Adapted from:
Sarah Good
Mountain View High School
Sarah.good@mvla.net
Project Menu for
Algebra 2 Honors
Project Menu for Algebra 2 Honors (can be adapted to Trigonometry/Math Analysis)
You will complete and present 2 projects each semester. You must do one by the end of
the quarter, but can do both projects first quarter. You will be given a chance to revise
your project based on feedback (if it is turned in early enough).
Bonus 1: If you know of an application I haven’t listed, you can propose your own
project for any chapter. (I’ve included some suggestions from last year)
Bonus 2: If homework is a waste of your time, you can complete one of the projects for
each chapter instead of doing homework for the chapter. The points given for the project
will equal the total number of homework points for the chapter.
Good projects require:
Processing Skills (making sense of new content)
Content (facts, concepts, skills, principles and attitudes)
Resources (use of appropriate research skills)
Product (a well designed product)
Citation of sources (include any websites, books, interview subject information, etc.)
Chapter 2: Functions in the real world:
Graphs can be used to represent “real world” situations where one variable is related to
another.
 Correct scale and labeling of axes is important.
 Graphs may have limited ranges of validity.
 Graphs can be used to misrepresent data.
1. Pick several of the “word problems” from section 2.3 and draw the graphs that go
along with them (labeling the axes properly in units that can be measured). Make up
several more of your own. What are the domain and range for each graph? Can the
2.
3.
4.
5.
domain and range be extended in the positive direction? The negative direction?
Why or why not? Illustrate your graphs for a lovely poster presentation.
Given a set of graphs, make “real world” problems that are represented by the graphs.
Label the axes correctly in units that can be measured. What are the domain and
range for each graph? Can the domain and range be extended in the positive
direction? The negative direction? Why or why not? Illustrate your graphs for a
lovely poster presentation. Cite your sources, if any.
Pick a “real world” example from another class (social studies, PE, science) where
one aspect varies with another aspect with a constant of variation. Cite your sources.
Show several examples (graphically) with different constants of variation. Compare
and contrast the graphs. What are the domain and range for each graph? Can the
domain and range be extended in the positive direction? The negative direction?
Why or why not? Illustrate your graphs for a lovely poster presentation.
Lies, damn lies and statistics I. Find several graphs from the newspaper, your text
books and/or magazines that are in some way unclear (I’ve found USA Today has
graphs that misrepresent data). Evaluate the graphs, write your evaluation of the
graphs in paragraph form. (Are the scales correct? Does the graph represent what it
claims?) If you were to improve the graph, what improvements would you make?
Can you continue the x-axis scale to go beyond the scale in the graph? Present your
graphs and “arguments” in poster form. Cite your sources.
Lies, damn lies and statistics II. Graphs can be used in the media or in reports that
have correct scale and are correctly labeled but that can be used to misrepresent the
data. Pick some data from an area that interests you and represent the data in three
different graphs that make the results “look” very different. Under what circumstance
would you use each of the graphs to persuade an audience? Cite your sources.
Present your graphs and “arguments” in poster form.
Chapter 3: Linear functions
Graphs can be used to represent “real world” situations where one variable is related to
another by a linear equation.
 Graphs of linear functions are similar (what is the effect of a negative slope? a
zero slope? an undefined slope?)
 Slope and y-intercept have “real world” meaning.
 Positive, negative and zero slopes have “real world” meaning.
 Different positive slopes have “real world” meaning.
 The domain and range of the problem may have limited validity.
 When we use linear models we may be ignoring some “real life” effects.
1) Section 3.3 gives three different forms of a Linear Function. Each of these equations
is useful in different situations.
a) For each form, explain the easiest method for graphing the equation (do not say
change it to another form). Give an example and show/describe graphing steps.
b) For each form, write a word problem that utilizes that form (that would be
graphed as you explained in part a).
c) Discuss the limits of the model (word problem) for each situation in part b).
