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ALgebra Midterm Review - 2022

Total questions: 80

Worksheet time: 4hrs 5mins

Name
Class
Date
1.

5x=25

a)

6

b)

5

c)

4

d)

50

2.

4(4+4x)=96

a)

5

b)

1.5

c)

No solutions

d)

∞ solutions\infty\ solutions

3.

4=2r-10

a)

7

b)

15

c)

14

d)

9

4.

297=7(8x-6)+3

a)

13

b)

12

c)

6

d)

10

5.

6(3−x)=−6(x+5)6\left(3-x\right)=-6\left(x+5\right)  

a)

No Solutions

b)

∞ solutions\infty\ solutions  

c)

19

d)

5

6.

-119=1-6(3n-4)

a)

11

b)

8

c)

14

d)

9

7.

7 (1 + 2n) = -105

a)

2

b)

7

c)

-8

d)

90909090909

8.

11b+7=40

a)

45

b)

8

c)

4

d)

3

9.

30=5(x+1)

a)

5

b)

50

c)

15

d)

6

10.

-87 = -3 (3r + 8)

a)

8

b)

7

c)

20

d)

5

11.

13=r9+813=\frac{r}{9}+8  

a)

45

b)

5

c)

17

d)

15

12.

k4+3=14\frac{k}{4}+3=14  

a)

21

b)

44

c)

12

d)

32

13.

−4+x14=−5-4+\frac{x}{14}=-5  

a)

5

b)

8

c)

-16

d)

-14

14.

-5 (5 + 2n) - 6 =-81

a)

-10

b)

-6

c)

5

d)

4

15.

Two high schools planned senior trips. High school A rented 1 van and 6 buses. They took 372 students. High school B rented 4 vans and 12 buses. They took 780 students. How many students does a van and bus hold?

a)

A van holds 18 students and a bus holds 59 students.

b)

A van holds 59 students and a bus holds 18 students.

c)

A van holds 24 students and a bus hold 54 students.

d)

A van holds 54 students and a bus holds 24 students.

16.

When we add two numbers, x, and y, we get 12. When we subtract the two numbers, we get 4. What are the two numbers?

a)

The numbers are 8 and 4.

b)

The numbers are 6 and 6.

c)

The numbers are 12 and 0.

d)

The numbers are 11 and 1.

17.

A movie theater charges $10 for each adult ticket and $5 for each child ticket. At a showing where 150 tickets were sold, the theater collected $1200. How many child and adult tickets were sold?

a)

There were 90 adult tickets and 60 child tickets sold.

b)

There were 60 adult tickets and 90 child tickets sold.

c)

There were 50 adult tickets and 40 child tickets sold.

d)

There were 40 adult tickets and 50 child tickets sold.

18.

You and a friend go to Chick-Fil-A. You order 2 chicken sandwiches and 5 cookies. Your bill is $17. Your friend orders 3 chicken sandwiches and 2 cookies. Their bill is $20. How much does a chicken sandwich and a cookie cost?

a)

A sandwich costs $6 and a cookie costs $1.

b)

A sandwich costs $1 and a cookie costs $6.

c)

A sandwich costs $5 and a cookie costs $2.

d)

A sandwich costs $2 and a cookie costs $5.

19.
Which property of real numbers justifies the work shown from Step 1 to Step 2?
a)
Distributive Property
b)
Commutative Property
c)
Identity Property
d)
Associative Property
20.
Which property of real numbers was used to get from Step 3 to Step 4?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Additive Inverse Property
d)
Substitution Property
21.
Which property justifies the work in solving this equation?
a)
Addition Property of Equality
b)
Additive Inverse Property
c)
Identity Property of Addition
d)
Subtraction Property of Equality
22.

