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Unit 4B Review #2 - 01.24.25 -Calculating Average Rate of Change

Total questions: 35

Worksheet time: 3hrs 32mins

Name
Class
Date
1.

Calculate the average rate of change of f(x) = 3x^2 + 2x + 1 for 2 ≤ x ≤ 4.

a)

10

b)

20

c)

37

d)

40

2.

Which is the best estimate for the average rate of change for the quadratic function graph on the interval -12 ≤ x ≤ -4?

a)

-2

b)

-3

c)

2

d)

3

3.

Which is the best estimate for the average rate of change for the quadratic function graph on the interval -8 ≤ x ≤ -4?

a)

-1

b)

-2

c)

1

d)

2

4.

Which is the best estimate for the average rate of change for the quadratic function graph on the interval -4 ≤ x ≤ 4?

a)

-1

b)

-2

c)

-3

d)

-4

5.

Which is the best estimate for the average rate of change for the quadratic function graph on the interval $0 \leq x \leq 4$?

a)

-1

b)

-2

c)

-3

d)

-4

6.

Which is the BEST estimate for the average rate of change for the function given in the table, over the interval \(1 \leq x \leq 3\)?

a)

6

b)

12

c)

18

d)

24

7.

Solve the quadratic equation for x. What is one of the roots? (x - 5)^2 = 9

a)

-8

b)

-4

c)

4

d)

-2

e)

2

8.

Solve the quadratic equation for x. What is one of the roots? (x + 6)^2 = 49

a)

-13

b)

-6

c)

-7

d)

-1

e)

13

9.

Solve the quadratic equation. \((x - 4)^2 = 36\)

a)

x = 2 or -10

b)

x = 10 or -2

c)

x = ±4

d)

x = ±10

e)

x = -2 or -4

10.

When solved for x, what is the product when the roots of the quadratic equation are multiplied? \[ x^2 - 8 = 8 \]

a)

-16

b)

-8

c)

0

d)

16

e)

8

11.

Solve the quadratic equation: $2x^2 = 98$.

a)

±7√2

b)

7√2

c)

7

d)

±7

e)

±98

12.

When solved for x, what is the product when the roots of the quadratic equation are multiplied? 3x² - 75 = 0

a)

-25

b)

-5

c)

5

d)

25

e)

75

13.

What is the value of $ a $, if $ a^2 - 64 = 0 $ and $ a > 0 $?

a)

0

b)

4

c)

8

d)

16

14.

For what values of x does -x^2 + 7x + 5 = 0?

a)

-7 ± √69

b)

7 ± √59 / -2

c)

-7 ± √59 / -2

d)

7 ± √69 / -2

15.
Find the rate of change
a)
3
b)
-3
c)
20
d)
Not a constant slope/Non-Linear
16.
Find the slope of the line.
a)
-2
b)
2
c)
-1
d)
1
17.
Determine the slope.
a)
m=3/2
b)
m=6
c)
m=-3/2
d)
m=1/6
18.
Determine the slope.
a)
m=1/7
b)
m=-1/7
c)
m=-7
d)
m=7
19.
Find the slope of the line.
a)
Undefined
b)
0
c)
1
d)
-1
20.
Find the slope of the line.
a)
Undefined
b)
0
c)
1
d)
-1
21.
a)
m = 5/0
b)
m = -2/3
c)
m = 2/3
d)
m = 3/2
22.
Write the equation in slope-intercept form (solve for y):
2y = 10x + 14
a)
y = 10x + 12
b)
y = 10x + 7
c)
y = 5x + 14
d)
y = 5x + 7
23.

Write the equation in slope-intercept form (solve for y):

y + 4 = 8x

a)

y = 2x

b)

y = 8x - 4

c)

y = 2x

d)

y = 8x + 4

24.
What is the slope of the line through the points (2, 4) and (2, -11)?
a)
m = 0
b)
m = -15/0
c)
m = 13/2
d)
m is undefined
25.
Which equation matches the table?
a)
y = x + 5
b)
y = 5x
c)
y = x - 5
d)
x = y - 5
26.
What is the algebraic equation for this table?
a)
y = x + 3
b)
y = 3x
c)
y = x ÷ 3
d)
y = x - 3
27.

What is the algebraic equation for this table?

a)

y = 480x

b)

x = y/480

c)

x + 480 = y

d)

480 - x = y

28.
Pablo has $12. He earns $7 for every lawn he mows. Write an equation to find the amount of money "y" he will have after "x" number of lawns.
a)
y = 12x + 7
b)
y = 7x + 12
29.
Jeff earns $10 per hours raking leaves. Write an equation to find the amount of money "y" he earns for "x" number of hours.
a)
y = 10x
b)
x = 10y
c)
y = x + 7
30.
Elliot wants to sign up for a gym membership. The gym require a $35 fee to sign up, then $12 every month. Write an equation to find the amount Elliot will pay for his gym membership "y" after "x" amount of months.
a)
y = 35x + 12
b)
y = 12x + 35
c)
y = 12x - 35
31.
Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.
y=3x+10
What does the y-intercept of the graph of this equation represent?
a)
The monthly fee
b)
How much Rich pays per visit
c)
The number of times Rich goes to the gym
d)
The total cost at the end of the month
32.
Dona plays a game with her brother.  The both start with 75 points.  For each round that they win, they receive 30 points.  The equation that models each person's score is
y = 30 x + 75, where x is the number of games a person wins.  What is the meaning of the slope?
a)
the number of games won
b)
the amount of points that a player begins with
c)
the change in points for each game a person wins
d)
the number of points needed to win the game
33.

y=7x

What is the missing number?

a)

5

b)

4

c)

8

d)

7

34.
y=x-6
What is the missing number?
a)
12
b)
10
c)
14
d)
13
35.
Nancy can type 50 words per minute. Look at the table below to write an equation that matches the data.
a)
m=50 + w
b)
w= 50m
c)
w= 50 + m
d)
m= 50 - w

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