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Algebra 1 Benchmark3 Review

Total questions: 80

Worksheet time: 7hrs 40mins

Name
Class
Date
1.
Meg's teacher asked her to find the zero(s) of the equation below.  Meg decided to factor to find the zero(s). 
0= x2-4x +4

(x + ___) (x + ___)
a)
(x + -2)(x + 2)
b)
(x + -4)(x + 2)
c)
(x + -4)(x + 4)
d)
(x + -2)(x + -2)
2.
Solve the equation
4(2x-5)=7(2x+4)
a)
8
b)
-8
c)
-1.5
d)
1.5
3.

Give the solution to the system
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
a hoppy hippo
4.
Solve the equation for y
4x+2y=16
a)
y=4x+16
b)
y=-2x-8
c)
y=2x+8
d)
y=-2x+8
5.
Simplify:
9 - 4(8 - 3) + 10 ÷ 2
a)
-6
b)
30
c)
-3
d)
5
6.

What is the solution set for −4x + 10 ≥ 5x + 55?

a)

F

b)

G

c)

H

d)

J

7.

Emily makes $10 per hour at her job. Her paycheck was $370. If h represented the number of hours Emily worked, which equation below represents Emily's paycheck?

a)

h=10370h=\frac{10}{370}

b)

370h=10370h=10

c)

370(10)=h370\left(10\right)=h

d)

10h=37010h=370

8.

What is the correct value that represents the slope for the line of best fit for the data?

a)

1.8

b)

-0.5

c)

0.5

d)

-1.8

9.

Solve the equation.

4(2x−5)=7(2x+4)4\left(2x-5\right)=7\left(2x+4\right)  



(a)  

10.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
11.
Is the pictured graph growth, decay, or linear or none?  
a)
Growth
b)
Decay
c)
Linear
d)
None
12.
An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? 
a)
101
b)
102
c)
103
d)
104
13.

At a farmer’s market the total cost of 3 pounds of red apples and 4 pounds of green apples is $8, including tax. The total cost of 6 pounds of red apples and 1 pound of green apples is $6.20, including tax. What is the price per pound of the green apples?

a)

$1.40

b)

$0.80

c)

$3.00

d)

$2.20

14.

Which of the following graphs best represents the solution to the system of linear equations shown below?

a)

A

b)

B

c)

C

d)

D

15.

Which graph best represents the solution set of

−4x ≤ 6y − 54?

a)

A

b)

B

c)

C

d)

D

16.

The graph of part of linear function gis shown on the grid.

a)

F

b)

G

c)

H

d)

J

17.
What type of function is f(x)=2(1/7)x ?
a)
Exponential Growth
b)
Linear
c)
Exponential Decay
d)
None of the Abovee
18.

The population of Center City is modeled by exponential function f, where x is the number of years after the year 2015. The graph of f is shown on the grid.

a)

x ≥ 0

b)

y ≥ 250,000

c)

0 ≤ x ≤ 110

d)

250,000 ≤ y ≤ 1,000,000

19.
A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges at the end of the month, which linear equation can be used to determine a user's monthly bill?  
a)
c = 60 - 0.05d
b)
c = 60.05d
c)
c = 60d - 0.05
d)
c = 60 + 0.05d
20.
The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = 8600 − 22x . In this function, x represents the number of
a)
computers repaired per week
b)
hours worked per week
c)
customers served per week
d)
days worked per week
21.
To watch a varsity basketball game, spectators must buy a ticket at the door. The cost of an adult ticket is $3.00 and the cost of a student ticket is $1.50. If the number of adult tickets sold is represented by a and student tickets sold by s, which expression represents the amount of money collected at the door from the ticket sales?
a)
4.50as
b)
4.50(a + s)
c)
(3.00a)(1.50s)
d)
3.00a + 1.50s
22.
a)
A
b)
B
c)
C
d)
D
23.
a)
A
b)
B
c)
C
d)
D
24.
a)
A
b)
B
c)
C
d)
D
25.

The elephant population in northwestern Namibia and Etosha National Park can be predicted by the expression 2,649(1.045)b, where b is the number of years since 1995.


What does the value 2,649 represent?

a)

the predicted increase in the number of elephants in the region each year

b)

the predicted number of elephants in the region in 1995

c)

the year when the elephant population is predicted to stop increasing

d)

the percentage the elephant population is predicted to increase each year

26.

A scientist is studying wildlife. She estimates the population of bats in her state to be 270,000. She predicts the population to grow at an average annual rate of 2.9 percent.