2) Find “real world” data that seems to follow a linear model. (Include the data and cite
your source).
a) Graph your data on a large graph (by hand) that can be seen from the back of
the room. Describe how you picked your scale. Label the axes clearly and
give your graph a title.
b) Find the equation of the linear model. (You may need to do a line of best fit.)
Show your work neatly and completely.
c) Describe the “real world” meaning of the slope in your model.
d) Describe the “real world” meaning of the y-intercept in your model.
e) Describe the limits of your model.
f) Ask three well worded questions that can be answered by your graph. Include
a question predicting the future that can be answered with your graph. (You
don’t have to answer your questions on your poster, but should be able to
answer them if asked.)
3) Parallel lines.
a) Graph three parallel lines and give their equations.
b) Section 3.3 gives three different forms of a Linear Function. Describe how
you can tell if lines are parallel from each of the three forms.
c) Write a “real world” problem that involves parallel lines.
d) Graph your model on a large graph (by hand) that can be seen from the back
of the room. Label the axes clearly and give your graph a title.
e) Describe the “real world” meaning of the slopes in your model.
f) Describe the “real world” meaning of the y-intercepts in your model.
4) Find someone who uses linear equations in their job. (Provide me with the name of
the person you interview, their email address (if any) and phone number). Interview
them to find out how they use linear equations. Write up your interview in report
form. Describe your interviewee and their job. Describe how they use linear
equations. Include at least one example of a linear equation they use. Graph the
example on graph paper by hand using appropriate scale. Label the axes. Explain the
“real world” meaning of the slope and y-intercept in the example you provide.
Summarize your findings.
5) Perpendicular lines.
a) Graph two perpendicular lines and give their equations.
b) Section 3.3 gives three different forms of a Linear Function. Describe how
you can tell if lines are perpendicular from each of the three forms.
c) Write a “real world” problem that involves perpendicular lines.
d) Graph your model on a large graph (by hand) that can be seen from the back
of the room. Label the axes clearly and give your graph a title.
e) Describe the “real world” meaning of the slopes in your model.
f) Describe the “real world” meaning of the y-intercepts in your model.
6) Vertical lines:
a) What is the equation of a vertical line?
b) How does the equation of a vertical line differ from the equations of lines
given in section 3.3.
c) Why can’t you use the slope formula to find the slope of a vertical line?
d) Why can’t you divide by zero? Explain why the slope does not exist. Do
some research about dividing by zero. (Cite your sources). Be prepared to
convince your classmates why you cannot divide by zero.
e) What is the equation of a line perpendicular to a vertical line? Why do all of
our formulas work for this kind of line? Why doesn’t this contradict the
definition of slopes of perpendicular lines on pg. 88?
f) Present your project in report form with well written paragraphs.
Chapter 4: Systems of Equations
Systems of equations and linear inequalities can be used to describe real world
situations.
 The point(s) of intersection are the solution(s) to both equations.
 Some systems have no solutions.
 Some systems have infinitely many solutions.
 There are many ways to solve systems of linear equations.
 “No solution” and “ infinitely many solutions” appear differently in the different
methods.
 Systems of 3 equations in 3 unknowns can be solved in similar methods.
1) Make a model that can be used to demonstrate graphing in 3-dimensions. You
should be able to show graphing a point in 3-dimensions. You should also be
able to graph planes in 3-space. Be able to show the examples described in
problem 5 on page 138.
2) Research the 4th dimension. If a point on a line shows zero space in 1
dimension and a line in a plane shows 1 dimension in 2 dimensions and a
plane in 3 dimensions shows 2 dimensions in 3 dimensions, how would you
extend the 3 dimension coordinate system into the 4th dimension. Present
your research results in either poster or report form. Include drawings/models
to illustrate what you’ve learned. Cite resources.
3) Systems of equations are defined as “inconsistent”, “dependent” or
“independent”. Look up these words in the dictionary. (cite your sources)
What are the definitions of these words when you are not talking about
systems of equations (the non-mathematical definition(s)). What are the
definitions of these words when you are talking about systems of equations
(the mathematical definition). How can you connect the mathematical and
non-mathematical definitions of these words? Illustrate your examples with
graphs of systems. Present your results in paper or poster form.
