Calculus

2017-2018

Semester 1

Required materials for mathematics classes
Your school-issued laptop, charged!
Two (2) hardbound theme books (i.e. Mead Composition Book) for journaling (no spirals!).  Use one for homework (enter assignments chronologically) and the other for Journal Reflections (this theme book stays in the classroom).
Texas Instruments TI-83+ (or TI-84+) Graphing Calculator + extra AAA cells.  DO NOT expect the school to provide you extra cells!
Basic drawing supplies (ruler that measures in centimeters, compass, protractor).
Several pencils or mechanical pencil with extra lead + a pen for writing JRs.


Desmos Graphing Calculator.
 
Click HERE for the Stewart Calculus 7e Website wherein you will find homework hints, "Tools for Enriching Calculus (TEC), additional topics, etc.

Join Wolfram Alpha, which provides step-by-step solutions.

Homework help from Slader.

Greetings
 Date

Entry Task

Activity

Assignment/Homework*

9/6
Find your seat.
Meet your peers & teacher.

Debrief Summer Homework and compile a list of needed review items.

JR: What are your goals in this class for this year?
Complete Getting to Know You.

Download the course Syllabus.  Sign and return the signature sheet.

List in your homework notebook what you believe you know well and what you need to know better.

Bring two hardbound "theme books"--one for journal and one for homework.
9/7
Get ready for the Expectations 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. Clarify expectations, both from the class syllabus and the Student Handbook.

JR:  What do you believe will be your biggest challenge this year in Calculus?
Graph the Olympic Games data.
9/8
Address this problem without talking to your classmates.  Write your response in your homework notebook.

Phred is designing a house and allocated a section of the floor plan to be 8' by 10'.  He then began to consider making the room larger.
  • How much additional area will the room have if Phred added 2' to each dimension (length and width)?
  • Draw a diagram of the revised room if Phred added a feet to each dimension.
  • Write an equation to determine the additional area of the revised room if Phred added a feet to each dimension.
  • Write an equation to determine the entire area will the room have if Phred added a feet to each dimension
  • Explain how the answers to the last two bullets are related.
Debrief the ET.

Explore at your 4-top: For the function f(x) = x2, how does the slope AT x = 3 differ from the slope TO that point?  WHY are they different? Include a diagram.

JR:  What preparations have you made to ensure your success in calculus this year?
Complete the Calculus Readiness Test.  The intent of the "test" is to find out what students can do, what students believe they can do but do incorrectly, and what they find unable to do.  If you believe you know how to do a problem, work it out and see if you get one of the answers.  If you don't know what to do please make sure your difficulty with that problem type gets communicated to Edge.  When finished, write a short statement about your strengths and weaknesses.
9/11
Check papers at your 4-top--indicate correct and wrong responses using consensus.  Compile a list of topics to examine further.  Begin correcting your errors. Compile a list of content and processes to address.  Consult the sample solutions.

Receive textbooks to take home.  Read "To the Student" on page xxiii.

JR:  List the mathematics content and processes you believe you command.
Complete the CLAST On-Line Practice Quiz.  Show work in your homework notebook.  Calculators are NOT allowed!  Answer all questions.  Copy your results into your homework notebook.
9/12
Work on the following problem alone.  Expand (a + b)(a - b)2. At your 4-top, begin correcting your errors from the CLAST practice quiz.  Use your homework notebook to show your work.

JR:  Write what you remember of The Law of Cosines.
Select six problems from the CalcPrep "Algebra" area: three you know how to do and three for which you are uncertain.  Work them in your homework notebook as thoroughly as you can.
9/13
At your 4-top, take turns presenting your CalcPrep to each other.  Begin with the ones for which you were uncertain.  Make note of those you could not reach consensus on solution or method. Problem demonstrations--rotate tables and presenters.

Mini lesson: linear equations (slope-intercept versus point-slope forms).

JR:  Explain in simple language the meaning of negative exponents.  Include an example and numbers that are the base of the exponent but in the denominator of a fraction.
Solve the following problems showing all your work.  Use the function f(x) = x3 - 2x2 - 5x + 6.
  1. Determine the slope of the function at x = 3.
  2. Create a linear equation that will be tangent to f(x) at x = 3.  Hint: use the slope you determined in #1.
  3. Find another place on f(x) where the slope is the same as you determined in #1.  Hint: if you are unable to use a mathematical technique, consider making a paper graph, then use the graph to find the point.
  4. Create a linear equation that will be tangent to f(x) at the coordinate you determined in #3.
Note: remember to explain your processes!
9/15
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. Quiz.  Expect Questions on basic algebra.  No calculator or notes.

