1. Today, we will review for the module 5 end of module assessment.
Learning Objective
Today, we will review for the module 5 end of module assessment.
CFU

2. Tie to LO Module 5 Review 11 4 = 𝑦 𝑥 𝑦= 11 4 𝑥
1. The amount of water that flows out of a certain hose in gallons is a function of the amount of time in minutes that the faucet is turned on. The amount of water that flows out of the hose in 4 minutes is 11 gallons. Assume water flows at a constant rate.
a. Write an equation in two variables that represents the amount of water, 𝑦, in gallons, as a function of the time in minutes, 𝑥, the faucet is turned on.
11 4 = 𝑦 𝑥
𝑦= 11 4 𝑥
b. Use the equation you wrote in part (a) to determine the amount of water that flows out of a hose in 8 minutes, 4 minutes, and 2 minutes.
𝑦= =11 2 =22
𝑦= =11
𝑦= = 11 2 =5.5
Tie to LO

3. Module 5 Review
c. The input of the function, 𝑥, is time in minutes, and the output of the function, 𝑦, is the amount of water that flows out of the hose in gallons. Write the inputs and outputs from part (b) as ordered pairs, and plot them as points on the coordinate plane.
(8, 22)
4, 11
2, 5.5
CFU

4. Module 5 Review
2. Sylvie claims that the table of inputs and outputs below will be a linear function. Is she correct? Explain.
Input
Output −3
−25 2 10 5 31 8 54
Rate between lines 1 & 2: 10− −25 2− −3 = = 35 5 =7
Rate between lines 2 & 3: 31−10 5−2 = 21 3 =7
Rate between lines 3 & 4: 54−31 8−5 = 23 3
Because the rates are not all constant, Sylvie is incorrect. The inputs and outputs do not form a linear function.
CFU

5. Module 5 Review
3. A function assigns the inputs and corresponding outputs shown in the table to the right.
Input
Output −2 3 8 10 −3 20 −8
a. Is the function a linear function? Check at least three pairs of inputs and their corresponding outputs.
−2−3 8− −2 =− 5 10 =− 1 2
−3− −2 10−8 =− 1 2
−8− −3 20−10 =− 5 10 =− 1 2
Because the rates of change are all constant, the function is linear.
b. What equation describes the function?
The equation that describes the function is 𝑦=− 1 2 𝑥+2.
Using 𝑦=𝑚𝑥+𝑏 we get:
3=− 1 2 −2 +𝑏
3=1+𝑏
𝑏=2
CFU

6. Module 5 Review
4. Brothers, Paul and Pete, walk 2 miles to school from home. Paul can walk to school in 24 minutes. Pete has slept in again and needs to run to school. Paul walks at constant rate, and Pete runs at a constant rate. The graph of the function that represents Pete’s run is shown below.
a. Which brother is moving at a greater rate? Explain how you know.
Paul’s rate: 2 𝑚𝑖 24 𝑚𝑖𝑛 = 1 12 𝑚𝑖/𝑚𝑖𝑛
Pete’s rate: 8 𝑚𝑖 60 𝑚𝑖𝑛 = 2 15 𝑚𝑖/𝑚𝑖𝑛
Since > Pete moves at a greater rate.

7. Module 5 Review
5. The graph below is the graph of a function. Do you think the function is linear or nonlinear? Show work in your explanation that supports your answer.
a. The graph of the function forms a line.
b. The rate of change between any two points is a constant −2.
c. The function can be described by the equation 𝑦=−2𝑥+4.
The function is definitely linear. Its graph forms a line, it has a constant rate of −2 and it can be described by the equation 𝑦=−2𝑥+4, which is of the form 𝑦=𝑚𝑥+𝑏. All of these facts are characteristics of a linear function.