4) Write a program for the graphing calculator that will solve a system of two
linear equations in two variables. See problem 20, page 125 for the details of
this project. You will demonstrate your program for me and explain to me the
steps of the program.
5) Linear Programming: Write your own linear programming problem. Define
the problem in two variables. Write the restriction statements (at least six).
Model the structure of your problem on #1) Music Shop Problem or #2) Oil
Refinery Problem in section 4-11. Solve your problem. Graph your data on a
large graph (by hand) that can be seen from the back of the room. Label the
axes clearly and give your graph a title. Present your problem in poster form.
6) “Hot! Hot! Hot!” project for the Algebra 2 Regular book. This project
involves using linear programming in a business example. You will collect
data and create a linear programming model to maximize profit when making
two kinds of salsa. Ask for handout.
7) An article “System at the brink” by Shawn Neidorf about airline fares (SJ
Mercury News November 5, 2001) talks about how systems of equations are
used to set the prices of tickets. Read this article and research other ways
systems of equations are used to make business decisions. Present your
results in paper form. Cite your sources.
8) Mission Impossible: Keeping Secrets page 783 in Prentice Hall’s Pre-calculus
book. This project involves using matrices to code and decode messages. Ask
for handout.
Chapter 5: Quadratic Functions and Complex Numbers
Quadratic Equations can be used to model “real world” situations.
 Graphs of quadratics are all similar (what is the effect of a positive “a”? a
negative “a”?).
 Graphs of quadratics have symmetry involving the axis of symmetry and the
vertex.
 Zeros/roots/solutions of quadratic functions represent the x-intercepts of the
graph.
 Quadratic equations can have 0, 1 or 2 real solutions.
 x 2  1  0 has solutions in the complex number system.
 A set of three non-linear points has a unique quadratic function.
 There are an infinite number of equations with a given pair of x-intercepts.
Everyone will do a project for chapter 5. These are additional projects are for
students who want to do a project instead of doing homework for the chapter.
1) Find an example of the graph of a quadratic function in a work of art or
architecture. Draw a coordinate graph system over the picture of the work of art
or architecture that you’ve chosen (you may need to enlarge the quadratic part of
the artwork to draw a set of coordinate axes. If so, please include a copy of the
original work of art or architecture as well). Mark the scale clearly. Find the
coordinates of three points on your graph and use these three points to find the
equation of your quadratic function. Show the work for finding your equation.
Find the coordinates of another point on your graph and check to make sure your
model works for that point by substituting into your equation. Show this work
too. Present your results in a well written report or neat, well organized poster.
Cite your sources.
2) The Vertical Motion Equation: h  16t 2  v0 t  h0 is used in physics to
represent the path of a projectile being “shot” up with an initial velocity, v0 , and
an initial height, h0 . Find an example of projectile motion. Write a problem for
your example. Include finding the equation of the path of the object (explain
where the -16 comes from in the equation). Ask questions about the height of
your projectile at different times. Show that your projectile can have heights that
it reaches twice, once and never. Describe how these different situations are
related to the graph of your equation. Solve your problem. Present your results in
paper form. Cite references/sources.
3) y  x 2  bx  8 project. Look at the effects of changing “b”. This project
involves graphing lots of quadratics and looking for patterns. Ask for handout.
4) Read the article “Unraveling the scientific secrets of the elusive “Splash Hit”” by
Carl T. Hall in the SF Chronicle on August 16, 2004. Create a quadratic
problem/model based on hitting a splash hit at SBC Park (or whatever it is called
now). Use the same rubric from the “Score That Goal” project. Explain why the
actual path of the ball is not a quadratic. Use what you’ve learned from the
article. Present your results in paper or poster form.
Chapter 6: Exponential and Logarithmic Functions
Exponential and logarithmic equations can be used to model “real world” situations.
