# 2017-2018

Semester 1

Required materials for mathematics classes
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.

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

Grab THIS document showing the "Essential" and "Recommended" sections of Stewart Calculus 7e.

Linked herein is the topic outline for the course, adapted from the College Board.

Desmos Graphing Calculator.

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

AP/BC Review Questions (from the end of each chapter).

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

 Date Entry Task Activity Assignment/Homework* 9/15 Check to see if the limit exists then compute the left- and right-hand limits Limit as x --> 5 of (x - 5)/|x - 5| Limit as x --> 5 of (x - 5)2/|x - 5| Debrief ET. The Revenge of Orville Redenbacher activity. The Derivative Function activity (see second page of Revenge. JR:  Must a function be continuous at a point to be differentiable at the point?  Why/why not (include an example).  If a function is continuous at a point must it be differentiable at the point?  Why/why not (include an example). Pgs. 123-124 #13, 23, 33. 9/18 Let f(x) = sec(x)/(1 + tan2(x)).  Perform f '(x) and simplify. The Chain Rule.  Do the Unbroken Chain activity. JR:  Under what circumstances would The Chain Rule be used?  Explain in simple language and give an example. Pg. 154 #7, 23, 25, 47, 51. 9/19 Determine dy/dx for x3 + y3 = 6xy. Implicit Differentiation.  Review at your 4-top Pgs. 157-161. JR:  What is the meaning of the result to the ET? Pgs. 161-162 #7, 23, 25. 9/21 At what rate is the volume of a cube increasing when the length of a side is 10.0 cm and the rate of increase of a side is 2.5 cm/min? Rates of Change in the Natural and Social Sciences and Related Rates. Follow That Particle activity (§ 2.7). JR:  The sides of a rectangle are the lengths a and b.  Over a particular time interval a increases at 5.0 mm/s and b decreases at 5.0 mm/s.  Under what conditions is the area of the rectangle decreasing? Pg 174 #15; Pgs. 180-181 #9, 13, 15. 9/22 Summarize the concept of "related rates" paying particular attention to the terms "related" and "rates" as they apply to calculus. More work on Related Rates. Nobody Escapes the Cube activity (§ 2.8). JR:  A moderately sized amount of water will form a sphere in microgravity (as when aboard the ISS) due to surface tension and cohesion).  The rate at which the volume changes is proportional to the surface area of the sphere.  Prove the rate of change of the radius of the sphere is always constant under these conditions. Pg. 175 #29; Pg. 181 #23. 9/25 The following is a graph of f ', the derivative of some function f. Where is f increasing? Where does f have a local minimum? Where does f have a local maximum? Where is f concave up? Assuming that f(0) = −1, sketch a possible graph of f. Address remaining Chapter 2 issues and work selected problems (such as the following ones). 1.  Two chimpanzees on bikes are separated by 350 meters—Chimp A is due West of Chimp B.  Chimp A starts riding North at a rate of 5.00 m/sec and seven minutes later Chimp B starts riding South at 3.00 m/sec.  At what rate is the distance separating the two chimps changing twenty-five minutes after Chimp A starts riding? 2.  Airplane fuel tanks are located in the wings, which lead to inaccurate fuel quantity measurement using the depth of fuel in the tank.  Consider the cross section (slice the wing front-to-back, look at it from the side) of a wing where part of the tank appears rectangular (twenty-four inches from the wing spar to where it starts curving in the front, ten inches high) and the front of the tank (the leading edge of the wing, therefore curved) can be modeled by an equilateral triangle (all sides = ten inches).  The fuel tank is thirty inches along the wing spar.  Note: a gallon occupies 231 cubic inches. Create an equation that will provide the volume of the tank in gallons versus the depth of the fuel in the tank, d. Compute the volume of the fuel tank in both cubic inches and gallons. Assume the engine burns eight gallons per hour.  Compute the depth of the fuel in the tank after one hour of flight time. At what rate is the depth of the fuel changing at one hour of flight time. JR:  Assume the voltage, V, across a resistor is modeled by V(t) = sin(t)/(1 + t).  Compute the rate of change of the voltage at 2.0 seconds. Chapter 2 AP AB/BC Review Questions, Pg. AP2-1 (following page 196). 9/26 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 on Related Rates.  You may use an AP approved calculator and a note card. JR:  Explain a strategy that will result in a passing score on a Related Rates problem even if you do not know the mathematical relationships within.  :-) Pg. 182 #31, 33, 38.
*Unless otherwise noted, homework is due the next class day.

