Click HERE for Semester 1.
|Date|| Entry Task
||Download the Course syllabus and save it to your computer's desktop. Scan through each page and take particular note of required materials, assessment procedures, and assignment requirements.||Introducing
My Mother's Gifts activity.
JR: Explain how quadratic functions can be used to determine an optimal situation. Hint: see Examples 5 & 6, pp. 250-251.
each function below, use algebra to: a) express f
in standard form; b) determine the vertex; c) identify x-
and y- intercepts; and, d) determine the local min
or max for f.
||Explain how to
identify the vertex of a quadratic function using algebra.
quadratic function, explain how to
JR: Explain the process of determining a maximum outcome for a situation using algebra.
|pp. 252-253 #47,
|2/7 or 2/8
||Perform the division of (x2 -2x -3)/(x +2). Explain what the quotient and the remainder represent. Identify all asymptotes and/or points of discontinuity.||Polynomial
activity. Perform all computations in your homework
notebook and paste or tape in the associated graphs.
JR: Explain how to determine x- and y-intercepts and whether any asymptotes exist.
268 #87, 88.
||Perform the division of (2x3 - 7x2 + 5)/(x - 3).||Synthetic
Division. Read through pp. 270-271 to learn a
different, and perhaps more efficient, method for
JR: Explain the process of Synthetic Division.
|p. 273 #3, 4, 7.
||A fuel tank is
to be constructed of a cylindrical center section that is
4.00 feet long and two hemispherical end sections.
The volume of the tank must be 100.0 cubic feet.
Compute the radius of the tank.
division to determine if 1, 2, 3, -1, -2, and -3 are roots
(zeros) of the polynomial y = 2x3
+ x2 - 13x + 6. Reference:
Rational Zeros Theorem, pp. 276-277.
JR: List several real-world situations where determining the zeros (roots) of a polynomial would be necessary. Be explicit!
|p. 285 #99, 102.
||Determine all three roots of x3 - 3x2 + x - 3.||Give
the minimum number of real roots (zeros) for each degree
Create the expanded polynomial P(x) that has degree 4 and roots i, -i, 2, and -2. Write your answer in expanded form.
JR: Explain why complex zeros come in conjugate pairs. Include an example.
293-294 #29, 39.
|2/14 or 2/15||Investigate the
effect the parameter c has on the graph of the
function f(x) = x/(x2 -
c). Try both positive and negative numbers;
numbers close to zero and those further away.
Include the following
||Review the Asymptology
activity from last week. Which values of c
seemed to produce asymptotes? Determine where and
why these asymptotes happen.
Explore Section 3.6 (pp. 295-307). Note the conditions for the specifics of a rational function that determine
|pp. 308-309 #23,
24, 33, 37.
On a standard graphing calculator (e.g. TI-84+)
Tmin= 0In the function editor, enter
a rational function that has intercepts at (2, 0), (3, 0)
and vertical asymptotes at x = 1, x
& problem demonstrations.
JR: Explain how to determine the rational function given specified intercepts and asymptotes. Include an example.
310 #89, 90.
2/21 or 2/22
|Civil engineering has several categories. One of them is called "transport engineering." List several responsibilities of a transport engineer.||Discovery
JR: Explain, in simple language, the contributions of Cardano, Galois, and Gauss to the study of polynomials.
|pp. 308-309 #25, 35, 41, 63, 69.|
||Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring. No calculator or note card.||Quiz 3.1.
No calculator or note card. Expect questions
||p. 310 #91, 92.|
||Complete p. 320 #25 in your homework notebook.||Debrief &
JR: Explain how to algebraically determine the absolute maximum and minimum of a quadratic function over a closed interval. Use y = x2 - x - 6 over [-4, 4] as an example.
|p. 320 #25, 26, 27, 73, 85.|
||p. 323 #2.
demonstrations from yesterday's homework.
JR: Explain how to determine the slant asymptote of a given rational function. Give an example.
|p. 323 #2, 5, 6, 7, 9, 11 (include the rational function in your answer and specify the item in the question).|
|2/28 or 3/1
roots of x3 - 3x2 + 4x
individually on the practice
JR: Explain how to create the expanded, simplified polynomial from its
|Prepare for the
||Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring. No note card, calculator OK.||Quiz
3.2. No note card, calculator OK. Expect
||Find your graph of Pressure vs. Altitude (from 12 September). Create an exponential function that has the same basic shape over the entire dataset. Graph on your calculator (or computer if a calculator is not available)|
|Date|| Entry Task
promised me a penny today, then doubling the gift
tomorrow. Each day he will double the previous
amount. How much money will Gordo give me by the end
of the month?
basics of exponential functions. Comparisons activity.