JR:  Assume you are tutoring an Algebra I student who wants to determine the equation of the line that contains two given points.  Derive a formula that will produce the linear equation containing the points (a, b) and (c, d).
Spend at most one hour on the algebra diagnostic test.
9/18
Given the following system of equations, compute sets of the form (a, b) that satisfy both equations simultaneously.  No calculator, work alone.
4(a + b) = -8
a2 = 8b + 1
Debrief ET.

Debrief last three HW.

JR:  What is the purpose of inverse functions?  Give several examples.
Begin the Inverse Functions activity--complete Pgs 2, 3 #1 - 6.  Show all work in your homework notebook.
9/19
List all angles that have a cosine of 0.5.  Include diagrams.
Debrief ET.

Debrief the last HW.

JR:  Let f(x) = 2x + 4.  Create f-1(x) and give two examples how it is used.
Continue the Inverse Functions activity--complete Pg 4 #1, 2; Pg 6 #4.  Show all work in your homework notebook, copy the graph.
9/20
Which of the following are functions?  Explain why or why not (for each).
  • y = 2x+1
  • y = abs(x)
  • y = sin(x)
  • (x - 1)^2 + (y - 1)^2 = 9
  • y = 4
  • x = 3
Graph each of the following functions on the interval [-7, 7].  Use separate axes for each function.   Draw the line y = x and plot reflected points of the function across the line.
  • y = 2x + 1
  • y = x^2 - 2
  • y = 4
  • y = abs(x + 2)
  • y = cos(x)
Discuss at your 4-top: Which of these have inverses?  How do you know?

Radian measure: modified Can You Do the Can-Can? activity.  Measure circumference and diameter, divide, determine if the ratio makes sense.  Use a protractor to measure the central angle that would result in one radius of the can to "bend around" the rim of the can.

JR:  Explain the meaning of "radian" relative to what you learned from the Can You Do the Can-Can? activity.
See the inverse trig discussion on The Math Page.  Write all the problems and correct answers into your homework notebook.
9/22
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. Quiz: Inverses.  No calculator or note card.

JR:  Give at least two different functions for which f[f -1 (x)] ≠ x.  Explain why this can be so!
See the trig identities discussion on The Math Page.  Write all the problems and correct answers into your homework notebook.
9/25
Write an inequality with variable n to represent the following situations:
  • The fuel tank on the Drof Behemoth can hold at most 20 gallons of gasoline. 
  • The girl scouts needed to sell more than 250 boxes of cookies to get the national award. 
  • Rover earned $25 mowing lawns over the weekend.
Solve the following inequalities, show the number line graph of the solution set, and write the answer in interval notation.
  • 2x - 7 < 4x - 2
  •  -5 ≤  2x + 6  < 4
  •  x2 - x < 6
  • (9x + 6) - 7x ≥  2(x + 3)
  • (x -1 )/(x + 2) ≥  0
JR:  Draw the coordinate graph of (x - 1)2 + ( y - 1)2 ≤ 25.  Shade as appropriate.  Create a context for the inequality like those used in the ET.
See the inequality discussion on The Math Page. Write all the problems and correct answers into your homework notebook.
9/26
Solve the following and write your answer in interval notation.
  • -3 + 4x > 2(2x + 5/2)
  • (x + 1)(x - 3)(x + 2) ≥ 0
Sketch the coordinate graph of the second inequality with appropriate shading.
Debrief ET and discuss inequalities and graphs.

JR:  Draw the graph of y = |x| / x.
See the absolute value discussion on The Math Page.  Write all the problems and correct answers into your homework notebook.
9/27
In your homework notebook

Draw the graph of y = |x + 3|.  Use the graph in each of the expressions below.
  • Solve |x + 3| = 2.
  • Solve |x + 3| < 2.
  • Solve |x + 3| ≥ 4.
Debrief the ET.

Play The Inequality Game with a table partner.

JR:  Write an algebraic and a geometric definition for absolute value.
Take at least one of the inequalities quizzes from Maisonet Math.  Note which quiz(zes) you took and your score(s) in your homework notebook.
9/29
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. Quiz: inequalities.  No calculator or note card.

