Free Printable Algebra EOC Review

Worksheets

Algebra EOC Review

Total questions: 100

Worksheet time: 8hrs 20mins

Name

Class

Date

What is the slope between the points
(-3, -4) & (7, 6)?

Undefined

-1

Simplify the exponential expression.

2x⁶y¹²

2x⁵y⁷

8x⁶y¹²

8x⁵y⁷

If f(x)=3x-9, find f(5).

f(5) = 6

f(5) = 16

f(5) = -4

f(5) = 24

Solve for n:
6 - (8 - 4n) = 2(2n - 1)

No solution

n = 0

All real solutions

n = -2

Find the equation of the line shown

y = 4x - 2

y = -2x + 4

y = 2x + 4

y = -4x - 2

Write the equation of the line that goes through the points (4, 7) and (0, -5)

y = 1/3x + 7

y = 3x + 7

y = 1/3x - 5

y = 3x - 5

Write the equation of the line with slope = 5 and that goes through point (3, -5)

y = 5x - 5

y = 5x - 20

y = 5x + 20

y = 5x + 15

Solve for x:
4 - 5x < 22 - 2x

x > -6

x < -6

x > 6

x < 6

Given the list of ordered pairs, what is the x-intercept?
(8,10), (3, -4), (0, 8), (4, -3), (9, 0)

(8,10)

8, 3, 0, 4, 9

(0,8)

(9,0)

10.

Which of the following relations represents y as a function of x?
I. {(1, 4), (2, 5), (3, 6)}
II. {(1, 4), (2, 4), (3, 4)}
III. {(1, 4), (2, 4), (1, 3)}
IV. {(1, 4), (1, 2), (1, 3)}

I, II, and III only

II and IV only

III and IV only

I and II only

11.

The length of a rectangle is 4a⁴b⁵ and the width is 3a²b³, what is the area of the rectangle?

12a⁶b⁸

7a⁶b⁸

12a⁸b¹⁵

1a²b²

12.

Factor the following polynomial:
x²-x-6

(x+3)(x-2)

(x-3)(x+2)

(x+4)(x-2)

(x-4)(x+2)

13.

Find the slope and y-intercept:

6x + -2y = 18

slope = -6, y-intercept = -2

slope = -3, y-intercept = 9

slope = 3, y -intercept = -9

slope = 6, y-intercept = 3

14.

What is the RANGE of this graph?

-7<x<5

-7≤x<5

-3<x<1

-3≤x<1

15.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t
When will the object reach its maximum height?

4 ft

0 seconds

0 ft

4 seconds

16.

How fast would you reach the water if you jump off of a cliff using the formula: h(t) = -16t² + 8t + 24?

8 seconds

1 second

1.5 seconds

1/4 second

17.

A college student needs 11 classes that are worth a total of 40 credits in order to complete her degree. The college offers both 4-credit classes and 3-credit classes. Which system of equations can be used to determine f, the number of 4-credit classes the student can take to complete her degree, and h, the number of 3-credit classes?

f + h = 40
4h + 3f = 11

f + h = 11
4h + 3f = 40

f + h = 40
4f + 3h = 11

f + h = 11
4f + 3h = 40

18.

One type of redwood tree has an average height of 65 feet when it is 20 years old. If the tree is more than 20 years old, the average height, h, can be modeled by the function h = 1.95(a − 20) + 65, where a is the age of the tree in years. Which statement about this situation is true?

Every additional 1.95 ft of length over 20 ft adds 45 years to the age of this type of redwood tree.

For this type of redwood tree, the average height increases by 1.95 ft per year throughout its lifetime.

Each additional year of age over 20 years adds 1.95 ft to the average height of this type of redwood tree.

For this type of redwood tree, the average height increases by 65 ft for every 20 years of growth.

19.

The length, in feet, of a small train at an amusement park can be modeled by the function f(c) = 9c + 14, where c is the number of passenger cars attached to the locomotive. The original passenger cars were replaced, and the length of the train is now modeled by the function h(c) = 12c + 14. Based on this information, which statement describes the change in this situation?