 Date Entry Task Activity Assignment/Homework* 9/28 Find a positive number such that the sum of the number and twice its reciprocal is as small as possible. Discuss the activities The Shape of a Can. The Waste-Free Box. Do the Calculus in England activity. JR:  The textbook outlines a method for solving optimization problems (see Pgs. 250-251).  At which step would it be best to check  your work using a graphing calculator?  Include what you would graph on the calculator. Pg. 257 #9, 19, 29. 9/29 List the procedure for determining the extrema of a given function. Complete last year's Test 3.1 (hard copies provided).  Work alone. JR:  Pg. 277 #45. Chapter 3 AP AB/BC Review Questions, pg. AP3-1 and AP3-2 (following page 282). 10/2 Score Test 3.1. Optimization workshop Locate or invent a worthy optimization problem. Write the problem for all to see (whiteboard, projection screen, ...). Work the problems with minimal, if possible, assistance. Participate in problem debrief/demonstration. JR:  A company estimates that the marginal cost (in dollars per item) of producing x items is 2.07 – 0.002x.  If the cost of producing one item is \$561.00, compute the cost of producing 100 items. Complete last year's Test 3.2.  Work alone. 10/3 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: optimization.  Note card and calculator OK. JR:  State Fermat's Theorem in plain language. Pg. 277 #47, 48.
*Unless otherwise noted, homework is due the next class day.

 Date Entry Task Activity Assignment/Homework* 10/5 How is The Chain Rule related to "The substitution Rule?" Give an example. Clearing The Hill activity.  Loki's Dilemma activity (handouts). JR:  Explain how to identify what to use for a "u-substitution" and why.  Give an example. Pgs. 335-336 #3, 13, 21; Pg. 336 #23, 39, 47, 59. 10/6 See problem #13 on page 339.  Explain why "u-substitution" is not necessary to evaluate the integral. Review exercises: Concept Check (Pg. 337) and True-False Quiz (Pg. 338).  Include stem and correct answer for the T/F Quiz.  Show all work! Chapter 4 AP AB/BC Review Questions, pg. AP4-1 (following page 342).  Write processes and answers in your homework notebook.  Show all work! JR:  State the Net Change Theorem and explain its application.  Include several examples. Finish the review and prepare for the quiz. 10/9 Work alone on pg. 318 #17. Process and quirks of FTC. What it says, fundamentally. How it works, fundamentally. Working with non-simple limits of integration. Why there are two parts. JR:  List the conditions under which the FTC can be applied. Watch the You Tube FTC video.  Do Pg. 339 #37, 38; Pg. 340 #53. 10/11 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 4.1.  Free response: you may use one 3 x 5 note card and an AP approved calculator.  Expect questions on FTC. U-substitution in integrals. Related Rates. JR:  List the topics from Chapter 4 you believe you should review more deeply. What role did Newton and Leibniz play in the "invention" of calculus?  You may use your computer to find sources of information (remember to reference sources of information you use!!!!!).
*Unless otherwise noted, homework is due the next class day.