JR:  List the pre-calculus concepts and procedures you believe you still need to know better to have success in calculus.
Complete the Diagnostic Tests (Stewart Pgs. xxiv through xxviii) through Analytic Geometry (Diagnostics Tests A and B).
10/2
60 degrees (π/3 radians) and 120 degrees (2π/3 radians) are different angles, yet their sine is the same ratio.  Explain why this is so and include diagrams. Precalculus Crossmath activity.  Write all work and answers in your homework notebook.

JR:  Write a function that exists for all real numbers except for π.  Explain why.
Finish the CrossMath.
10/3
Work at your table group to identify and list the concepts and procedures that still need bolstering. 
Debrief Diagnostic Tests, Crossmath, etc.

JR:  Suppose you have two functions, f(x) and g(x).  Explain the meaning of f(g(x)) and give an example.
Diagnostics Tests C and D (Stewart Pgs. xxiv through xxviii).
10/4
Locate a problem in the CalcPrep Website you do NOT know how to solve.
Problem demonstrations.  Find or invent a problem you know how to do and addresses one of the "need to bolster" items from yesterday.  Problem sources may be
  • The CalcPrep Website.
  • An online mathematics resource.
  • The Diagnostic Tests.
  • Within the PreCalculus textbook.
  • Your imagination.
Take no more than ten minutes for the above task.  Each student will present her/his problem.

JR:  List the "concepts and procedures" demonstrated today and the name of the student who made the presentation.
Complete the U Mass Calculus Readiness Test.  Take no more than one hour.
10/6
Prepare to ask questions.
Explanations & demonstrations.

JR:  Explain in simple language the meaning of "y = sin(2x)."
Prepare for Monday's quiz by reviewing notes, watching videos related to the areas you know you need to understand better, working more problems, etc.
10/9
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. Quiz: essential PreCalculus concepts.  No calculator or note card.

JR:  Copy the facts from Example 5 on Pg. 14.  Explain the meaning of the function C.
"Skim" Section 1.1 (Pgs. 10-19).  Note important ideas and definitions in your homework notebook.  List questions you have--these will be addressed during tomorrow's debrief.
*Unless otherwise noted, homework is due the next class day.



Chapter 1: Functions and Limits
 Date

Entry Task

Activity

Assignment/Homework*

10/10
"Skim" Section 1.3 (Pgs. 36-41).  Note important ideas and definitions in your homework notebook.  List questions you two have--these will be addressed during the debrief. Label Label Label, I Made it Out of Clay and Which is the Original activities.

JR:  Explain how to construct the graph of y = |  f(x) | from the graph of yf(x) without using the absolute value function.  Demonstrate with the graph of y = x2 - 4.
Pgs. 42-43 #19, 26, 29.
10/11 Pg. 42 #5.  Include original graph. Continue yesterday's activities.

JR:  Explain the meaning of the graphs in Figure 9 ((Pg. 39).  What is the "parent function" for these graphs?  What is done to the parent function to achieve these graphs?
Pg. 42 #4, 9,11,15.  Include original/standard function also!

10/16
Let f(x) = x2 and g(x) = 2x + 3.  Compute f(g(2)).
Explore It's More Fun to Compute activity.

JR:  Explain the relationship between the two ways to write composite functions. Include an example.
Pg. 42 #13, 15, 17.
10/17
Write down what you remember of the definitions of "secant line" and "tangent line" from PreCalculus and then discuss these topics at your 4-top.
"Skim" Section 1.4 (Pgs. 44-48).  Note important ideas and definitions in your homework notebook.  List questions you have--these will be addressed during the debrief.

What's The Pattern? activity (handouts provided).

JR:  Define slope in simple language and explain why "rise over run" is inappropriate.
Pg. 49 #1, 5.
10/18
Determine the slope of y = (2/3)x3 + 2 at x = 2. Slope Patterns activity (graph the functions, such as y = 0.1x2  on your calculator to determine slopes).

JR:  Create the equation of the line tangent to y = (2/3)x3 + 2 at x = 2.
Pg. 49 #3, 7.
10/20
A "rocket dragster" completed a 1/4 mile race in 3.58 seconds reaching a top speed of 386 mph.  Compute the dragster's acceleration.