8. Module 5 Review
6. A function has the rule so that each input of 𝑥 is assigned an output of 𝑥 2 . Do you think the graph of the function will be linear or nonlinear? What shape do you expect the graph to take? Explain.
Input (𝒙)
Output 𝟏 𝟐 𝒙 𝟐 −4 8 −2 2 4
The graph of the function is non-linear because a linear function would form a line. This graph did not form a line. I expect the graph to take the shape of a curve (or U).
CFU

9. CFU Module 5 Review 𝐴= 𝑠 2 𝑠 𝑠+4 𝐴= 𝑠+4 2 𝐴= 𝑠+4 2 − 𝑠 2
7. Write a function that would allow you to calculate the area, 𝐴, of a 2-inch white border for any sized square figure with sides of length 𝑠 measured in inches.
a. What is the length of the smaller, inner square?
b. What is the formula for the area of the smaller, inner square?
𝐴= 𝑠 2
c. What is the length of the larger, outer square? 𝑠
d. What is the formula for the area of the larger, outer square?
𝑠+4
𝐴= 𝑠+4 2
e. Using the answers from parts (b) and (d), what is the function that would allow you to calculate the area, A, of a 2-inch white border for any sized square figure?
𝐴= 𝑠+4 2 − 𝑠 2
CFU

10. CFU Module 5 Review 𝑉=𝑙∙𝑤∙ℎ 𝑙=11 𝑖𝑛. ℎ=6.4 𝑖𝑛. 295.68 𝑖𝑛 3 .
8. The volume of the rectangular prism is in 3 . What is its width?
11 in.
6.4 in.
What is the formula for finding volume of a rectangular prism?
𝑉=𝑙∙𝑤∙ℎ
What is the length of the prism?
𝑙=11 𝑖𝑛.
295.68= 𝑤
What is the height of the prism?
295.68=70.4𝑤
ℎ=6.4 𝑖𝑛.
70.4
70.4
What is the volume of the prism?
𝑤=4.2
𝑖𝑛 3 .
The width of the prism is 4.2 in.
Using the formula for volume of a rectangular prism, substitute in for the values that you know, solve for the value that you don’t know.
CFU

11. Module 5 Review
9. Use the diagram to find the total volume of the three cones shown below
Since all 3 cones have the same height and radius, we need to only find the volume of 1 cone and multiply it times 3.
𝑉= 1 3 𝐵ℎ
𝑉= 𝜋 (3)
𝑉= 4𝜋∙3 3
𝑉=4𝜋
The volume of one cone is 4𝜋 𝑓𝑡 3 . So to find the total volume, we multiply 4𝜋
by 3 to get 12𝜋.
The total volume of the three cones is 12𝜋 𝑓𝑡 3 .
CFU

12. Module 5 Review
10. Use the diagram below to determine which has the greater volume, the cone or the cylinder.
The volumes of the cylinder and the cone are the same.
Volume of the cylinder:
Volume of the cone:
𝑉=𝐵ℎ
𝑉= 1 3 𝐵ℎ
𝑉=96𝜋 𝑐𝑚 3
𝑉=𝜋
𝑉= 1 3 𝜋
𝑉=𝜋 16 6
𝑉=96𝜋 𝑐𝑚 3
𝑉= 1 3 𝜋 36 8
𝑉= 288𝜋 3
CFU

13. CFU Module 5 Review 11. What is the volume of the sphere shown below?
Volume of a sphere:
𝑉= 4 3 𝜋 𝑟 3
Since the diameter of the sphere is 6 in, the radius is 3 in.
𝑉= 4 3 𝜋 3 3
𝑉= 4 27 𝜋 3
𝑉=36𝜋 𝑖𝑛 3
𝑉= 4 3 𝜋 27
CFU
𝑉=4 9 𝜋

14. Module 5 Review
12. Which of the two figures below has the greater volume?
The volume of the sphere is greater.
Volume of the sphere:
Volume of the cone:
𝑉= 4 3 𝜋 4 3
𝑉= 1 3 𝜋
𝑉= 𝜋
𝑉= 4 3 𝜋 64
𝑉= 1 3 𝜋
𝑉=19.5𝜋 𝑚𝑚 3
𝑉= 256𝜋 3
𝑉= 𝜋 3
CFU
𝑉=85.3𝜋 𝑚𝑚 3

15. CFU Module 5 Review What is the definition of a function?
For every input x, there is only one distinct output y.
What makes a function linear?
1. When you graph it, you get a line
2. It has a constant rate of change
3. The exponents on the variables are raised to the positive one power only.
What is another word that means constant rate of change?
slope
CFU