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Discrete Functions Unit Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course always be sure to use
the following guidelines to help you do your best:
Provide full solution, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don't use self-developed short form notations.
1. A high performance all-terrain vehicle (ATV) is bought at a price of $20,000. It
loses 10% of its value every year. Express this scenario as a sequence
recursively and explicitly (provide its general term). (3 marks)
2. Following one side of a new street in a neighbourhood, the house numbers
increase by six. The house number of the first house on the street is 319.
Express this sequence recursively and explicitly. (3 marks)
3. $100 is deposited at the end of every week for five years in an account that
pays 14%/a, compounded weekly. (2 marks each)
a. What type of annuity is this?
Listen
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b. Find the future value of the annuity using the formula.
c. Find the future value of the annuity using a spreadsheet. In your answer
include the formulas that you typed.
d. Find the future value of the annuity using the TVM solver on a graphing
calculator or on a website. In your answer, include what values you typed
for each parameter.
4. Vanna has just financed the purchase of a home for $200,000. She agreed to
repay the loan by making equal monthly blended payments of $3,000 each at
4%/a, compounded monthly. (2 marks each)
a. Create an amortization table using a Microsoft Excel spreadsheet. In your
answer include all the formulas used.
b. How long will it take to repay the loan?
c. How much will be the final payment?
d. Determine how much interest she will pay for her loan.
e. Use Microsoft Excel to graph the amortization of the loan Hint
f. How much sooner would the loan be paid if she made a 15% down
payment?
g. How much would Vanna have saved if she had obtained a loan 3%/a,
compounded monthly?
h. Write a concluding statement about the importance of interest rates and
down payments when taking out loans.
5. A lottery offers two options for a prize, A and B, as shown below.
a. Which option would the winner choose if you expect to live for another: (2
marks)
20 years?
50 years?
b. Use technology to determine the range of life expectancies when each
option is preferred. Show your work. (2 marks)
c. Write a brief reflection about which option you would choose, and why. (3
marks)
Option A: $1,000 a week for life.
Option B: $1,000,000 in one lump sum.21.11.2023 13:17
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If you choose Option B, you have the opportunity to
place the winnings into an investment that also makes
regular payments, at a rate of 3%/a, compounded
weekly. The annuity will pay out a specific amount
weekly based on how long you want the annuity to
last.
6. Mary would like to save $10,000 at the end of 5 years for a future down
payment on a car. (3 marks each)
a. How much should she deposit at the end of each month in a savings
account that pays 1.2%/a, compounded monthly, to meet her goal?
b. If you currently have a part-time job, consider your hourly wage. If you do
not have a job, use the minimum hourly wage in your jurisdiction. How
many hours each month would you have to work, just to make those
payments? Write a brief reflection on the advantages and disadvantages to
long-term saving for a purchase, compared to borrowing a large sum of
money and paying it off over time. Note that interest rates for savings
accounts are always lower than interest rates for borrowing.
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
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Exploring Functions Unit
Assignment
Congratulations! You’ve reached the first assignment in your course. To submit
your assignment, just navigate to the next page, upload your file(s), and select
the “Submit” button to submit the activity to your teacher. Before completing an
assignment, we recommend that you complete all of the practice activities in the
unit and wait for feedback. The feedback from the practice activities will help you
improve your understanding and will help you to achieve the best possible mark
on your assignments.
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, please e-mail your teacher for assistance.
Important
When answering questions in a mathematics course always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Make sure all graphs are titled with labeled axes.
Listen
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1. Answer the following for each of the given
relations. (4 marks each)
a.
:See image
b.
c.
d.
Determine the domain and range using set
notation.
Determine the inverse relation.
Is the relation a function? Justify your answer fully.
Is the inverse relation a function? Justify your
answer fully.
2. A set of transformations is applied to
in each case to produce
.
Determine the value of each transformational parameters, and describe the
transformations using the language presented in the course content. (5 marks
each)
a. Figure 1
b. Figure 2
Figure 1
Figure 2
3. The graph of
is provided. Neatly and precisely graph the image of
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step)
a.
(4 marks)
b.
(6 marks)
4. Given
and
, evaluate the following: (3 marks
each)
a.
b.
c.
5. So that a credit card number can be sent as a message securely, it is encoded
in the following way: the coded digits are found by subtracting each of the
original digit from 9. (1 mark each)
a. Code the credit card number 8347 3266 8887 0997.
b. A coded credit card number is 5145 9042 7903 0144. What is the original
credit card number?
c. Determine
if represents a single input digit.
d. Determine
.
e. Determine the domain of
and
.