JR:  Explain in words and pictures how average velocity differs from instantaneous velocity.  Give a real-world example.
Pg. 49 #6, 8.
10/23
Sketch the graph of y = x2 + 1 for 0 ≤ x ≤ 4.  Draw two lines in different colors (if you can): one depicts the average velocity and the other the instantaneous velocity at x = 3.
Average and Instantaneous Velocity activity.  THIS file has an enlarged graph.  :-)

Review Pg. 50 in your textbook and discuss at your 4-top how the mathematical idea of a "limit" relates to average and instantaneous velocity.
 
JR:  Toidi Diputs entered the two hundred mile ACE Club Air Rally (ACAR) and estimated his flight to average 100.0 miles per hour.  The winner of the ACAR will be the pilot who completes the course closest to his/her estimated rate.  Toidi had some initial problems with ground operations and navigation, hence, averaged only 50.0 miles per hour over the first 100.0 miles.  How fast must he fly over the remaining 100.0 miles to complete the race at his estimated rate?  Show all work!
Pg. 49 #9.
10/24
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. Quiz: tangent and velocity problems.  You may use a calculator and a note card.

JR:  Explain a situation where average and instantaneous velocity are the same over 0 ≤ x < 2 then different when x ≥ 2.  Include a diagram.
See the limits discussion on The Math Page.  Write down any questions that you have and explain Definition 2.2 in your own words.
10/25
Use the word "limit" in a sentence.  Make the context mathematical!
Limits.  Discuss, together, the examples in Section 1.5 (Pgs. 50-58).

Short- and Long-Term Behavior activity.

JR:  Use the meaning of "limit" to explain why 2n = 1 when n = 0.  Generalize for an = 1 when n = 0 if a is any non-zero real number.
Pg. 59 #1, 3, 5.
10/27
Compute the exact value of sin(π/4).
Why Can't We Just Trust the Table? activity.  Note: your "digit" is the number of your "4-top" starting in the NW corner of the room and moving clockwise.

JR:  Compute the limit of (x2 + x - 6)/(x - 2) as x approaches 2.
Pg. 60 #11, 13, 19.
10/30
Pg. 60 #12.
Debrief limits.

Read Limit Laws (Section 1.6; Pgs. 62-69) with your table partner and phrase them in your own terms.  Consider copying the laws into your homework notebook.

Examine the Greatest Integer Function (see Pg. 68, Example 10).

JR:  Create a function that does not exist at a value a but the limit as the function approaches a is a real number.  Explain why this is so.
Pgs. 69-70 #1, 7, 15.
10/31
Working alone, invent a problem that must use the the concept of limits to solve. Work selected invented problems in your homework notebook.

Two Kinds of Holes activity.

JR:  Is it possible for a function to be continuous at a point but for the limit to not exist at that point?  Explain.
Catch up on all missing homework.  Make sure you include the date assigned, facts of the problems, and diagrams.
11/1
Is y = tan(x) continuous at π/2?  Why/why not? Skim Pgs. 81-90 and discuss with your table partner.

Continuity and Limits activity.

Intermediate Value Theorem: work through Pg. 92 # 51, 53 with your 4-top.

JR:  Let f(x) = (x + 1) / (x2 - 1).  For what values of a does the limit as x approaches a of f(x) equal f(a)?  Include a diagram.
Pg. 90 # 1, 3, 5.
11/3
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. Quiz: limits.  No calculator, note card OK.

JR:  Explain a situation where a function exists at a value a but has no limit at a.  Draw a graph of the function.
Pgs. 70-71 #17, 51.
11/6
What is the limit as x --> infinity of 4x3 + 2x + 7? Include a diagram. Activity: Chapter 1 Concept Check (Pgs. 93-94) through number 16.

JR:  What is the limit as x -- > infinity of any polynomial p(x)?  Explain.
Finish Ch. 1 Concept Check through # 16.
11/7
Identify each as continuous or discontinuous then explain your choice.
(i) The temperature at a specific location as a function of time.
(ii) The height of the ground above sea level as a function of the distance due East of Seattle.
(iii) The cost of a taxi ride as a function of the distance traveled.
Continuity (Section 1.8; Pgs. 81-90).

Pgs. 90-91 #13, 15, 17.

JR:  Is it necessary for a function to be continuous at a specified point to have a limit at that point?  Explain.  Is it necessary for a function to have a limit at a specified point to be continuous at that point?  Explain.
Complete the assigned problems.
11/8
Define the number sets: Integers, Rational, Irrational, and Real. Complete the Exploring Continuity activity.