The locomotive is now 9 feet long, and the length of each passenger car remained the same.

The locomotive is now 12 feet long, and the length of each passenger car remained the same.

Each passenger car is now 9 feet long, and the length of the locomotive remained the same.

Each passenger car is now 12 feet long, and the length of the locomotive remained the same

20.

Which statement about the quadratic parent function is true?

Its graph is symmetrical about the x-axis.

Its graph is symmetrical about the y-axis

Its domain is the set of all non-negative numbers.

Its range is the set of all real numbers.

21.

The approximate distance in miles between Los Angeles and a commercial jet flying from Boston to Los Angeles can be found using the function
m = −475t + 2,650,
where t is the number of hours the jet has been flying. Which number of hours and minutes is closest to the amount of time that the jet has been flying if the jet is 1,500 miles from Los Angeles?

2 hours and
25 minutes

8 hours and
44 minutes

3 hours and
16 minutes

9 hours and
13 minutes

22.

Two functions are given below.
f(x) = −4x + 1 1
g(x) = −4x + 2
How does the graph of f compare with the graph of g?

The graph of f is less steep than the graph of g.

The graph of f has the same y-intercept as the graph of g.

The graph of f is parallel to the graph of g.

The graph of f is steeper than the graph of g.

23.

Which of the following describes all the solutions to the inequality
5x + 7y ≥ 22
when y = −4?

x ≤ 10

x ≤ −10

x ≥ 10

x ≥ −10

24.

A candy company sells cases of chocolate bars. The company has fixed costs of $30,000, and each case of chocolate bars costs an additional $5 to make. The company sells each case for $10.
How many cases of chocolate bars will this company need to sell in order for costs and revenue to be equal?

3,500

6,000

35,000

60,000

25.

What is the vertex of the parabola: y=2(x-3)²+4

(3,4)

(-3,4)

(3, -4)

(-3,-4)

26.

.How many zeros does this parabola have?

27.

Which answer choice describes y = -3x² +7x - 2 accurately?

opens up with a maximum

opens up with a minimum

opens down with a maximum

opens down with a minimum

28.

Match the equation to its description.

Vertical Stretched by 2 and translation up 4

Vertical Compressed by 2 and translation up 4

Horizontal Stretched by 2 and translation left 4

Horizontal Compressed by 2 and translation right 4

29.

Solve for x:

x = yb - v

x = by - v

x = by + v

30.

Convert the equation y= (x+8)²+7 into standard form.

y= x²+16x+71

y= x²+8x+71

y= x²+16x+64

y= x²+15x+7

31.

Based on the information in the graph, which conclusion appears to be true?

The car lost about one-half of its value every three years.

The car lost about one-quarter of its value every year.

The car lost less of its value between years 9 and 10 than between 1 and 2.

The car lost more of its value between years 9 and 10 than between years 1 and 2.

32.

Which inequality represents the domain of the graph shown?

33.

Which expression is equivalent to 6x²+ 13x + 5?

Hint: factor

(2x + 5)(3x - 1)

(2x - 5)(3x + 1)

(2x + 1)(3x + 5)

(2x - 1)(3x - 5)

34.

Which graph represents the linear function -3x + 5y = -15?

35.

What system of equations is best represented by this graph?

36.

The area of a rectangle is 54x⁹y⁸ square yards. If the length of the rectangle is 6x³y⁴ yards, then what is the width?

9x³y²

48x⁶y⁴

9x⁶y⁴

60x⁹y⁸

37.

Which graph below matches the function: f(x) = (1/3)^x

38.

Write an equation: You invest $400 for 5 years and the interest rate is 4.29% each year.

y=400(0.0429)⁵

y=400(1.0429)⁵

y=400(4.29)⁵

y=400e^0.049*5

39.

Which sequence is represented by the equation a_n=2(7)^n-1 ?

7, 14, 28, 56...

2, 14, 98, 686...

