)

h=2t²+24t-16

64.

Solve by factoring: $5x^2-12=17x$

a)

$\left\{-3,20\right\}$

b)

$\left\{-\frac{3}{5},\ 4\right\}$

c)

$\left\{-4,\ \frac{3}{5}\right\}$

d)

$\left\{-20,3\right\}$

65.

Find the solution(s):
y = x² - 4x + 6
y = x + 2

a)

(1, 4)

b)

(-1, 1) and (4, 2)

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

66.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

67.

Identify the values of A, B, and C

5x²+ x - 18 = - 9x + 3x²

a)

A=2, B=10, C=-18

b)

A=5, B=1, C=-18

c)

A=8, B=-8, C=-18

d)

A=2, B=9, C=-18

68.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

69.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

70.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

71.

What is the domain of the quadratic function?

a)

All Real Numbers

b)

$y\ge3$

c)

y ≤ 5

72.

Find the inverse of $f\left(x\right)=\frac{1}{4}x-7$

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x+28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x+28

73.

$f\left(x\right)=\frac{8x-3}{5}$
Find $f^{-1}\left(x\right)$

a)

$5\left(8x+3\right)$

b)

$\frac{5x}{8}+3$

c)

$\frac{5\left(x+3\right)}{8}$

d)

$\frac{5x+3}{8}$

74.

Write the equation of this transformation: reflection across x-axis, left 3, up 15

a)

y= -(x+3)²+15

b)

y= -(x+3)² - 15

c)

y= (x+3)²+15

d)

y= -(x+15)²+3

75.

Which has a higher median?

a)

Florida

b)

Texas

76.

What is Thanksgivings maximum?

a)

30

b)

15

c)

22

d)

24

77.

The list below shows the most recent test scores for students in Mr. Garcia’s study group.

78, 90, 94, 72, 80, 68, 72, 88, 94, 98, 86, 96

Which box-and-whisker plot correctly represents the data in the list?

a)

b)

c)

d)

78.

Which box and whisker plot has the lowest minimum?

a)

Top plot

b)

Bottom plot

79.

What percent of the total population surveyed were electrical engineers that like math?

a)

33.9%

b)

48.6%

c)

16.5%

d)

21.7%

80.

How many people purchased no food and no drink?

a)

60

b)

10

c)

20

d)

200

Alg Optional EOC Review

Total questions: 80

Worksheet time: 3hrs 3mins

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