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
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Exponenti al Functi ons Mi d-Uni t Assi gnment
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Exponential Functions Mid-Unit
Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
1. Express the following expression in the form
. Use exact values
only. (9 marks)
a.
b.
c.
2. Prove that and are equivalent using both the graphical and algebraic
approach. If they are not, provide a counter-example that shows how they are
not equivalent.
f g
(6 marks)
Listen
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a.
b.
3. Solve:
(5 marks)
4. Transform the graph of
into
. Show a table of
values and a graph (neatly sketched by hand) for each step of the
transformation starting from
. (15 marks)
5. State the domain, range, -intercept(s), -intercept(s) and asymptote(s) of the
given function:
. (7 marks)
6. You have learned about quadratic and linear function in earlier grades.
Explain in a variety of ways how you can distinguish the exponential function
from the quadratic function
and linear function
. Hint (8 marks)
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Exponential Functions Unit
Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Make sure all graphs are titled with labeled axes
Note
Before working on this assignment, wait for feedback on the previous
assessments. In the meantime, you may review concepts covered in this
unit or begin the next topic.
1. Determine the exact value of x. (3 marks each)
a. 3
2x = 5 (3
x
) + 36
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b. (
1
8
)
x−3 = 2 × 16
2x+1
c. 3
x
2+20 = ( 2
1
7
)
3x
2. Determine the rule of an exponential function that has the given properties.
Validate your answer using a graph. (4 marks each)
a. Has a base of 6, an asymptote at , has parameter , and
passes through the coordinate points (3, –4) and (4, 11).
y = −7 k = ±1
b. Has an initial value of 4893, passes through the coordinate point (–2, 93)
and has a range of {y|y > −7, y ∈ R}.
c. Has a range of , has a base of 2, has no horizontal
translation from the base function, and passes through the coordinate
points (0, –37.6) and (7, –75.2).
{y|y < 0, y ∈ R}
3. The plutonium isotope Pu-239 is a radioactive material. The half-life of
plutonium isotope Pu-239 is 24 360 years. Ten grams of plutonium is released
in a nuclear accident. (4 marks each)
a. Determine the rule, domain, and range of the function model.
b. How long will it take for the 10 grams to decay to 1 gram? Round off your
answer to the nearest year.
4. A bacteria culture population of 50 bacteria doubles in size every 20 minutes.
(4 marks each)
a. Establish the function rule that models this situation and graph it.
b. How long will it take for the bacterial culture grow to a population of
250 000?
5. The temperature of a cooling liquid over time can be modeled by the
exponential function
, where is the temperature in
degrees Celsius, and is the elapsed time in minutes.
T (x) = 60(
1
2
)
x
30 + 20 T(x)
x
a. Graph the function and determine how long it takes for the temperature to
reach 28 °C. (5 marks)
b. What was the initial temperature? (2 marks)
6. The initial dryweight of , a green microalgea, is 50 mg/L.
Under the right conditions of light, temperature, salinity and pH, the algea
triples every three hours for the first 15 hours of growth. ( )
Botryococcus braunii
3 marks each
a. Determine the rule, domain, and range of the function model.21.11.2023 12:43
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b. Graph the function model.
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Sequences and Seri es Mi d-Uni t Assi gnment
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Sequences and Series Mid-Unit
Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, email your teacher for assistance.
Important
When answering questions in a mathematics course always be sure to use
the following guidelines to help you do your best:
Provide full solution, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don't use self-developed short form notations.
1. Compare and contrast the following in details: (2 marks each)
a. An arithmetic sequence and a geometric sequence.
b. A sequence and a series.
c. Discrete data and continuous data.
d. An explicit and a recursive representation.
2. Determine the values of the following tables. Show all of your work. Be mindful
of possible multiple solutions. (5 marks each)
a. Table One
Listen
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b. Table Two
Table One
n
a
d
tn
Sn
16
10
8
20
50
–178
0.2
1.2
59
Table Two
n
a
r
tn
Sn
8
1
128
10
0.2
–3
12
5120
–2.5
3. Express the following expansions as a binomial in the form
. Leave
clear evidence of your reasoning. (3 marks each)
a.
b.
c.
d.
4. Determine the constant term of each binomial expansion. (3 marks each)
a.
b.
c.
5. Consider the Fibonacci sequence.21.11.2023 13:16
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a. Express it recursively. (2 marks)
b. Evaluate the explicit formula to find the 20th and 50th term of Fibonacci
sequence. (2 marks)
c. Search the web for the explicit formula for a Fibonacci sequence term.
