MCV4U: Calculus: Culminating Assignment Draft Name: ____________________________ In the 1920’s, a scientist (J.P. Maxfield) at Bell Laboratory did research to determine the most optimal design for...

MCV4U: Calculus: Culminating Assignment Draft
Name: ____________________________
In the 1920’s, a scientist (J.P.
Maxfield) at Bell Laboratory
did research to determine
the most optimal design for
ecording music on a vinyl
disk. In 1948, RCA Victor
eleased a new style of
ecord that competed well
against those developed by
CBS and Columbia. RCA’s new record eventually became
the dominate medium for releasing new singles and may
still be found today in jukeboxes all across the world.
For your final assignment, you will incorporate what you
have learned in the Calculus component of the course
into a creative presentation.
Objective:
Create a project that demonstrates a thorough
understanding of one particular aspect of Calculus.
Ideally, this project will EXTEND the knowledge you have
acquired during the course.
Format:
The format of this project is flexible; choose a format that best allows you to demonstrate your
understanding of your chosen topic. Options include (but are not limited to):
• Written report with graphs and diagrams
• Visual and/or audio presentation (Powerpoint slides, video, etc.)
• Creation of physical models with supporting written work
Topics covered in class:
• Rates of Change
• Limits
• Continuity
• Derivatives
• Higher Order Derivatives
• Optimization
MCV4U Assignment 2021
https:
www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwj5zKbnoefaAhWHz4MKHXAAAjwQjRx6BAgBEAU&url=https:
www.pinterest.com/pin/ XXXXXXXXXX/&psig=AOvVaw2QEirUTms1VlMWfm9MxIuA&ust= XXXXXXXXXX
https:
www.google.ca/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwix-66poufaAhXo34MKHfElA-EQjRx6BAgBEAU&url=https:
londonjazzcollector.wordpress.com
ecord-labels-guide
ca/the-rca-labels/&psig=AOvVaw2QEirUTms1VlMWfm9MxIuA&ust= XXXXXXXXXX
Project Ideas:
Where is the Math?
Research a topic that connects Calculus to one or more of the following: technology, art, music, nature,
economics or sports. Clearly identify the connection to what you have learned in class, providing ACTUAL
examples.
Letter to the Editor
Write and answer a fake letter to the Editor of Calculus Times from a businessman, a politician or a
scientist that poses a simple problem for which you need the use of Calculus to solve. The problem should
e detailed and involved. The answer MUST utilize the skills you have learned in this course.
Optimize Me!
Optimize a 3-dimensional container. Pick a container in the shape of something NOT covered in class.
Your container should only have two measurements since you want to have two variables. You can choose
to maximize the container’s volume or minimize its surface area. If possible, use a REAL container and
include a picture of it with your project.
Real Data Function Modelling
Using REAL DATA, analyze some sort of a phenomenon. Tell me something interesting about this
phenomenon in terms of functions, their derivatives, etc.
• Spread of a real disease such as Covid-19, Malaria, AIDS etc.
• Record for a specific event in the sporting world
• Rate of oil consumption or production
• Life expectancies in different countries
My Look-Fors:
✓ Topic: the topic chosen is about the application of Calculus
✓ Background: background on the topic is included
✓ Visual Aid(s): shows time, effort, and creativity
✓ Mathematics: the mathematics in the topic is connected to course work; clearly explained,
including real examples of the mathematics studied in class
✓ Complexity & expertise: demonstration that something old was consolidated or something new
was learned
✓ Organization: organized, clear, and neat
✓ References: Any references that are used in the completion of your project must be cited using
APA format. Include references somewhere near the end of your project
eport. For help with APA
format, consult the website http:
www.citationmachine.net/ and click on the “APA” button at the
top of the page. This website works for any type of source material: book, magazine, newspaper,
journal, web site, etc.
http:
www.citationmachine.net

MCV4U – Culminating Assignment Ru
ic - Draft
Criteria Level 4
(Excellent Work)
Level 3
(Good work)
Level 2
(Satisfactory work)
Level 1
(Could be better)
Overall Quality Report is of excellent
quality, highly
creative, interesting,
and visibly
appealing.
Report is of good
quality, somewhat
creative, interesting
and visibly appealing.
Report is of
satisfactory quality,
not very creative,
interesting or visibly
appealing.
Report is of poor
quality and lacking in
creativity, interest and
visible appeal.
Application of
Mathematics
The mathematics in
the report is clearly
evident and reference
to course work is
demonstrated and
explained. The report
is co
ect and shows
significant insight.
The mathematics in
the report is
somewhat evident
and reference to
course work is mostly
demonstrated and
explained. The
majority of the report
is co
ect.
The mathematics in
the report is evident
ut very little
eference to course
work is demonstrated
or explained.
The mathematics in
the report is trivial
and not explained. No
eference or
connection to course
work is evident.
Readability Report has few or no
e
ors in spelling,
punctuation, and/or
grammar. Report is
easy to read. All
sources are cited.
Report has some
e
ors in spelling,
punctuation, and/or
grammar. Report is
eadable. Most
sources are cited.
Report has many
e
ors in spelling,
punctuation, and/or
grammar. Report is
challenging to read.
Few sources are cited.
Report is unreadable.
Sources are not cited.
Complexity &
Depth of
Understanding
Report shows
excellent depth of
understanding of
elevant concepts and
principles.
Report shows
proficient depth of
understanding of
elevant
mathematical
concepts and
principles.
Report shows
satisfactory depth of
understanding of
elevant mathematical
concepts and
principles.
Report shows limited
depth of
understanding of
elevant mathematical
concepts and
principles.
MCV4U Assignment Ru
ic 2021