Using the scientist’s prediction, create an equation that models the population of bats, y, after x years.

a)

y = 270(1.29)x

b)

y = 1.029(270000)x

c)

y = 270000(1.029)x

d)

y = 270000(1 + 2.9)x

27.
a)

-5

b)

-1

c)

0

d)

2

e)

11

28.
The graph of which equation would translate the parent function up 2 and to the left 4?
a)
y = (x - 4)2 + 2
b)
 y = (x + 4)2 + 2
c)
y = (x + 4)2 - 2
d)
y = (x - 4)2 - 2
29.

What is the rate of change of the following table function?

a)

4

b)

14\frac{1}{4}

c)

−14-\frac{1}{4}

d)

-4

30.

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

a)

The additional fee of $8.

b)

The initial fee of $25.

c)

The additional fee of $25.

d)

The initial fee of $8.

31.
What is the explicit rule for the sequence:
11, 22, 44, 88...
a)
an = 2(11)n-1
b)
an = 11x2
c)
an = 11(2)n-1
32.

Given the following table of values, construct the function that represents the sequence.

a)

y = 3(4)x

b)

y = 3x + 4

c)

y = 4(3)x

d)

y = 4x + 3

33.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a reflection across the line x = -4
b)
a reflection across the line y = -4
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
34.
Which system of inequalities is shown?
a)
y ≥ -x - 1
y < x + 4
b)
y < -x - 1
 y ≥ x + 4
c)
y > -x - 1
y ≥ x + 4
d)
y > -x - 1
y ≥ x + 3
35.
Which system of linear inequalities is represented by the graph?
a)
y≤2x-1
y>-2x+3
b)
y>2x-1
y≤-2x+3
c)
y<2x-1
y≥-2x+3
d)
y≤2x-1
y>2x+3
36.
a)

A

b)

B

c)

C

d)

D

37.
a)

A

b)

B

c)

C

d)

D

38.

The table shows the temperature T(m), of a cup of hot chocolate that is allowed to chill over several minutes, m.

Which expression best fits the data for T(m)?

a)

150(0.85)m

b)

150(1.15)m

c)

150(0.85)m-1

d)

150(0.85)m+1

39.

What are the most appropriate units for the rate of change in the graph?

a)

1dollars x sticker⁡s\frac{1}{dollars\ x\ stic\ker s}

b)

dollarssticker⁡s\frac{dollars}{stic\ker s}

c)

sticker⁡sdollars\frac{stic\ker s}{dollars}

d)

dollars x sticker⁡s1\frac{dollars\ x\ stic\ker s}{1}

40.

Which student describes the function correctly?

a)

Student 1

b)

Student 2

c)

Student 3

d)

Student 4

41.

Two students solve the equation 4(x−1)+3x=6−x+64(x-1)+3x=6-x+6  .
Which statement is true?

a)

Both students solve the equation correctly and each makes no mistakes.

b)

Both students solve the equation incorrectly and each makes mistakes.

c)

Only Student 1 solves the equation correctly, while Student 2 solves the equation incorrectly.

d)

Only Student 2 solves the equation correctly, while Student 1 solves the equation incorrectly.

42.

Name the correlation in this graph

a)

Negative correlation

b)

No correlation

c)

Lots of correlation

d)

Positive correlation

43.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
44.
Is this function linear or nonlinear?
a)
Linear
b)
Nonlinear
45.
The graph of which equation would translate the parent function up 2 and to the left 4?
a)
y = (x - 4)2 + 2
b)
 y = (x + 4)2 + 2
c)
y = (x + 4)2 - 2
d)
y = (x - 4)2 - 2
46.
a)

A

b)

B

c)

C

d)

D

47.
a)

A

b)

B

c)

C

d)

D

48.

Find the equation that matches the table.

a)

F

b)

G

c)

H

d)

J

49.

Find the Equivalent

a)

F

b)

G

c)

H

d)

J

50.
a)

F

b)

G

c)

H

d)

J

51.

Which pair BEST represents a causation relationship?

a)

a person's age and his/her shoe size

b)

the number of ice cream cones sold and the amount of sunscreen sold

c)

the temperature at a football game and the number of hot drinks sold

d)

the number of people attending a ballgame and the length of the ball game

52.

Which arithmetic sequence rule produces the term values in the table shown?

a)

an=4na_n=4n

b)

an=4n+1a_n=4n+1

c)

an= 4n+5a_n=\ 4n+5

d)

an=4n+9a_n=4n+9

53.