Include the source of where you found the formula in APA style formatting.
(3 marks)
6. Compare each the arithmetic and geometric sequences to a function that we
covered in a previous unit. Use an example in your explanation. (4 marks)
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The Ambi guous Case Mi d-Uni t Assi gnment
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The Ambiguous Case Mid-Unit
Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, use the following
guidelines to help you do your best:
Provide full solution, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don't use self-developed short form notations.
Important
All work be completed in . Radians are another option that you
will learn about in Grade 12, they are not covered in this course. For this
course all work must be completed in degrees.
must degrees
1. Determine whether –105° and –465° are co-terminal angles. Justify your
answer fully. (5 marks)
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2. Determine and sketch the principal angle for the reference angle 35° in
quadrant II. (6 marks)
3. In Δ ,
,
,
ABC
(3 marks each)
a. Determine the number of possible solutions.
b. Determine the measure(s) of
if it exists.
4. Determine the following ratios within their given context. Sketch each triangle
appropriately. (3 marks each)
a. Determine the exact value of
given that is in quadrant III and
.
b. Determine the exact value of
given that is in quadrant IV and
.
c. Determine the exact value of
given that is in quadrant II and
.
5. Two hunters leave the same camp site in the morning, on their four wheelers.
One heads 30° north of east for 50 km, and the other goes for 64 km heading
80° west of south, and they stop for a break. Calculate the distance that
separates the two hunters (Express your answer to 4 decimal place). (4
marks)
Case Study - The Ambiguous Case
6. Consider triangle :
,
, and
ABC
a. Sketch the triangle(s). (4 marks)
b. Solve for side using Cosine law. (3 marks)
c. Solve for the missing angles using Sine law only and then separately using
Cosine law only.
(6 marks)
d. Investigate the discrepancy (i.e. one has two solutions, and the other one
solution). Which is correct? Justify/explain. (7 marks)
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contribute to your overall final grade in this course.21.11.2023 13:21
Tri gonometri c Functi ons and Graphs Mi d-Uni t Assi gnment
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Trigonometric Functions and Graphs
Mid-Unit Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Important
All work be completed in . Radians are another option that you
will learn about in Grade 12, they are not covered in this course. For this
course all work must be completed in degrees.
must degrees
1. Determine the period of each of the following periodic relations and whether
the relation is a function or not. (3 marks each)
Listen
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a.
b.
c.
2. A cosine function has been vertically stretched by a dilation factor of 45,
reflected by the -axis, horizontally stretched by a dilation factor of 10 and
translated up by 33 units. Determine the values of the parameters , and
.
, ,
(3 marks)
3. For the following sinusoidal functions, graph one period of every
transformation from its base form, and describe each transformation. Be
precise. (6 marks each)
a.
b.
4. For each, determine the amplitude, the axis of the curve, the range, the
period, the phase shift, and the zero(s) within one period. Keep your solutions
neat and organized. (7 marks each)
a.
b.
c.
5. A sine function that has an amplitude of 16 units, a period of 5 units, a vertical
displacement of 3 units up, and a phase shift of 2.5 units left. Graph this
function and show each step. (5 marks)
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Trigonometric Functions and Graphs
Unit Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
please, submit your calculations as a single file document (preferably as a pdf). If
you aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Important
All work be completed in . Radians are another option that you
will learn about in Grade 12, they are not covered in this course. For this
course all work must be completed in degrees.
must degrees
1. The average monthly temperatures in New Orleans, Louisiana, are given in
the following tables: (2 marks each)
Listen
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a. What is the range of this function?
b. What is the average yearly temperature?
c. Can this data be modelled using a sinusoidal function? Justify your answer.
d. Graph the data using a scatter plot. Does this confirm the answer from
question c. above?
e. Given the general sinusoidal function
, what
do , , , and represent in the real world situation being modelled?
f. Determine the temperature function
. Hint
Month J
F
M
A
M
J
°C
16.5
18.3
21.8
25.6
29.2
31.9
Month J
A
S
O
N
D
°C
32.6
32.4
30.3
26.4
21.3
18.0
2. The city of Windsor, Ontario, receives its maximum amount of sunlight of
15.28 hours on June 21, and its least amount of sunlight of 9.08 hours on
December 21. (4 marks each)
a. Due to the Earth's revolution about the sun, the hours of daylight function is
periodic. Determine an equation that can model the hours of daylight
function for Windsor, Ontario.
b. On what day(s) can Windsor expect 13.5 hours of sunlight?