 Graphs of exponential functions are all similar (what is the effect of positive “a”?
of negative “a”? of “b” > 1? of “b” < 1?).
 Properties of exponents are derived from repeated multiplication.
 Exponentiation properties extend to negative, zero, reciprocal and fractional
exponents.
 Logarithmic and exponential functions are related.
 Properties of logarithms are related to properties of exponents.
 Translating graphs of exponential functions works in the same way as translating
graphs of linear and quadratic equations.
 Graphs of log functions and exponential functions have an asymptote.
 Inverse functions can be found graphically and algebraically. .
1) Find someone who uses exponential or logarithmic equations in their job.
(Provide me with the name of the person you interview, their email address (if
any) and phone number). Interview them to find out how they use exponential or
logarithmic equations. Write up your interview in report form. Describe your
interviewee and their job. Describe how they use exponential or logarithmic
equations. Include at least one example of an exponential or logarithmic equation
they use. Graph the example on graph paper by hand using appropriate scale.
Label the axes. Explain the limits of the model, if any. What is the real world
meaning of the asymptote? Summarize your findings in your paper.
2) Pick a “real world” example from another class (social studies, science, music)
where one aspect varies exponentially or logarithmically with another aspect.
Cite your sources. Show several examples (graphically) as the base or the starting
value changes. Compare and contrast the graphs. What are the domain and range
for each graph? Can the domain and range be extended in the positive direction?
The negative direction? Why or why not? Illustrate your graphs for a lovely
3)
4)
5)
6)
poster presentation. (You might get some ideas from the word problems in the
chapter or in the Log chapter in the Prentice Hall PreCalculus book)
Research Logarithmic Scale. There is graph paper that has a logarithmic scale on
one axis or on both axes. Find an example of data that is best represented using a
logarithmic scale in at least one dimension. Explain why the logarithmic scale is
useful, and show the display of data in both rectangular and logarithmic scales.
Present your problem/data in poster form with graphs you have drawn by hand.
Show the scale clearly on both graphs. Summarize what you have learned about
logarithmic scale in one or two paragraphs on your poster. Include your data in
chart form and cite your sources.
“McNewton’s Coffee: Mission Impossible” Project from Prentice Hall
PreCalculus book, pg. 343. Uses Newton’s Law of Cooling. Ask for handout.
Read about/research the “logistic growth model”. When is the logistic growth
model used? Find/pick two problems that can be solved/explained using the
logistic growth model. Present the problem and its solution in a neat, clearly
explained paper. Include a graph. Explain how “a”, “b” and “c” are found or are
related to the problem. Cite your sources.
Russian Log problems.
Solve five of the following problems. Show all work neatly and completely. If
you had help on the problems, tell me who you worked with.
a. (log( x  1) 2 ) 4  (log( x  1)3 ) 2  25
b. 3 log x 2  (log(  x)) 2  9 (hint: let k=-x)
c. 9 x  6 x  2 2 x 1
d. log 4 x1 7  log 9 x 7  0
e. x 2(log x )  10 x 3
f. log 4 (log 2 x)  log 2 (log 4 x)  2
2
g. log 2 3 4  log 8 (9 x1 1)  1  log 8 (3x1  1)
h.
i.
log 2 (9  2 x )
1
3 x
log a x  log a 2 x  log a 3 x  11
j.
log 3 x9  4 log 9 3x  1
7) Find “real world” data that seems to follow an exponential model. (Include the
data and cite your source). Four examples I’ve seen are the numbers of users of
cell phones each year from 12/84 – 12/93 with an update in the SF Chronicle on
2/11/02, the cost of first class postage from March 1863 – January 1999, Dow
Jones Industrial Average from the SF Chronicle 3/30/1999, the number of songs
downloaded from i-tunes from the SJ Mercury News 4/28/2004. (If you use this
data, use your model to predict amounts for today, and check to see if today is in
the reasonable domain of the model)
a. Graph your data on a large graph (by hand) that can be seen from the back
of the room. Describe how you picked your scale. Label the axes clearly
and give your graph a title.
b. Find the equation of the exponential model. (You may need to do a line of
best fit.) Show your work neatly and completely.
c. Describe the “real world” meaning of the base in your model.
d. Describe the “real world” meaning of the y-intercept in your model.
e. Describe the limits of your model.
f. If your data is not current (as in the examples above), use your model to
predict today’s value and compare your prediction to the actual value
today.
g. Ask three well worded questions that can be answered by your graph.