2, 9, 16, 23...

7,9,11,13...

40.

Which recursive formula best describes the following sequence:
3, 8, 13, 18, 23...

a_n = (3)^n-1 ; a₁=5

a_n = (5)^n-1 ; a₁=3

a_n = a_n-1+3 ; a₁=5

a_n = a_n-1+5 ; a₁=3

41.

On the first day of camp I swam 2 laps. On the second day of camp I swam 4 laps. The third day I swam 8 laps. If this pattern continues, how many laps would I swim on the fifth day?

16 laps

32 laps

64 laps

128 laps

42.

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?

9890

9006

9765

5433

43.

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

g(x) rate of change is ALWAYS greater than f(x) rate of change.

g(x) is NEVER greater than f(x) rate of change.

g(x) will eventually exceed the rate of change of f(x).

There is not enough information to compare the rate of change of f(x) to g(x).

44.

When do we have growth?
f(x) = (a)(b^x)

a < 1

b > 1

0 < b < 1

a > 1

45.

Which of the following functions are considered exponential growth? Check all that apply.

a(x) = 20(3.5)^x+ 1.3

b(x) = 20(0.5)^x

c(x) = 27(0.95)^x+ 0.45

d(x) = 30(1.05)^x+ 10

e(x) = (5)^x- 13

46.

Solve by elimination
5x+6y= -10
3x-2y= -6

(-2,0)

(0,-2)

(2,0)

(0,2)

47.

Which point is a solution to the system?

(0, 6)

(-3, 4)

(1, 0)

(-4, 3)

48.

The height (H in inches) of a candle is represented by the linear function: H(t)=-0.25t+6, where t represents the time passed in hours. What is the meaning of the slope?

The height of the candle will decrease by 0.25 inches per hour

The height of the candle will increase by 0.25 inches per hour.

The candle is 6 inches tall before it is lit.

The candle is 0.25 inches tall before it is lit.

49.

The arithmetic sequence -5, 1, 7, 13,...
write a function to describe the sequence

f(n) = 4n - 9

f(n) = -4n - 9

f(n) = 6n - 11

f(n) = -6n - 11

50.

Solve: |v + 8| − 5 = 2

{-1,-15}

{-1,-5}

{-15,15}

No Solution

51.

Solve: -|−2r − 1| = 11

{-6,5}

{5,-6}

-6

No Solution

52.

Solve the system of equations:

5x + 2y = -6

-2x - 2y = -6

(-4, 7)

(0, 3)

(0, -3)

(4, -13)

53.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

y=8(15,000)^x

y=15,000(1.08)^x

y=15,000(0.92)^x

y=15,000(0.08)^x

54.

Find the 4th term in the geometric sequence a_n=3^n-1

243

55.

A new savings account is opened with $400 and gains 3% every year. How much is in the account after 5 years?

$415

$463.71

$343.49

$460.12

56.

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

57.

Find the product.
(d+9)²

d²+81

d²+18d+81

d²-81

d²-18d-81

58.

What is this type of function called?

Discrete Function

Segment Function

Step Function

Jump Function

59.

Which graph does NOT pass the vertical line test?

Graph 1

Graph 2

Graph 3

Graph 4

60.

What are the zeroes for the quadratic function
f(x) = x² + 2x - 15?

x = 5 and x = -3

x = -5 and x = 3

x = 5 and x = 3

x = -5 and x = -3

61.

If the parent function (y = x) is changed to have a slope of (2/3) and a y-intercept of 4, then which is true?

The new line is steeper than the original and the y-intercept has been translated down.

The new line is less steep than the original and the y-intercept has been translated up.

The new line is steeper than the original and the y-intercept has been translated up.

The new line is less steep than the original and the y-intercept has been translated down.

62.

A local theater sells admission tickets for $9.00 on Thursday nights. At capacity, the theater holds 100 customers. The function M(n)=9n represents the amount of money the theater takes in on Thursday nights, where n is the number of customers. What is the domain of M(n) in this context?

all whole numbers

all non- negative rational numbers

all non-negative integers that are multiples of 9

all non-negative integers less than or equal to 100

63.