If (-3p2 + 2 - 9p) is subtracted from (7p + 4p3 - 8), the result is

a)

-3p2 + 4p3 -15 + 9

b)

3p3 + 4p2 - p + 3

c)

4p3 +3p2 +16p -10

d)

4p3 +3p2 + 16p + 10

23.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
24.
Simplify:
(3x - 5) ( 4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
25.
What is the definition of function?
a)
Has inputs and outputs
b)
Every input has only ONE output
c)
Inputs have different outputs every time
d)
x-values and y-values
26.
All of the x values or inputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
27.
All of the y values or outputs are called what?
a)
Domain
b)
Range
c)
Relation
d)
Function
28.
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.
29.
Which set of values is a function?
a)
(9,5) (10,5) (9,-5) (10,-5)
b)
(3,4) (4,-3) (7,4) (3, 8)
c)
(6,-5) (7, -3) (8, -1) (9, 1)
d)
(2, -2) (5, 9) (5, -7) (1, 4)
30.
For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.
a)
D: {1, -3, -4,}
R: {0, 1, 2, -4}
b)
D:{0, 1, 2, -4}
R:{1, -3, -4}
c)
D:{0, 1, 2, 3, 4}
R:{1, -3, -4}
31.
Which ordered pair could you add to the following list of points to create a function?  (3, 5) (4, 9) (2, 5) 
a)
(3, 7)
b)
(4, 1) 
c)
(1, 9)
d)
(2, 6)
32.
Which graph does NOT pass the vertical line test?
a)
Graph 1
b)
Graph 2
c)
Graph 3
d)
Graph 4
33.
Which parent function matches the graph?
a)
f(x) = x
b)
f(x)= x2
c)
f(x) = |x|
d)
f(x) = abx
34.
Which parent function matches the graph?
a)
f(x) = x
b)
f(x)= x2
c)
f(x) = |x|
d)
f(x) = abx
35.
What type of function is shown?
a)
exponential
b)
linear
c)
quadratic
d)
square root
36.
Domain is: 
a)
All x values, from left to right.
b)
All y values, from bottom to top.
c)
All x values from bottom to top. 
d)
All y values from left to right.
37.
Range is:
a)
All x values, from left to right.
b)
All y values, from left to right. 
c)
All y values, from bottom to top.
d)
All x values, from bottom to top.
38.
What is the Range?
a)
y ≥ 6
b)
y ≤ 6
c)
-10 ≤ y ≤ 6
d)
-10 ≤ x ≤ 6
39.
Find the Range.
a)
All Real numbers
b)
0 < y < 11
c)
y ≥ 0
d)
y > 0
40.
Find the Domain.
a)
All real numbers
b)
x > 3
c)
x > 0
d)
x ≥ 0
41.
What is the Range?
a)
All real numbers
b)
y ≥ 3
c)
y > 3
d)
3 ≤ y ≤ 8
42.
What is the Domain?
a)
-10 ≤ y ≤ 6
b)
y ≤ 6
c)
-10 ≤ x ≤ 6
d)
All Real Numbers
43.

Identify the solution to the system graphed here.

a)

(1, 5) and (-4, 0)

b)

(1, 5) and (-2, 0)

c)

(1, 5) and (0, -4)

d)

No solution

44.

Find the solution(s) to the system.

a)

(0,-3)(1,-2)

b)

(0,-3)

c)

(-2,0)(2,0)

d)

No solution

45.

Which of the following graphs correctly represents:
y=x2y=x^2  
y=−2x+1y=-2x+1  

a)
b)
c)
d)
46.
A new savings account is opened with $400 and gains 3% every year. What is the exponential function?
a)
f(x)=400(1+3)x
b)
f(x)=400(1-0.03)x
c)
f(x)=400(1+0.03)x
d)
f(x)=400(0.03)x
47.
In an exponential function, what does the 'a' represent? 
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
48.
Identify the y-intercept (initial value) of the function f(x)=2(4)x.
a)
2
b)
4
c)
(2)x
d)
8
49.

Which function models this table?

a)

f(x)=2⋅4xf\left(x\right)=2\cdot4^x

b)

f(x)=4xf\left(x\right)=4^x

c)

f(x)=4⋅2xf\left(x\right)=4\cdot2^x

d)

