UMC High School
MHF4UX Final Culminating Evaluation
Student Name: ______________________________________________________________________
Due Date: Presentation April 29th, 2021 & Final Submission April 30th, 2021
Teacher: Ms. Jenna Mok
Course Name: Advanced Functions, Grade 12 University Preparation
Course Code: MHF4UX
Total Pages: 13
Worth: 30%
Final Grade:
Part A
Line Rider
Part B
Problem
Solving
Knowledge/
Understanding
20%
Thinking/Inquiry
30%
/20
/30
/20
/20
/30
/20
Total
Department Head: ______________________________
Communication Application
20%
30%
/100
Total
points
Worth
(30%)
/30
/100
/20%
/30
/100
/10%
/30%
Principal: ______________________________
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Overall Expectations
A. Exponential and Logarithmic Functions
A1. Demonstrate an understanding of the relationship between exponential expressions and logarithmic
expressions, evaluate logarithms, and apply the laws of logarithms to simply numeric expressions;
A2. Identify and describe some key features of the graphs of logarithmic functions, make connections
among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related
problems graphically;
A3. Solve exponential and simple logarithmic equations in one variable algebraically, including those
in problems arising from real-world applications;
B. Trigonometric Functions
B1. Demonstrate an understanding of the meaning and application of radian measure;
B2. Make connections between trigonometric ratios and the graphical and algebraic representations of
the corresponding trigonometric functions and between trigonometric functions and their reciprocals,
and use these connections to solve problems;
B3. Solve problems involving trigonometric equations and prove trigonometric identities;
C. Polynomial and Rational Functions
C1. Identify and describe some key features of polynomial functions, and make connections between
the numeric, graphical, and algebraic representations of polynomial functions;
C2. Identity and describe some key features of the graphs of rational functions, and represent rational
functions graphically;
C3. Solve problems involving polynomial and simple rational equations graphically and algebraically;
C4. Demonstrate an understanding of solving polynomial and simple rational inequalities.
D. Characteristics of Functions
D1. Demonstrate an understanding of average and instantaneous rate of change, and determine,
numerically and graphically, and interpret the average rate of change of a function over a given interval
and the instantaneous rate of change of a function at a given point;
D2. Determine functions that result from the addition, subtraction, multiplication, and division of two
functions and from the composition of two functions, describe some properties of the resulting
functions, and solve related problems;
D3. Compare the characteristics of functions, and solve problems by modelling and reasoning with
functions, including problems with solutions that are not accessible by standard algebraic techniques.
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This PART A – LINE RIDER is worth 20% of your final grade and will include the
following curriculum expectations:
(Observation & Conversation)
Line Rider Instructions: You are to work individually to complete this task. Apply your knowledge
of all types of functions to design a ride for a water park or theme park like Canada’s Wonderland. J
You will be using the programs: Line Rider and Desmos.
https://www.linerider.com
https://www.desmos.com/calculator
Your design should satisfy each of the conditions below:
a) Your ride is going to be designed for one of the following age groups: under 6, ages 6 to 12, or over
the age of 12. You will be required to describe the ride and argue why it’s appropriate for your
age group.
b) Your ride needs to have the following functions:
• Two different polynomial functions (degree 2 or greater)
• Two rational functions (one with remainder zero & one with remainder non-zero)
• One sinusoidal function
• One exponential, logarithmic function or composite function
c) The rider must ride on at least four of the above functions (in black colour). The rest can be part of
the background (in green colour).
d) Each of the above functions must include the following descriptions in the following order:
Note: Screen capture each function and place the screen captured image in Desmos for analysis.
• Table of values (15 coordinates determined by mouse zoom)
• Equation (curve of best fit determined by Excel)
https://www.extendoffice.com/documents/excel/2642-excel-best-fit-line-curve-function.html
• Intercepts (if any)
• Vertical Asymptote(s) (if any)
• Other Asymptote (if any)
• Domain and Range
• End Behaviours
• Interval of Increase
• Interval of Decrease
• Whether or not the function is continuous
• Whether the function is even or odd
e) Determine the greatest rate of change for each section of your ride. You will be required to justify if
your ride is safe for your age group chosen.