Include a question predicting the future that can be answered with your
graph. (You don’t have to answer your questions on your poster, but
should be able to answer them if asked.
8) Research Pyramid Schemes, Ponzi schemes and Chain Letters. Explain how the
schemes work and why, in a very short time, participants will lose money. Give
an example using all of the students at the school where each person is asked to
send the letter (or money or good luck) to four or five other people. How long
would it take to include all of the students in the school? All of the people in
Mountain View? All of the people in California? All of the people in the United
States? Use exponential equations to explain the schemes. Present your results in
a poster form that will convince us that we should not participate in such a
scheme (even if the chain letter tells us that something bad will happen if we
break the chain). Cite your sources.
Chapter 7: Rational Algebraic Functions
 The factored forms of polynomial functions can be used to find
roots/zeros/solutions and to sketch the graph of the polynomial function.
 Rational functions can be sketched using x- and y-intercepts, vertical and
horizontal asymptotes and holes, if any
 Extraneous solutions may arise when solving rational equations.
 To factor completely you may need to use more than one factoring strategy.
 Long and synthetic division of polynomials are related
 The factor theorem can be used to find roots/zeros/solutions.
 Direct and Inverse Variation functions can be used to model “real world”
situations.
1)
2)
Make up a rational function that has the following characteristics: crosses the
x-axis at 3; touches the x-axis at -2, has a vertical asymptote at x = 1 and at x
= -4; has a hole at x = 5; has a horizontal asymptote at y = 2. Explain how
you arrived at each part of your equation to satisfy each condition of the
graph. Find the y coordinate of the hole that has the x-coordinate of 5.
(for Trig: use an oblique asymptote instead of a horizontal asymptote)
Problem 90 pg. 343. LCM, GCF and Musical Harmony Problem. Do all parts
of the problem. Share your results in poster form and demonstrate the results
of the problem. (Play or sing the notes with a partner to show which notes
harmonize and which do not).
3)
4)
5)
6)
7)
Research continued fractions. Explain how to find the irrational number
represented by the continued fraction. Show at least two examples. Present
your results in paper or poster form or explain to the class. Cite your sources.
Research the formula for solving cubics. Explain the derivation of the
formula that gives you zeros when you substitute in the four coefficients, and
show how it works. Present your results in paper or poster form or explain it
to the class. Cite your sources.
Write a program for the calculator that can be used to find the real zeros of a
3rd degree polynomial, a 4th degree polynomial, etc. (pg. 354 #49, 50)
Write a program for the calculator that can be used to evaluate continued
fractions. (I don’t know if it can be done….) (pg. 382-3 #43, 44)
Explore the limits of the size of human beings. Read the article “On Being the
Right Size” by J.B. Haldane in The World of Mathematics, Vol. II, page 952
or find a similar scientific article on why people cannot be excessively large
or excessively small. Summarize the article then do Problem #23 on page
400-1. Show all your work neatly and completely. Show you results in paper
form. Cite your sources.
Chapter 8: Irrational Algebraic Functions
Functions with fractional exponents can be used to represent “real world” situations.
 Solving radical equations is similar to solving linear and quadratic equations.
 Operations with radical expressions use rules for fractional exponents.
 Extraneous solutions may arise when you solve radical equations.
 Translating graphs of radical functions works in the same way as translating
graphs of linear, quadratic and, exponential equations.
1) Research continued radicals. Explain how to evaluate the continued radical.
Show at least two examples not shown in the book. Present your results in paper
or poster form, or explain to the class. Cite your sources.