JR:  For a function f(x), f(1) = -5 and f(3) = 5.  Must there be a value of x between 1 and 3 where f(x) = 0?  Include a diagram.
Review exercises: Pg. 95 #1, 3, 4, 5.  Show all work!  Prepare questions to ask during tomorrow's review.
11/13
Pg. 96 #22.  Remember to begin by transcribing the facts!
Complete the review problems: Pg. 95 #10, 17, 19.  Show all work!

JR:  State the Intermediate Value Theorem in simple language.  Include an example.
Complete the assigned problems.
11/14
Prepare to ask questions.
In-class review--answering questions brought by students. 

JR:  If a function exists at a point, say (a, b), must it be continuous?  Must the limit at a exist?  Explain and include diagrams.
Prepare for the tests.
11/15
Get ready for the test!  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. Test 1.1.  No calculator, note card OK.  Expect questions on
  • Functions (domain & range, composition).
  • Limits.
  • Continuity.
  • Average & instantaneous slope.
**Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

JR:  Which concepts in this chapter do you believe you should know better?
Prepare for tomorrow's test.
11/17
Get ready for the test!  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. Test 1.2.  No calculator, note card OK.  Expect a question on
  • The Intermediate Value Theorem.
JR:  Explain the importance of continuity and limits.
Let f(x) = ax2 + bx + c.  For any real number, v, the point (v, f(v)) is, therefore, on the curve.  Let h be an arbitrary amount, so the point to the right of v would be (v + h, f(v + h).  Write an expression for the slope of the secant line containing  (v, f(v)) and (v + h, f(v + h).  Simplify.
11/20
List the functions commonly used in PreCalculus for data modeling.
Rounding the Bases activity.
The Small Shall Grow Large activity.

JR:  Give an example of a real-world situation that could be modeled with a linear function.
Pgs. 33-34 #1, 13, 15.
11/21
What do all members of the family of linear functions f(x) = 1 + m(x + 3) have in common?  Graph at least three "members of the family" on the same coordinate axes and label the graphs.
Skim Section 1.2 (Pgs. 23-32).  Focus on the different function types and their graphs.
Creating Models activity.

JR:  Create a cubic function for which f(1) = 6 and f(-1) = f(0) = f(2) = 0.
None.  :-)
*Unless otherwise noted, homework is due the next class day.


Chapter 2: Derivatives
 Date

Entry Task

Activity

Assignment/Homework*

11/27
Write a function wherein f(0) = 4 and the graph crosses the x-axis at 1 and 2 and merely touches the x-axis at x = 2. Introduce Straight Line Kinematics video and graphs.

Begin computing the slopes from the displacement:time graph.  Consider using the associated grid paper.  Graph the slopes using the same scale and units on the x-axis.

JR:   Explain in simple terms how to create the graph of slopes of the DISTANCE VS. TIME graph and what it means.
1.  From the displacement:time graph, calculate "slopes" in mi/hr for: (a) 0 - 6 s, (b) 18 - 38 s, (c) 48 - 57 s, (d) 13 s, (e) 43 s, (f) 59 s, (g) 65 s, (h) 70 s, (i) 77 s, (j) 85 s, (k) 90 s, (l) 95 s, (m) 100 s.  Draw these on the graph and show your calculations.

Hint: (mi/s)(3600 s/hr) = mi/hr

2.  Plot, by hand, the above 13 slopes versus time to obtain a velocity:time graph. Scale: 1 inch = 10 s, 1 inch = 10 mi/hr.
11/28
Explain in detail how to produce a velocity vs. time graph from a displacement vs. time graph.
Debrief Straight Line Kinematics velocity graph assignment.  Compare to the actual velocity graph.

JR:   Why is mi/h/s an appropriate unit for acceleration for this data? 
Create the speed:time graph from the acceleration vs. time graph.  Organize your data into an easy to read table BEFORE graphing.
11/29
What is meant by (a, f(a))?  Give an example. Use the graph of y = x2 + 1.  Draw tangent lines at each interval of 0.50 over 0 ≤ x ≤ 4.0 and compute the slope at each of the points.  Graph the slopes on the same graph paper using a new scale for the y-axis (on the right side).

Complete Oiling Up Your Calculators.

JR:  By the values you have collected so far from the slopes of y = x2 + 1, explain what you expect from the graph of the slopes.  Include a sketch.
Complete the analysis of the slopes of y = x2 + 1.  Perform a linear regression on the x vs. slope at x values.  Report entire calculator output!
12/1
Explain in simple language how average velocity and instantaneous velocity differ.  Include a visual representation of each. Transitioning from slope to "derivative."