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f) How to submit your work:
• Please save your work every 5 min. ^_^
• Upload your work (Line Rider file, Excel file, and MS Word file) on the Schoology page.
• Each section has its own due date.
g) Class Presentation – April 29th, 2021
Your ride will be played in class. Your presentation should include a minimum of the following items:
• Describe the ride and argue why it’s appropriate and safe (discuss rates of change here) for your
age group.
• Describe the key/relevant properties of the functions you chose and explain how the equations
represent the ride.
• Explain the process you went through to determine your equations.
h) Self and Peer Evaluations
Each individual will be required to complete two evaluations.
Self-evaluation: it will be based on what you learned and the effort you put forth in this assignment.
Peer-evaluation: it will be for one of the other student’s presentation. It will outline what you think of
his or her ride and how they shared their information with the class.
Deadlines:
1) Basic design of your roller coaster: Friday, April 9th, 2021
2) Polynomial / rational / sinusoidal functions roller coaster design + excel spreadsheet
charts + properties in part (d): Monday, April 19th, 2021
3) Exponential, logarithmic, or composite functions roller coaster design + excel
spreadsheet charts + properties in part (d): Monday, April 26th, 2021
4) Presentation: Thursday, April 29th, 2021
5) Self/Peer-evaluation: Thursday, April 29th, 2021 (After presentations)
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Self-Evaluation
Each statement in this chart is to be answered about you.
Rate each of the following criteria on a scale of 1 to 5 with excellent or strongly agree being 5 and poor
or strongly disagree being 1.
Statement
Rate (1-5)
I contributed an enough amount of time to complete this assignment.
I learned more properties of functions that I did not think of before from this
assignment.
I do not feel that I could have contributed more to this assignment to make it better
than it is already.
I think that I put in the effort and as a result my work is better than the other
assessments I have worked in this course.
State one thing you would do differently, if you were assigned this exact same project again. If you would
do nothing differently, justify this response.
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Peer-Evaluation
Peer’s Name: ______________________________________
Rate each of the following criteria on a scale of 1 to 5 with excellent or strongly agree being 5 and poor
or strongly disagree being 1.
Statement
Rate (1-5)
About the Ride Itself
The ride looked fun to ride.
The ride was appropriate for the age group chosen and safe to ride.
The ride was presented in an awesome way (poster, model, animation).
The ride was made of up appropriate function equations.
Overall this ride was awesome!
About the Presentation
The presentation contained all the information asked for in this project.
The presenter was clear and the presentation was interesting.
The presenter was prepared.
Make up one question to ask the student at the end of their presentation. Write your question in the space
below.
State one great thing and one thing that could be improved about this student’s project (ride or
presentation).
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Observation & Conversation Rubrics (PART A – LINE RIDER)
Understanding of the Concepts (K/U:
12 Marks
Devises a
method
appropriate to
be applied to the
development of
a great ride.
Level 4
(100%~80%)
Level 3
(79%~70%)
Level 2
(69%~60%)
Level 1
(59%~50%)
Leve
lR
Demonstrates
thorough
knowledge/unde
rstanding of
content/concepts
Demonstrates
considerable
knowledge/unde
rstanding of
content/concepts
Demonstrates
some
knowledge/unde
rstanding of
content/concepts
Demonstrates
limited
knowledge/unde
rstanding of
content/concepts
No
Work
/Out
of
topic
12-11-10
9
8
7-6
5 -0
Level 3
(79%~70%)
Level 2
(69%~60%)
Level 1
(59%~50%)
Level R
(50% >)
Designing a Ride (T/I:
5 Marks each
Ensure the
functions chosen
accurately creates
a ride suitable for
the age group
chosen.
Demonstrates that
connections,
through
investigation
using graphing
technology,
between the
equations of
function and its
corresponding
graph have been
made.
/15 marks)
Level 4
(100%~80%)
Uses planning
skills with a high
degree of
effectiveness
Uses planning
skills with
considerable
effectiveness
Uses planning
skills with some
effectiveness
Uses planning
skills with
limited
effectiveness
No Work
/Out of
topic
5-4
Uses processing
skills with a high
degree of
effectiveness
3.5
Uses processing
skills with
considerable
effectiveness
3
Uses processing
skills with some
effectiveness
2.5
Uses
processing
skills with
limited
effectiveness
2-0
No Work
/Out of
topic
5-4
Has chosen
reasonable rates
of change to
create a safe, yet
fun ride.