A linear function passes through the points (10,5) and (-15, -5). A second function is represented by the equation 4x-3y=6. What is the y-intercept of the function with the greater rate of change?

-3

-2

64.

Find the difference.

(7p + 4p³ - 8) - (-3p²+ 2 - 9p)

-3p²+ 4p³ -15 + 9

3p³ + 4p² - p + 3

4p³ + 3p² +16p -10

4p³ +3p² + 16p + 10

65.

Factor x²- 6x + 8

(x-4)(x-2)

(x+4)(x+2)

(x-4)(x+2)

(x+4)(x-2)

66.

Write using negative exponents.
1/81

-9

9^-2

-81

1/-81

67.

According to the table, what is the relative frequency of Students ages 14 - 17 who skip breakfast?

About 27%

About 35%

About 15%

About 30%

68.

How many employees are there that make between $33,000 and $43,000

250

500

550

750

69.

Which dot plot has the greatest variability?

70.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

68%

34%

16%

2.5%

71.

Choose the correct data set for this box and whisker plot

2, 11.5, 23.5

2, 7.5, 8, 11.5, 12, 14.5, 23.5

7.5, 11.5, 14.5

11.5, 3.2, 1.1, 8.90

72.

What percent of the data is between 25 and 30 on the number line?

25%

`50%

75%

100%

73.

What is the interquartile range (IQR)?

74.

This data is normally distributed. What percent of the data is in the shaded region?

68%

95%

99.7%

50%

75.

√5 + √20

3√5

2√3

76.

Choose the correct answer.

77.

9^-1/2

-3

-4.5

1/9

1/3

-1/3

78.

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).

14x-10

-8x+2

2x+2

2x-2

79.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

x²+x+9

x²-x+9

x²-x

x²-x+18

80.

g(x) = 2x - 5

h(x) = 4x + 5

Find (g - h)(3)

hint: subtract g(x) and h(x), then plug in 3

-16

81.

Describe the transformation from the Absolute Value Parent Function.

Stretches more narrow, shifts up 4 units

Stretches more narrow, shifts down 4 units

Compresses wider, shifts down 4 units

Compresses wider, shifts up 4 units

82.

For what value of c will the graph of k be 9 units above the graph of g?

-3

83.

Which dashed line is an asymptote for the graph?

line q

line r

line s

line t

84.

Greg sells cars. He makes a base salary of $25,000, plus $1500 per car he sells. The function that models this situation is S = 1500x + 25000. After working at the car dealership for 2 years, he gets a raise. He now makes $1700 per car he sells. What is the new function that models this situation?

S = 1700x + 1500

S = 1500x + 1700

S = 1700x + 25000

S = 25000x + 1700

85.

Consider the pictured piecewise defined function. Which of the following are true? Select all that apply. Consider each grid represents 1 unit.

$f\left(1\right)=\frac{1}{2}$

$f\left(1\right)=-\frac{1}{2}$

$f\left(-2\right)=-1$

$f\left(-2\right)=1\frac{1}{2}$

$f\left(0\right)=0$

86.

What is the standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

6.89

10.1

7.26

87.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

28,000 km and 32,000 km.

24,000 km and 34,000 km.

26,000 km and 34,000 km.

27,000 km and 31,000 km.

88.

f(x)=2x+3 g(x)=x²
g(f(x))=

4x²+12x+9

4x²+9

4x+9

2x²+3

89.

Which graph matches the function:
y = -2|x - 3| + 5

90.

p(x) = 3x + 4
q(x) = 2x²
Find q(p(-2))

-8

None of these.

91.

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

-16, -21, -26, -31

5, -11, -27, -43

-16, -80, -500, -200

-16, -11, -6, -1

92.

The GPA of students in a course at UC Davis is approximately normal with a mean of 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8?

81.5%

47.5%

68%

Cannot be determined

93.