JR: Explain how to distinguish between exponential and power functions. Include examples.
336 #7, 8, 11, 13.
|3/6 or 3/8
||Use the compound
interest formula (p. 334) to complete the tables located
on page 337, problems 55 & 56.
||I've Grown Accustomed
to Your Growth activity.
JR: Explain how to determine if a set of data is linear or exponential then how to create an equation that models the data.
#17-20. Note: make graphs, not sketches!
a cow was improperly washed before milking, some e-coli
tainted the milk. Assume the population doubles
every twenty minutes. If one hundred bacteria are in
a quart of milk at noon, at what time will the bacteria
become toxic (exceed a million)?
338 #61, 63, 66.
JR: Explain Newton's "Rule of 72" and its purpose. Include an example.
the assigned problems.
function used for logistic growth in Example 3, p.
340. Explain the meaning of each part of the
function (e.g. what role does the 10,000 have both in the
function and the scenario).
||When will 60% of
the population (Example 3, p. 340) become infected?
JR: Explain the meaning of "continuously compounded interest." When is it used?
|p. 341 #5, 6,
7. Graph in your homework notebook.
|What is meant by
a "learning curve." Give an example.
JR: Explain the relevance and use of the number e and include an example.
|p. 342 #25, 26.|
|3/14 or 3/15
"celebrated jumping frog" can make great leaps despite its
diminutive size. It can jump every second but only
half as far as its last jump. If its first leap is
two meters how much time must pass for it to have jumped a
total of four meters?
||pp. 342-343 #28, 30, 31, 32.|
following points on the same axes, by hand, in your
homework notebook (either with grid within or paste in a
sheet of graph paper). Decide on a reasonable window
before graphing and make the graph as large as
possible. Draw the continuous, extended function.
Red: (1, 0.5); (0, 1); (2, 4); (3, 8).
Blue: ((1, 0); (2, 1); (4, 2); (16, 4).
|Why do the
graphs appear the way they do? Give an algebraic
JR: Explain, in simple language and graphically, how an exponential function is related to its equivalent logarithmic function.
|p. 353 #97, 98, 100.|
|Use only the
following facts (no calculator!!!) to simplify the
expressions below: log(2) = 0.30103, log(5) = 0.69897.
Logarithms. Determine a way to re-write each of the
||Every Nest Egg Needs a
and Logarithmic Equations (pp. 360-367). Discuss
each example with your table partner(s). Select a
few "interesting" ones to copy into your homework
JR: Solve p. 369 #99. Compare your answer to Part b. with your graph and data from the Pressure vs. Altitude homework (12 September) using 13,000 feet for the altitude.
|3/21 or 3/22
A jug of milk, taken out of a refrigerator, will slowly
warm up from the temperature inside the refrigerator to
the temperature of the room. The following equation
models the warming of the milk: T = 24 - 18 (0.78)t
where T is the temperature of the milk in the jug (in °C)
and t is the number of minutes that passed after
taking the jug out of the refrigerator.
Water Cool. Determine the "common ratio" from
measurements and create an exponential equation from which
you predict a future temperature.
Activity: collect cooling data from a cup of hot water. Model the data with an exponential function and use the function to forecast the temperature specified times in the future. Record date in a table like the following
JR: Explain the principle involved in Newton's Law of Cooling (see pp. 377-378) and why does it work for warming also.
|pp. 369-370 #97, 101.|
||Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Place your homework notebook near you for scoring. No note card, calculator OK.||Quiz 4.1.
No note card, calculator OK. Expect questions on
solving a scenario-based problem. Logarithms and
exponential functions will be involved.
JR: Provide some details about a real-world relationship that involves exponential functions. Explain why this relationship is exponential.
|p. 369 #90, 95.|
|3/28 or 3/29
Click here for the Reference Pages from Stewart Calculus (7th Edition).
Create and print your own graph paper at THIS Website.
Below are various documents on the
operation of the class
the additional items