2022-Quiz1-answers
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University of Toronto *
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135Y1
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
9
Uploaded by UltraRoseSeal55
8/20/23, 10:59 AM
Quiz: Quiz 1
https://q.utoronto.ca/courses/277721/quizzes/287377/take?preview=1
1/9
Quiz 1
This is a preview of the published version of the quiz
Started: Aug 20 at 8:43a.m.
Quiz Instructions
Quiz period
: October 3, 2022 between 7pm and 9:30pm
Quiz time
: 75 minutes from first access (up to 9:30pm)
You can submit the quiz several times within the 75 minutes.
You can submit it an unlimited number of times. Your
last submission
is the only one that will count.
Beware:
If you start a new submission, you can't cancel it, so the previous one will no longer be
graded. Also, the questions will change.
Allowed Aids
: Calculators (including online calculators like Desmos or Geogebra), textbook, and your
notes
Forbidden Aids
:
Consulting with anybody else or use any other internet resource.
This Quiz must be completed by the student registered in this class, alone and without any assistance
from another person - face-to-face or digital. The following are considered academic offences in this
course:
Having someone else write this quiz on your behalf
Writing the quiz on behalf of someone else
Posting this quiz online, even if you have completed it
Submitting questions from this quiz online
Viewing questions from this quiz online
Searching questions for this quiz
Talking about the answers to this quiz - even if it is just hinting at it while it is open (before 9:30pm).
Communicating with another person enrolled in the course while the quiz is open (between 7–
9:30pm), either before or after you submit it
8/20/23, 11:00 AM
Quiz: Quiz 1
https://q.utoronto.ca/courses/277721/quizzes/287377/take?preview=1
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Students at UofT are bound by the Student Code of Conduct. Any suspected, potential, or confirmed
violations of Academic Integrity standards will be referred to the Office of Student Academic Integrity for
full investigation.
0.1 pts
Question 1
Academic Integrity Statement
In submitting this assessment ...
In short
... I confirm that my conduct during this test adheres to the
Code of Behaviour on Academic Matters
(https://governingcouncil.utoronto.ca/secretariat/policies/code-
behaviour-academic-matters-july-1-2019)
.
I know the Code.
... I confirm that I have not acted in such a way that would
constitute cheating, misrepresentation, or unfairness,
including but not limited to, using unauthorized aids and
assistance, impersonating another person, and committing
plagiarism.
I didn't cheat.
... I confirm that the work I am submitting in my name is the
work of no one but myself.
This is my work.
... I confirm that all solutions have been submitted by myself.
I submitted the quiz.
... I confirm that I have not received help from others,
whether directly or indirectly.
I didn't receive help.
... I confirm that I have not provided help to others, whether
directly or indirectly.
I didn't provide help.
... I confirm that I have only used the aids marked as
approved in the "
Allowed List
" in the Quiz Information Page.
I only used allowed
aids.
... I am aware that not disclosing another student's
misconduct despite my knowledge is
an academic offence.
I know I must report
cheating.
Please
check all the boxes
below to confirm that you didn't commit an academic
offence.
8/20/23, 11:00 AM
Quiz: Quiz 1
https://q.utoronto.ca/courses/277721/quizzes/287377/take?preview=1
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I know the Code.
I didn't cheat.
This is my work.
I submitted the quiz.
I didn't receive help.
I didn't provide help.
I only used "OK" aids.
I know I must report cheating.
Note: If you don't select all the boxes below, you will receive 0 on this
quiz.
1 pts
Question 2
We want to sketch the graph
We will start with the graph of a basic function
, that you will have to determine,
and then we will make several “simple” transformations.
Step 1
. Sketch the graph of a basic function
f(x)=eˣ
Step 2
. Stretch the function vertically to get:
g(x)=10f(x)
Step 3
. Flip the function vertically (across the
axis) to get:
h(x)=–g(x)
Step 4
. Flip the function horizontally (across the
axis) to get:
k(x)=h(–x)
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Step 5
. Make a horizontal shift to get:
l(x)=k(x–23)
Step 6
. Make a vertical shift to get:
m(x)=l(x)–5
1.1 pts
Question 3
When the price of a stone was 10¥, the number of workers mining stones was 53.
When the price of a stone was 53¥, the number of workers mining stones was 10.
On days when 53 stones are mined, their price is 10¥.
When 10 stones are mined, their price is 53¥.
On a day when 53 workers are mining stones, then they mine 10 stones.
On a day when 10 workers are mining stones, then they mine 53 stones.
Consider the following functions:
is the number of miners working on a day when
stones are mined
is the price of a stone in yen (¥) on a day when
miners are working
Suppose both functions are invertible.
What is the
practical interpretation
of
1.4 pts
Question 4
Click below to access Desmos:
8/20/23, 11:00 AM
Quiz: Quiz 1
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https://www.desmos.com/calculator/vkfx5ezbbv
(https://www.desmos.com/calculator/vkfx5ezbbv)
You will find some plotted data.
Play with the sliders
and follow the instructions to find the
best fitting curve
to the
data: the one that
minimizes the Error
.
Hint:
With the right model, the error can be lower than
0.3
.
Then answer the questions below:
(a)
The type of function that best fits the data is
[ Select ]
For
(b)
and
(c)
, note that some models have restrictions on the value of
.
(b)
The parameter
[ Select ]
(c)
The best value for
is
[ Select ]
(d)
The parameter
[ Select ]
(e)
The best value for
is
[ Select ]
(f)
The parameter
[ Select ]
(g)
The best value for
is
[ Select ]
(h)
The parameter
[ Select ]
(i)
The best value for
is
[ Select ]
1 pts
Question 5
8/20/23, 11:00 AM
Quiz: Quiz 1
https://q.utoronto.ca/courses/277721/quizzes/287377/take?preview=1
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In a Nature paper (
https://www.nature.com/articles/s41598-022-08502-8
(https://www.nature.com/articles/s41598-022-08502-8)
), the authors are testing the
ability to describe the cancer risk in 8 different tissues.
The figure below is a
plot taken from the paper describing the risk
as a function of the quantity
.
They use the dotted red line with formula
as a good fit for the
data.
Assuming the the authors are correct, what is the implication of this line for the
original data:
vs
?
Note: You don't need to check the paper to be able to answer this question.
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1.2 pts
Question 6
You receive some data from an experiment:
1.005
2
2.95
3.995
4.95
7.01
7.995
5.30
5.40
5.33
4.58
4.56
3.58
3.16
We don't have any more details about the origin of the data.
The measurements in the table are represented by the white dots in the graph below.
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Quiz: Quiz 1
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The linear model, because even though it doesn't match the data points exactly, it captures
the essence of the data better.
The polynomial model, because it passes through all the data points exactly, so it captures
the data perfectly.
Which of the following functions model this data best?
1.2 pts
Question 7
You receive some data from some measurements:
0.004
1.27
2.5
3.729
4.959
6.189
7.419
0.508
0.754
1
1.246
1.492
1.738
1.984
The measurements are for the
height between the road and a point on the tire
of a
moving car.
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The linear model, because it captures the data perfectly and is the simpler model, so it will
allow us to make more reliable predictions.
The trigonometric model, because it captures the data perfectly and accounts for the wheel's
movement.
The measurements in the table are represented by the white dots in the graph below.
Which of the following functions model this data best?
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