MCV4U-01 Culminating Task
Biological Applications of Calculus in Real Life
Calculating Drug Sensitivity:
• One of the practices in medical field include measuring drug sensitivity
• It is important for doctors and nurses to understand the characteristics of certain drugs that are
eing prescribed to patients
• It is also crucial to know how well the drug will be abso
ed into the bloodstream and how long
it will remain active in the body
• All of these can be measured by comparing the strength of a drug to a patient’s sensitivity to the
drug
• *The drug strength for a certain drug is not applied for all drugs
• The strength of the drug is usually given by R(M)
• M measures the dosage in milligram (mg)
For example: ?(?) = ??√?? + ?. ??
We can use the product rule and the chain rule to find the derivative.
• The derivative of the function represents the sensitivity of the patient’s body to the drug
Assume the drug strength, with a dosage of 325mg, is being calculated
 The derivative calculated to be ?′(?) =
3?+40
√2?+40

 Substitute 325 mg into M
 ?′(325) =
XXXXXXXXXX
√ XXXXXXXXXX

• The sensitivity of a patient's body to the drug with a dosage of 325mg is about 38.64.
The graph ?(?) = 2?√ XXXXXXXXXX?
epresents the strength of a certain drug.
The derivative of the drug equation,
?′(?) =
3?+40
√2?+40
, represents the sensitivity of
patient’s body to the drug.


 By comparing the two graphs, it can be seen that the drug strength has changed
 By applying the derivative, drug sensitivity for a patient can be accounted for
 By knowing the drug sensitivity of a patient to certain drugs with respect to the dosage, doctors
and pharmacists are able to test the effects that it will have on the body
 Therefore, the drug will be able to work more effectively.
Example: Calculating Drug Sensitivity in Real Life using Optimization
• The sensitivity co
esponds to approximately how much change to expect in R as the result of a
unit change in the dosage.
• Generally, doctors prefer to prescribe dosages of maximum sensitivity.
• The strength of a patient’s reaction to a dose of M milligrams of a certain drug is
R(x) = ?1?
2(?2 − ?) where c1 and c2 are positive constants.
For what value of M is the strength a maximum, and what is that maximum reaction value?
For what value of M is the sensitivity a maximum? What is the maximum sensitivity?
Environmental Application of Calculus in Real Life
In the field of chemistry, calculus can be used to predict functions such as reaction rates and radioactive
decay.
We can use the following equation to calculate the average rate of reaction of a reactant product, A:
????? =
?????????????? ?? ? ?? ???? ?2 − ????????????? ?? ? ?? ???? ?1
?2 − ?1

Or
????? =
∆[?]
∆?

• The chemical symbol (A) placed inside the square
ackets indicate the entity’s concentration in
mol/L.
For the decomposition reaction of nitrogen dioxide, NO2(g), a
own gas
that can be formed from gasses in tailpipe emissions. It is a major
component of smog. The ground-level NO2(g) and one of the products of
its decomposition, NO(g), undergo further reactions that increases
ground-level ozone, which harms humans and other living things.

We can calculate the average rate at which the NO2(g) is
consumed over the first 50 s of the decomposition reaction.
????NO2(g) =
∆[NO2(g)]
∆?

=
[NO2(g)]?=50? − [NO2(g)]?=0?
50 ? − 0 ?

=
0.0079
???
? − 0.0100
???
?
50 ?

????NO2(g) = −4.2 × 10
−5 ???/? ∙ ?
We can also calculate the average rate for the disappearance of NO2(g) for each 50 s interval. Over the
same period the rate of oxygen production is given by
????O2(g) = +
∆[O2(g)]
∆?
= 2.2 × 10−5 ???/? ∙ ?
Environmental engineers can use the results from the average rate of reaction and engineering
principles to solve environmental problems, such as the decomposition of NO2(g).
Example: Calculating Ca
on Monoxide Level using the Chain Rule
An environmental study of a certain community suggests that the average daily level