2) “Why Mammals Are The Way They Are” (pg. 450 #11). Note: this is in section
8-6, which we do not cover in class. Find one of the articles cited by the problem:
“On Being the Right Size” by J.B. Haldane in The World of Mathematics, Vol. II,
page 952 or On Size and Life, by Thomas McMahon and John Bonner, published
by Scientific American Books in l983 (or a similar article if these are not
available). Read and summarize the article. Do the problem, showing your
answers in a clear, well organized way. Present your results in paper or poster
form. Cite your sources.
3) Prove that 2 is irrational. Include a definition of irrational. Present your proof
to the class. (see page 423 #57 - The hard part will be presenting the proof to the
class so that they understand why it works) If you research another method to
show why 2 is irrational, you can present your results in paper form, but must be
able to explain it to me to convince me that you understand. Cite your sources.
4) Write a program for the calculator that will evaluate continued radicals. See page
430 #49 and 50.
5) Research the “rule of thumb” cited in the Toothpaste Factory Problem (page 436
#2). Some of the questions raised in class were: What is the volume of 15 tons of
toothpaste? What is the volume of the boxes of tubes of toothpaste that would
hold 15 tons of toothpaste? How many tons of toothpaste is manufactured each
year? Where is the nearest toothpaste factory? Write a report summarizing the
results of your research and calculations on toothpaste, present in paper form.
Explain all calculations and show work neatly and completely. Cite your sources.
Chapter 9: Quadratic Relations and Systems
 Quadratic Relations can be applied to “real world” situations.
 Quadratic relation equations are based on distances.
 Quadratic relations are usually not functions.
1)
Create a “drawing” with a system of equations. You can use linear, quadratic,
exponential and/or conic equations. You must include at least two conic sections
in your “drawing”. Graph each equation by hand on graph paper with an
appropriate scale. Include the domain for each equation.
2)
Do #30 page 506. Show all your work neatly. Describe steps in words and math.
3)
Design and build a three dimensional parabolic hotdog cooker or marshmallow
roaster with your hotdog or marshmallow located at the focus point. Design the
cooker in two dimensions, including the appropriate graph. Explain the design in
words. Explain why the parabolic cooker is an efficient way to cook. Present
your design in a poster and present your cooker to the class.
4)
Mission Impossible: Building a Bridge over the East River. From Prentice Hall
Pre-Calculus book, page 681. This project involves building bridges with a
parabola and a semi-ellipse. Ask for handout.
5)
Research Whispering Galleries. Visit the Whispering Gallery at the
Exploratorium in San Francisco. Create a model of the Whispering Gallery,
drawing it on graph paper using an appropriate scale. Find the location of the foci
and the length of the hall. Using that information, graph and find the height of the
ceiling. Present your results in poster or paper form. Cite your sources. See
Example 9, page 689 and problem #61 on page 693 for a start.
6)
Create a model showing the “creation” of a hyperbola using the definition on page
694. Your model should make clear that difference in the distances remain
constant and should show both branches of the hyperbola. Present your model to
the class in poster form. Extra credit for showing the tracing of the hyperbola by
maintaining a constant difference similar to the tracing of the ellipses and the
circle shown in class.
7)
Present a report on the application of hyperbolas used in the LORAN navigation
system. Explain what the LORAN navigation system is and how it is used the
characteristics of a hyperbola. (see pages 704-706 to get you started) Do
problem #58, page 709. Show all of your work neatly and completely, and
illustrate your solution with a graph drawn to scale that shows the hyperbola
involved in your solution. Cite your sources.
8)
3-Dimensional paraboloids of revolution have many every day applications. The
shape of a car headlight, a reflecting telescope lens, a search light, a flashlight and
a satellite dish is a paraboloid of revolution. Find an actual paraboloid of
revolution and create a 2-dimensional cross section model (on graph paper) of
your object. The cross section should go through the middle of the shape and will
be a parabola. Include the focus, the vertex and the directrix in your model.