3. Tides are cyclical phenomena caused by the gravitational pull of the sun and
the moon. On a particular retaining wall, the ocean generally reaches the 3 m
mark at high tide. At low tide, the water reaches the 1 m mark. Assume that
high tide occurs at 12:00 p.m. and at 12:00 a.m., and that low tide occurs at
6:00 p.m. and 6:00 a.m. What is the height of the water at 10:30
a.m.? (5 marks)
4. The largest Ferris Wheel in the world is the London Eye in England. The
height (in meters) of a rider on the London Eye after minutes can be
described by the function
.21.11.2023 13:22
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a. What is the diameter of this Ferris wheel? (1 mark)
b. Where is the rider at
? Explain the significance of this value. (2
marks)
c. How high off the ground is the rider at the top of the wheel? (1 mark)
d. At what time(s) will the rider be at a height of 100 m? (2 marks)
e. How long does it take for the Ferris wheel to go through one rotation? (2
marks)
f. Determine where the minimum values of this function occur in the following
restricted domain:
(2 marks)
5. At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is
essentially a large pendulum of which the rider is the bob. A vertical net for
safety is included. The rider's horizontal distance to the safety net is given for
various times:
a. Create a graph of the distance of the pendulum from the net with respect to
time. (2 marks)
b. Find the graph's amplitude, period, vertical translation, and phase shift for
this function. Note (2 marks)
c. Determine the equation of the modelling function in the form:
(2 marks)
d. How could the amplitude be determined without creating the graph or
finding the function?
(1 mark)
e. What is the maximum horizontal displacement for this pendulum? (1 mark)
f. The time for one complete cycle is the period. How long would it take to
complete 15 cycles?
(2 marks)
Time (s)
0
1
2
3
4
5
6
7
8
9
Distance from net
(m)
55
53
46
36
25
14
7
5
8
15
6. A mass suspended on a spring will exhibit sinusoidal motion when it moves. If
the mass on a spring is 85 cm off the ground at its highest position and 41 cm21.11.2023 13:22
Tri gonometri c Functi ons and Graphs Uni t Assi gnment
https://lms.vi rtualhi ghschool.com/d2l/le/enhancedSequenceVi ewer/64443?url=https%3A%2F%2F7373ee8e-81ee-4ff2-abda-d6a83ec1978f.sequ…
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off the ground at its lowest position and takes 3.0 s to go from the top to the
bottom and back again, determine an equation to model the data. (5 marks)
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
contribute to your overall final grade in this course.21.11.2023 13:20
Tri gonometry Uni t Assi gnment
https://lms.vi rtualhi ghschool.com/d2l/le/enhancedSequenceVi ewer/64443?url=https%3A%2F%2F7373ee8e-81ee-4ff2-abda-d6a83ec1978f.sequ…
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out of
50
Trigonometry Unit Assignment
You may choose to complete your mathematical calculations by hand and scan or
take images to upload to the dropbox. To help your teacher review your work,
submit your calculations as a single file document (preferably as a pdf). If you
aren’t sure how to do this, e-mail your teacher for assistance.
Important
When answering questions in a mathematics course, always use the
following guidelines to help you do your best:
Provide full solutions, showing all of your steps.
Make sure that there is one step or idea per line.
Use one equal sign per line.
Make sure that equal signs line up vertically.
Don’t use self-developed short form notations.
Important
All work be completed in . Radians are another option that you
will learn about in Grade 12, they are not covered in this course. For this
course all work must be completed in degrees.
must degrees
1. Prove the following identities. Show all of your steps. (3 marks each)
a.
b.
c.
Listen
21.11.2023 13:20
Tri gonometry Uni t Assi gnment
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d.
2. Verify the following for
: (5 marks)
3. Verify the following algebraically: (5 marks)
4. Given that
for
.
a. How many solutions are possible for ? (2 marks)
b. In which quadrants would you find the solution(s)? (2 marks)
c. Determine the reference angle for this equation to the nearest degree. (1
mark)
d. Determine all the solutions to the equation to the nearest degree. (2 marks)
5. Solve the following linear trigonometric equations algebraically (without
graphing technology) for all solutions in the domain
. Use exact
solutions whenever possible. (3 marks each)
a.
b.
c.
6. Solve the following quadratic trigonometric equations algebraically (without
graphing technology) for all solutions in the domain
. Use exact
solutions whenever possible. (6 marks each)
a.
b.
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
contribute to your overall final grade in this course.
