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.
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?
21.11.2023 13:17 D?screte Funct?ons Un?t Ass?gnment
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 D?screte Funct?ons Un?t Ass?gnment
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 contribute to your overall final grade in this course.
23.11.2023 14:16 Explor?ng Funct?ons Un?t Ass?gnment
Listen
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.
out of
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.
23.11.2023 14:16 Explor?ng Funct?ons Un?t Ass?gnment
1. Answer the following for each of the given relations. (4 marks each)
a. b. c. d.
:See image
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 after it has gone through the follow transformations: (show a graph for each
23.11.2023 14:16 Explor?ng Funct?ons Un?t Ass?gnment
step)
a. (4 marks) b.
(6 marks)
4. Given and each)
a. b. c.
, evaluate the following: (3 marks
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 contribute to your overall final grade in this course.
20.11.2023 14:50 Exponent?al Funct?ons M?d-Un?t Ass?gnment
Listen
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.
out of
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.
1. Express the following expression in the form . Use exact values only. (9 marks)
a. b. c.
2. Prove that f and g are equivalent using both the graphical and algebraic approach. If they are not, provide a counter-example that shows how they are not equivalent. (6 marks)
20.11.2023 14:50 Exponent?al Funct?ons M?d-Un?t Ass?gnment
a.
b.
3. Solve: (5marks)
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)
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 12:43 Exponent?al Funct?ons Un?t Ass?gnment
out of
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.
1. Determine the exact value of . (3 marks each) a.
Listen
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.
x
63+)3(5= 3
x x2
21.11.2023 12:43 Exponent?al Funct?ons Un?t Ass?gnment
b. c.
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).
b. Has an initial value of 4893, passes through the coordinate point (–2, 93) and has a range of .
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).
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.
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 Botryococcus braunii, 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. (3 marks each)
a. Determine the rule, domain, and range of the function model.
1± = k
}R ∈ y ,0 < y|y{
}R ∈ y ,7− > y|y{
7− = y
)x(T
x
02+ )2(06=)x(T
x
1+x2
) 8 (
3−x 1
) 72 ( = 3
02+2x
x3 1
61 × 2 =
21.11.2023 12:43 Exponent?al Funct?ons Un?t Ass?gnment
b. Graph the function model.
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 13:16 Sequences and Ser?es M?d-Un?t Ass?gnment
Listen
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.
out of
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.
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
21.11.2023 13:16 Sequences and Ser?es M?d-Un?t Ass?gnment
b. Table Two
Table One
20 50 –178
Table Two
10 0.2 –3
–2.5
3. Express the following expansions as a binomial in the form clear evidence of your reasoning. (3 marks each)
a. b. c. d.
. Leave
4. Determine the constant term of each binomial expansion. (3 marks each) a.
b. c.
5. Consider the Fibonacci sequence.
nS nt r a n
nS nt d a n
21.11.2023 13:16 Sequences and Ser?es M?d-Un?t Ass?gnment
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)
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 13:19 The Amb?guous Case M?d-Un?t Ass?gnment
Listen
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 must be completed in degrees. 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.
out of
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.
1. Determine whether –105° and –465° are co-terminal angles. Justify your answer fully. (5 marks)
21.11.2023 13:19 The Amb?guous Case M?d-Un?t Ass?gnment
2. Determine and sketch the principal angle for the reference angle 35° in quadrant II. (6 marks)
3. In ΔABC, , , (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 .
b. Determine the exact value of .
c. Determine the exact value of .
given that given that given that
is in quadrant III and is in quadrant IV and 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 ABC:
, , and
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)
Submit this assignment to the dropbox. This assignment will be evaluated for a grade that will
21.11.2023 13:19 The Amb?guous Case M?d-Un?t Ass?gnment
contribute to your overall final grade in this course.
21.11.2023 13:21 Tr?gonometr?c Funct?ons and Graphs M?d-Un?t Ass?gnment
Listen
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 must be completed in degrees. 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.
out of
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.
1. Determine the period of each of the following periodic relations and whether the relation is a function or not. (3 marks each)
21.11.2023 13:21 Tr?gonometr?c Funct?ons and Graphs M?d-Un?t Ass?gnment
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 , , . (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.
, and
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)
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 13:22 Tr?gonometr?c Funct?ons and Graphs Un?t Ass?gnment
Listen
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 must be completed in degrees. 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.
out of
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.
1. The average monthly temperatures in New Orleans, Louisiana, are given in the following tables: (2 marks each)
21.11.2023 13:22 Tr?gonometr?c Funct?ons and Graphs Un?t Ass?gnment
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
MonthJ F M A M J
°C 16.5 18.3 21.8 25.6 29.2 31.9
MonthJ 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 Tr?gonometr?c Funct?ons and Graphs Un?t Ass?gnment
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) 0123456789
Distance from net (m)
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 cm
21.11.2023 13:22 Tr?gonometr?c Funct?ons and Graphs Un?t Ass?gnment
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 Tr?gonometry Un?t Ass?gnment
Listen
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 must be completed in degrees. 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.
out of
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.
1. Prove the following identities. Show all of your steps. (3 marks each) a.
b. c.
21.11.2023 13:20 Tr?gonometry Un?t Ass?gnment
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.