Follow That Car activity.

JR:  Let f(x) be a function and a is a value for which the function is defined.  If h is a very small number what does f(a + h) represent?  What does f(a + h) - f(a) represent? What does [ f(a + h) - f(a) ] h represent?
Pgs. 110-111 #1, 3, 11.
12/4
Perform The Power Rule (see Pg. 127) on each of the functions below
  • y = 2x3 - 3x + 5.
  • y = 2/x.
  • y = 2x^(1/2).
The Derivative as a Function.  See Section 2.2 (Pgs. 114-122).

Consider exploring these resources
JR:  For a function f(x), under what conditions would f '(x) = 0?  Explain using the definition of derivative (see Equation 2, Pg. 114).
Pgs. 122-124 #1, 13, 21.  Include the graphs!

THIS Website proves various trigonometric derivatives.
12/5
The Derivative Function activity (handouts provided). Differentiation Formulas (Section 2.3).

Back and Forth activity (handouts provided).

JR:  Copy all the differentiation rules in Section 2.3 (see Pgs. 126-136).
Pg. 136 #5, 7, 17, 23.
12/6
If f(x) = (x + 1)/(x - 1) determine f ' (x). Pgs. 123-124 #15, 18, 19, 21, 27, 35, 45.  Include the graphs!

JR:  Let f(x) = (x)^(1/3).  Is the function continuous, defined, and differentiable at x = 0?  Explain each.
Finish the assigned problems.
12/8
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. Quiz: use the definition of derivative (a limit, see Pg. 107) to create the derivative of a function.  Note card OK, no calculator.

JR:  Apply The Product Rule to d/dx [c f(x)] to create The Constant Multiple Rule.
Pgs. 136-137 #29, 51, 61.
12/11
Find and review your response Graph 5 from The Derivative Function activity.  Explain WHY the plot of slopes of sine give cosine. Derivatives of Trig Functions (Section 2.4).  See the TEC animation for Figure 1 (Chapter 2, V2.4: Slope-a-Scope).

The Magnificent Six activity.

THIS Website proves various trigonometric derivatives.

JR:  Copy all the trigonometric differentiation rules in Section 2.4 (see Pgs. 140-146).
Pg. 146 #5, 7, 15, 21.
12/12
Note that the derivative of sin (x) is very different from the derivative of sin (x2).  Determine the derivative of each and check on your calculator by comparing slope of one function against values of the slope function. The Chain Rule (Section 2.5).

Unbroken Chain activity.

JR:  Let f(x) = sin x2 and g(x) = sin2 x.  Compute f'(x) and g'(x) and explain why the answers MUST be different.
Pg. 154 #7, 23, 25.
12/13
Explain The Chain Rule in simple language. Chain Rule Without Formulas activity.

JR:  Explain the similarities and differences between The Product Rule and The Chain Rule.
Pg. 154 #13, 17, 31.
12/15 Why is The Chain Rule an essential process in differentiation of functions?
Watch Donald in Mathematic Land.

JR:  Explain how Donald in Mathematic Land applies to calculus.  Your response must be serious and substantive.
Explore the CalcPrep Website and work on your areas of weakness.  Recall that algebra is a common area of concern.  Do all work in your homework notebook.  Please email Dr. Edge with any questions you encounter.
1/2
Happy New Year!

The equation of a circle with center at the origin and radius 5.0 units is x2 + y2 = 25.  Take the derivative of the equation as it reads (without solving for "y").
Implicit Differentiation (Section 2.6).

MIT has THIS lecture   on implicit differentiation.
Higher Ed has THIS resource on implicit differentiation.
Check THIS resource from UC Davis.
Take the practice quiz.

JR:  Take the derivative implicitly of x2 +xy = 10 to determine dy/dx when x = 2.   Solve the original equation for "y" and determine y' again, computing the value at x = 2.  How do the answers from the two methods compare?  Why is this so?
Pgs. 161-162 #7, 23, 25.
1/3
Explain Implicit Differentiation in simple language. Implicit Curves activity.

Follow the lesson on Education Portal.
See Paul's Online Math Notes.
See Texas Instruments lesson.