f(x)=8xf\left(x\right)=8^x

50.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

51.
Find the average rate of change over the given interval. 
a)
4
b)
7
c)
7/3
d)
3/7
52.
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change? 
a)
200
b)
150
c)
300
d)
75
53.
What is the solution for the inequality
8 - 4x < 20
a)
x < -3
b)
x > -3
c)
x < 3
d)
x > 3
54.
Solve this inequality
4x + 14 < -2(4x - 1)
a)
x > 1
b)
x < 1
c)
x > -1
d)
x < -1
55.
Solve the formula for r.
C = 2πr
a)
r = 2Cπ
b)
r = 4Cπ
c)
r = c/2π
d)
2r = Cπ
56.
Solve for v.
a)
60
b)
-3
c)
15
d)
3
57.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥ 
b)
<, >
58.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
59.
x+2<-4 or -5x<-15
a)
-6<x<3
b)
x<-3 and x>6
c)
x<-6 or x>3
d)
No Solution
60.
Solve:  -3 ≤ 2x - 1 ≤ 5
a)
-1 ≤ x ≤ 3
b)
-1 < x < 3
c)
1 < x < 3
d)
1 ≤ x ≤ 3
61.
Solve the equation for x.
a)
6
b)
12
c)
0
d)
3
62.
When solving rational equations, once "they" match you completely eliminate...
a)
The numerators
b)
The denominators
63.
Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 
a)
(5, 8)
b)
(5, -8)
c)
(-5, -18)
d)
(-5, 8)
64.
3/4(6x + 2) = 15
a)
3
b)
6
c)
18
d)
20
65.
a)

17\frac{1}{7}

b)

4736\frac{47}{36}

c)

7

d)

23

66.

What is the smallest possible integer that makes this inequality true?

-2x + 7 < 19

a)

x = 6

b)

x = -6

c)

x = -5

d)

x = 5

67.
Factor:
x² - 5x - 14
a)
(x - 2)(x + 3)
b)
(x - 2)(x + 7)
c)
(x + 2)(x - 7)
d)
(x - 2)(x - 3)
68.
Factor out the GCF:
12x + 6
a)
6(2x + 1)
b)
3(4x + 2)
c)
6x(2x + 1)
d)
2(6x + 3)
69.

Identify the percent (%) increase or decrease for the following function.

f(x) = 35 (0.94)x

a)

Increase by 6%

b)

Decrease by 0.06%

c)

Increase by 0.06%

d)

Decrease by 6%

70.

What is the percent (%) of increase or decrease in the following function?


f(x) = 3000 (1 + 0.4)x

a)

Decrease by 4%

b)

Increase by 4%

c)

Increase by 40%

d)

Decrease by 40%

71.

Jimmy purchased a rare coin for $350. It will appreciate (increase) in value by about 6% each year. Write the equation that represents this.

a)

f(x)=350(0.06)x

b)

f(x)=0.06(350)x

c)

f(x)=350(1 - 0.06)x

d)

f(x)=350(1 + 0.06)x

72.

Luke purchased a car for $18,500. It will depreciate (decrease in value) 16% each year. Write an equation to represent the scenario.

a)

f(x)= 18,500 (1 + 0.16)x

b)

f(x)= 0.16 (18,500)x

c)

f(x)= 18,500 (1 - 0.16)x

d)

f(x)= 0.84 (18,500)x

73.
Between which seconds is the line INCREASING?
a)
Between 7 and 12 seconds
b)
Between 0 and 1 seconds
c)
Between 1 and 5 seconds
d)
Between 12 and 13.5 seconds
74.
Between which seconds is the line DECREASING?
a)
Between 7 and 12 seconds
b)
Between 0 and 1 seconds
c)
Between 1 and 5 seconds
d)
Between 12 and 13.5 seconds
75.
What happened during O to A point?
a)
not moving
b)
constant speed
c)
accelerating
d)
decelerating
76.

What is a plausible story for this graph?

a)

A student was jogging from school to home. She stopped to tie her shoe and take a drink from her water bottle, then continued at the same pace as before.

b)

A student was jogging from school to home. She walked for a while, then continued jogging.

c)

A sled rider was going down a hill. The hill was steep at first, then kind of flat. At the end, it was steep again.

d)

A car was slowing down, then contued moving at a constant rate. Finally, it slowed to a stop,

77.

A(n) _________________ function will ADD the same number each time.

a)

Linear

b)

Exponential

c)

Neither

78.

A(n) _________________ function will MULTIPLY the same number each time.

a)

Linear

b)

Exponential

c)

Neither

79.
What type of function describes the story below?
You have $5 and triple your money every day. 
a)
Linear
b)
Exponential
c)
Neither
80.
What type of function describes the story below?
You have $10 and earn $5 every week. 
a)
Linear
b)
Exponential
c)
Neither

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