What is the compound inequality that represents the solution to ∣−6b∣≤60\left|-6b\right|\le60

a)

−10≥b≥10-10\ge b\ge10

b)

b≤10b\le10

c)

−10≤b≤10-10\le b\le10

d)

all real numbers

54.

Which function is equivalent to the explicit formula of the sequence 5, 8, 11, 14,...?

a)

f(n) = 5 + 3n

b)

f(n) = 2 + 3n

c)

f(n) = 5 - 3n

d)

f(n) = 2 - 3n

55.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
56.
What is the common ratio for the sequence:
28, 14, 7, 3.5...
a)
2
b)
1/2
c)
-14
d)
-7
57.
What is the explicit rule for the sequence:
11, 22, 44, 88...
a)
an = 2(11)n-1
b)
an = 11x2
c)
an = 11(2)n-1
58.
Identify the y-intercept (initial value) in the function f(x)=13(.27)x
a)
(.27)x
b)
.27
c)
13
d)
3.51
59.
Factor:
x² - 5x - 14
a)
(x - 2)(x + 3)
b)
(x - 2)(x + 7)
c)
(x + 2)(x - 7)
d)
(x - 2)(x - 3)
60.
Factor:
2x² + 11x + 14
a)
(x + 7)(2x + 2)
b)
(x + 2)(2x + 7)
c)
(x + 14)(2x + 1)
d)
(x + 1)(2x + 14)
61.
a)

F

b)

G

c)

H

d)

J

62.
a)

A

b)

B

c)

C

d)

D

63.
a)

A

b)

B

c)

C

d)

D

64.
a)

F

b)

G

c)

H

d)

J

65.

The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.

a)

g(x) is shifted up 3 units

b)

g(x) is shifted down 3 units

c)

g(x) is shifted left 3 units

d)

g(x) is shifted right 3 units

66.

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

a)

g(x) is shifted up 6 units

b)

g(x) is shifted down 6 units

c)

g(x) is shifted left 6 units

d)

g(x) is shifted right 6 units

67.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

68.

What is the slope (also known as the rate of change) of the table?

(a)  

69.

A linear function can be used to model the linear relationship between a sweet tea stand’s daily profit and the number of glasses of sweet tea sold that day.

The sweet tea stand purchases supplies to make a fixed number of glasses of sweet tea each day and closes the stand if they run out of tea.

The relationship is shown on the graph.

Which response describes the rate of change of the profit with respect to the number of glasses sold?

a)

The profit increases by $1 per glass sold.

b)

The profit increases by $16 per glass sold.

c)

The profit increases by $0.70 per glass sold.

d)

The profit increases by $3.50 per glass sold.

70.
The scatter plot below shows the number of books read by students in Mrs. Hall’s English class and their final grades. Which statement represents the best description about the line of best fit?
a)
The more books students read, the lower their English grade.
b)
The more books students read, the higher their English grade.
c)
The fewer books students read, the higher their English grade. 
d)
No relationship exists between the number of books students read and their English grades. 
71.

What type of correlation (association)?

The outside temperature and the amount of layers you wear.

a)

A) Positive correlation

b)

B) Negative correlation

c)

D) No correlation

72.

Number of pets a person has and number of books a person has read

a)

positive correlation

b)

Negative Correlation

c)

No Correlation

73.

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

a)

High social media usage and reduced grades.

b)

Car ran out of gas and being stranded on the side of the road.

c)

Recess time and number of friends.

74.

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

a)

Rainfall and time spent reading.

b)

Eating more butter and increased divorce rates.

c)

It started raining and the baseball game was delayed.

75.

Which example shows CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)

a)

I put water in the freezer and now I have ice.

b)

The alarm clock went off and I woke up.

c)

Temperature and the amount of people at the beach.

76.

Which example shows a CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)

a)

It rained and the ground is wet.

b)

Ice cream sales increase as temperature increases.

77.
Describe the relationship between the variables.
a)
no correlation
b)
strong positive correlation
c)
strong negative correlation
d)
weak positive correlation
78.
Which sentence describes the relationship shown on this scatterplot?
a)
As the temperature decreases, the visitors increase. 
b)
As the temperature increases, the number of visitors increases. 
c)
As the visitors increase, the temperature decreases. 
d)
No correlation
79.

If

f(x)=3x−12f\left(x\right)=3x-12  , what is f(12)?

a)

-6

b)

36

c)

24

d)

4

80.
a)
x < 1
b)
x < -1
c)
x > 1
d)
x > -1

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