/12 marks)
Uses
critical/creative
thinking
processes with a
high degree of
effectiveness
5-4
3.5
Uses
critical/creative
thinking
processes with
considerable
effectiveness
3.5
3
Uses
critical/creative
thinking
processes with
some
effectiveness
3
2.5
Uses
critical/creativ
e thinking
processes with
limited
effectiveness
2.5
2-0
No Work
/Out of
topic
2-0
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Class Presentation & Written Product - (COM: 12 marks)
3 Marks each
Use of mathematical
language to explain and
justify solutions.
Communicates ideas
effectively and
coherently.
Demonstrates
understanding of key
concepts of functions
Level 4
(100%~80%)
Level 3
(79%~70%)
Level 2
(69%~60%)
Level 1
(59%~50%)
Uses
conventions,
vocabulary, and
terminology of
the discipline
with a high
degree of
effectiveness
3 – 2.4
Communicates
and purposes
with a high
degree of
effectiveness
3 – 2.4
Expresses and
organizes
mathematical
thinking with a
high degree of
effectiveness
Uses
conventions,
vocabulary, and
terminology of
the discipline
with
considerable
effectiveness
2.3 – 2.1
Communicates
and purposes
with
considerable
effectiveness
2.3 – 2.1
Expresses and
organizes
mathematical
thinking with
considerable
effectiveness
Uses
conventions,
vocabulary, and
terminology of
the discipline
with some
effectiveness
Uses
conventions,
vocabulary, and
terminology of
the discipline
with limited
effectiveness
2 -1.8
Communicates
and purposes
with some
effectiveness
1.7 – 1.5
Communicates
and purposes
with limited
effectiveness
1.4 - 0
No
Work
/Out of
topic
2 -1.8
Expresses and
organizes
mathematical
thinking with
some
effectiveness
1.7 – 1.5
Expresses and
organizes
mathematical
thinking with
limited
effectiveness
1.4 - 0
No
Work
/Out of
topic
3 – 2.4
2.3 – 2.1
2 -1.8
1.7 – 1.5
1.4 - 0
3 – 2.4
2.3 – 2.1
2 -1.8
1.7 – 1.5
1.4 - 0
Level R
(50% >)
Concise, well-organized,
written explanation of
the solution.
Level
R (50%
>)
No
Work
/Out of
topic
Problem-Solving Procedures (APP: 15 marks)
7.5 Marks each
Level 4
(100%~80%)
Level 3
(79%~70%)
Level 2
(69%~60%)
Level 1
(59%~50%)
Determines the equations of
the functions that represents
the ride created with success.
Applies and
transfers
knowledge
and skills with
a high degree
of
effectiveness
7.5 - 6
Makes
connections
within
contexts with a
high degree of
effectiveness
7.5 - 6
Applies and
transfers
knowledge and
skills with
considerable
effectiveness
Applies and
transfers
knowledge
and skills
with some
effectiveness
Applies and
transfers
knowledge
and skills
with limited
effectiveness
5.5 - 5
Makes
connections
within contexts
with
considerable
effectiveness
5.5 - 5
4.5
Makes
connections
within
contexts with
some
effectiveness
4.5
4
Makes
connections
within
contexts with
limited
effectiveness
4
Describe the key features of
the graphs of functions in the
context of the ride created.
3.5 - 0
3.5 - 0
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Check list
Due Date
Friday, April 9th, 2021
Task
Part A – Basic design
Monday, April 19th, 2021
Part A – First set
Monday, April 26th, 2021
Part A – Second set
Wednesday, April 28th, 2021
Part B – Problem Solving
Thurs. April 29th, 2021
Part A – presentation &
Result
Self/peer Evaluations
Friday, April 30th, 2021
Part A & B – Final submission
o Final rubric
o .json file
o Excel spreadsheets
o Word document
o Self/Peer evaluation
o Part B – problem solving
o Don’t forget to submit the learning log!
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