JR:  Let yx2 + yln(x) = 10.  Compute dy/dx.
Pg. 161 #5, 15, 19.
1/5
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. Quiz 2.2: Differentiation Rules (refer to Pg. 136).  No calculator, note card OK.  Expect problems that include
  • Power Rule.
  • The Chain Rule.
  • Quotient Rule.
  • Derivatives of trigonometric functions.
JR:  Let f(x) = sin(x) + cos(x).  At what value(s) of x for which 0 ≤ x ≤ 2π will a tangent line to f be horizontal?
Pgs. 161-162 #21, 35.
1/8
The position of a particle is given by s = f(t) = t3 6t2 + 9t.  Compute the velocity after 2.0 seconds and after 4.0 seconds.  Determine when the particle is at rest. Changes of Rate in the Natural and Social Sciences.

Follow That Particle activity.

JR:  Note this section of the text is about "rates."  List the rates involved in each example.  Include the units for the rates.
Pgs. 173-174 #1, 15.
1/9
Pgs. 191-193 #1, 3, 7, 10, 11, 14, 25, 61, 62, 69. Continue the review exercises.

JR:  Describe several ways in which a function can fail to be differentiable.  Illustrate with sketches.
Finish the assigned exercises.
1/10
The volume of a sphere is given by V = (4/3)π r3.  Differentiate implicitly to determine dV/dt. Related Rates.

Discuss the DEMOS for RELATED RATE Problems Website at your local group. 

JR:  Let a and b be the sides of a rectangle.  Side a is increasing at 3 cm/min and side b is decreasing at 3 cm/min.  Perform the following steps to determine the relationship between sides a and b for which the area of the rectangle is increasing.
  • Write an equation for the area of the rectangle in terms of a and b.
  • Implicitly differentiate the area equation vs. t (because it's a rate problem).
  • Substitute facts into the equation you just wrote.
  • Use algebraic logic to determine when the area increases.
  • Explain your reasoning.
Pg. 180 #3, 9.
1/12
Explain in simple language the meaning of "related rates." Pgs. 180-181 #5, 7, 11, 13, 15, 23.

JR:  Explain how "related rates" occurs in physics, chemistry, biology, and economics.
Finish the selected problems.
1/16
Explain in detail how dy/dx differs from dy/dt.  Give an example. Related Rates.

Nobody Escapes the Cube activity.

Find the Error activity.

JR:  Revisit Example 2 (Pg. 177) and compute the velocity of the ladder when it is 0.00100 inch above the ground.  Convert to units more easily comprehended, such as miles per second and compare to the escape velocity of Earth (slightly less than 18 miles per second).  Comment on this outcome.
Pgs. 182-183 #27, 31, 35.
1/17
Explain, in detail, how d/dx and dy/dx differ.  Give an example.
Differentiation Jeopardy.

JR:  What would you still like to review before the Chapter 2 test?
Pg. 190 T/F Quiz; explain your answers!  Pg. 193 #73, 76, 79.

Check your skill with differentiation using the Differentiation Jeopardy Q & A.  Look at the question, attempt it, then check your answer.
1/19
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.  Set your homework notebooks off to the side.
Quiz: Related Rates. No note card, calculator OK.

JR:  Describe your confidence regarding related rates.  Include what you believe you can do adequately and what you continue to struggle.
Pg. 191 #1, 3, 7, 10.
*Unless otherwise noted, homework is due the next class day.


Semester Final: Preparation and Administration
 Date

Entry Task

Activity

Assignment/Homework*

1/22
Prepare to ask questions.
Demonstration and/or explanation of student-provided examples and problems.

JR: Explain
Prepare for the next study session.
1/23
Prepare to ask questions. Demonstration and/or explanation of student-provided examples and problems.

JR: Explain
Prepare for the Final Exams.
1/24 or 1/25
Get ready for the exam!  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.  You may use calculator, ruler, protractor, compass. Final 1.1.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, compass, and extra cells for your calculator.  Expect questions on

JR: Explain
Prepare for the next Exam.
1/26
Get ready for the exam!  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.  You may use calculator, ruler, protractor, compass. Final 1.2.  You may use a calculator and a non-mechanically reproduced 3 x 5 note card.  Consider also bringing ruler, protractor, compass, and extra cells for your calculator.  Expect a question on

JR: Explain

*Unless otherwise noted, homework is due the next class day.

Semester Mini-Project
 Date

Entry Task

Activity

Assignment/Homework*

1/29



1/30



1/31 or 2/1




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

Course syllabus

Also note the additional items

    Email: richard.edgerton@highlineschools.org