Explain how the focus, vertex and directrix of a parabola are related. Explain
why the bulb/receiver, etc is situated at the focus of the parabola. Show that the
bulb/receiver, etc of your object is at the focus. Present your results in poster
form, include a photo of your object that shows me you actually had it in front of
you to do your measurements. Cite your sources, if any.
The rest still needs work. Many are topics that need more detail.
Chapter 11 Sequences and Series
1) Rice on the chessboard. Express the number of grains of rice as in summation
notation.
2) Twelve days of Christmas presents. Express the number of presents in
summation notation.
3) Interest rates and no payment until the year 2010.
4) Zeno’s paradox
5) Pascal’s triangle patterns
6) Fibonacci and Lucas numbers
Chapter 12 Probability:
1)
“You thought tying shoes was easy” by Kenneth Chang from the SF Chronicle
12/10/02
2)
“Counting Crowds” SJ Chronicles 2/21/03 and “40,000? 250,000? Making
crowd estimates a mix of guesswork, science and politics” by Lisa Krieger, SJ
Mercury News 1/28/03 sampling
3)
“Making it all add up: when math meets politics, it’s not a pretty sight”
compiled by Steven Harmon and Alvie Lindsay. San Jose Mercury News
9/9/07 pg. 4B sampling
4)
Find the probabilities for each of the hands in poker. Present your derivations
to the class, explaining the order of winning poker hands.
5)
Expected value
6)
Invent a game with spinners, explain the probabilities of winning. How can
you make a fair game?
Chapter 13 Trigonometric and Circular Functions
Chapter 15 Triangle Problems
1)
PROOF OF IDENTITY: Using the method studied in this chapter, prove the
following identity (about 20 steps): (check with me for the identities you can use)
For ∆ABC tan A + tan B + tan C = (tan A)(tan B)(tan C)
2)
SINUSOIDAL CURVE FITTING
In class we made a scatter plot of collected data about the time of sunrise for 1
year. Then we found a “best” sinusoidal curve fit to the scatter plot by finding
the amplitude, phase shift, vertical shift, and period. Other monthly or hourly
phenomena in a particular location which appear as sine waves include average
times of moonrise or moonset, high or low temperatures, hours of daylight or
darkness, and the range from high to low tide. The monthly gas or electricity
4)
5)
6)
7)
8)
9)
10)
11)
consumption in your own home over a year’s time is also sinusoidal. Do not use
data from the book.
a. Research to gather data. Include your source in your report.
b. Draw a scatter plot
c. Construct a best sinusoidal curve fit
d. Write the rectangular equation of the sinusoidal curve, explaining amplitude,
phase shift, vertical shift, and period.
e. Translate your rectangular equation into polar form and graph if you want to
go beyond the expected scope of the project.
3) Prentice Hall PreCalculus Book pg. 556. The Cow Problem: A cow is tethered to
one corner of a barn, 10 ft. by 10 ft., with a rope that is 100 ft long. What is the
maximum grazing are of the cow? Ask for illustration.
Ferris Wheel
Theodolite Project: Measure the height of a tree or building or person.
Triangulation. On TV the detectives are often tracking down people by finding
where the cell phone call is coming from. One method to do this is Triangulation.
Research triangulation and give examples of how triangulation can be use in other
areas as well.
Prentice Hall PreCalculus Book: Mission Impossible: Locating Lost Treasure pg.
551. Ask for handout. Present in paper form.
Prentice Hall PreCalculus Book: Mission Impossible: How Far and How High
Does a Baseball Need to Go for an Out of the Park Home Run? Pg. 501 This
involves right triangles and sum and difference formulas. Present in paper form.
Ask for handout.
Prentice Hall PreCalculus Book: Mission Impossible: Identifying the Mountains of
the Hawaiian Islands seen from Oahu pg. 453. This project using right triangle
trigonometric relationships. Ask for handout.
How far can you see out to sea? If you stand on a cliff how far can you see
Research use of a transit. Create one to find heights