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

 Date Entry Task Activity Assignment/Homework* 10/24 Let f(x) = (x - 4)1/3.  Compute f -1(-2). f -1(0). Let f(x) = 2x - 4.  Create f-1(x).  Enter both into the Function Editor of your calculator and examine the TABLE (START = 0; deltaTbl = 1).  What does it mean when a value in the X column appears in the Y2 column? Given f(1) = 2; f(2) = 3; and, f(3) = 1.  What are f(f(1)) f -1(f(1)) f(f -1(1)) JR:  Let f(x) = (x - 4)1/3.  Compute (f -1) ' (-2). Pg. 390 #1, 3, 5, 24. 10/26 Read and note the rules of exponents and derivatives of exponential functions in Section 6.2 (Pgs. 391-400).  Read and note the rules of logarithms and derivatives of logarithmic functions in Section 6.3 (Pgs. 404-408). Logarithms. Prove WHY d/dx (ln(x)) = 1/x. Irrational, Impossible Relations activity. Logarithmic Differentiation activity. JR:  Explain, extensively and definitively, why the log of a negative number does not exist.  Include a diagram. Pg. 408 #5, 7, 11.  Show all steps, do NOT use a calculator!!!  Pg. 418-419 #7, 9, 27. 10/27 A pain killer is administered every eight hours with the expectation that half of the dose will remain in the patient's blood half the time before the next dose is to be given.  Sketch a graph of the concentration of pain killer in the patient's blood over time.  How much of the initial dose would be expected in the patient's blood when the next dose is due? Exponential growth and decay (Section 6.5, Pgs. 446-451). The Sedative activity.  I case you are curious, the "previous exercise" dealing with Homer's Blood Pressure can be viewed HERE.  A comment on Newton's Law of Cooling.  Discuss, together, Example 3 (Pgs. 449-450). JR:  Explain the basics of "Newton's Law of Cooling" (Pg. 449) and include why it essentially works as a "differential equation" rather than an exponential. Pgs. 451-452 #3, 9, 13. 10/30 What does a = arcsine(b) mean?  Give an example and include a diagram. Inverse Trigonometric Functions. Inverse Trickery activity. Note the table of derivatives on the bottom of page 457. JR:  List the domain and range for sin-1 , cos-1 , and tan-1. Pg. 460 #23, 29, 31; 10/31 Given a circle with radius l.  Create a formula for the area of the sector subtended by the central angle theta. Intermediate forms and l'Hospital's Rule (see Pg. 470). See The Sector Ratio activity. JR:  Explain Cauchy's Mean Value Theorem in simple language. Pg. 477 #7, 9, 17, 19. 11/2 If f(x) = 2x - 1, compute f-1(3). Concept Check, Pg. 480-481; True-False Quiz Pg. 481 (copy stem!); Chapter 6 AP AB/BC Review Questions, Pg. AP6-1 (following page 486).  Omit all problems dealing with hyperbolic trigonometric functions. JR:  Is tan-1(x) =  sin-1(x) / cos-1(x) ? Why/why not?  Give evidence! Complete all problems from the class activity and include Pg. 482 #4, 21, 38, 59. 11/3 Let y = x^(e7x).  Differentiate the function. In-class review. JR:  Could there be logarithms having a negative number as their base?  Why/why not?  Give some examples. Prepare for the tests. 11/6 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 6.2. Multiple Choice: you may use one 3 x 5 note card and an AP approved calculator.  Expect questions on Use properties of logarithms to expand an expression. Perform derivatives and integrals involving inverse trig functions, either within the function or as a result Determine the equation of a line tangent to a curve at a specified point on an inverse trig function.. Evaluate limits of rational functions containing logarithms. Applications of L'Hospital's Rule. JR:  For which concepts in Chapter 6 are you still uncertain? Prepare for tomorrow's test. 11/7 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 6.1.  Free response: you may use one 3 x 5 note card and an AP approved calculator.  Expect questions on Given facts for a function f(x) that is the inverse of a function g(x), compute the derivative of g(x) at a value. Compute derivatives of various exponential functions, some of which will require logarithmic differentiation. Given a natural exponential function, calculate a point where the tangent line has a given slope. Solve a problem involving exponential growth. Applying the FTC to an exponential function. Compute a limit using L'Hospital's Rule. JR:  Explain what you know about "partial fractions" and give an example. Let u and v be functions in x.  Differentiate the product uv versus the variable x.
*Unless otherwise noted, homework is due the next class day.

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

 Date Entry Task Activity Assignment/Homework* 12/11 Draw y = sin(x) from x = 0 to π/2 on a half-sheet of graph paper as accurately as you can.  Measure the arc length in segments of 0.2 radians.  Record the data in a table.  Add the arc length segments and convert to the units of the sine graph. Arc Length.  Derive the arc length formula. How to Define π activity. JR:  Use the arc length integral to perform the ET. Pg. 567 #7, 11, 19. 12/12 Compute the volume generated by rotating y = sin(x) from x = 0 to π/2 about the x-axis. Areas of A Surface of Revolution. Gabriel's Horn activity.  North side of classroom do Page 495, South 496.  Discuss differences!!!  :-) JR:  How is finding a surface from a revolution the same as/different from finding an area? Pg. 574 #7,11,13. 12/14 Define the following and include appropriate units. Hydrostatic Pressure. Moment. Center of Mass. Centroid. Demand. Consumer Surplus. Cardiac output. Applications to Physics and Engineering (Section 8.3).  Applications of Economics & Biology (Section 8.4). Under Pressure activity. Homer’s Blood activity. JR:  Explain what will happen to a probability distribution as the sample size increases.  Hint: see Section 8.5. Pg. 584 #13; Pgs. 590-591 #10, 12, 16. 12/15 Chapter 8 AP AB/BC Review Questions; AP8-1, 2 (following page 602).  Do them all! Create a study plan to address your areas of weakness over the break.  Be specific and include sample problems. JR:  Define normal in the context of "normal distribution." Execute your study plan with particular emphasis on the few days just before break ends. 1/2 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 8.1. Free response: No note card, no calculator.  Expect questions on Arc length Area of surface of revolution Application (one of: physics, engineering, economics, or biology) JR:  Which of the applications in this chapter is most interesting to you.  Explain why. Solve the differential equation dy/dx = xy (for y).  Simplify!
*Unless otherwise noted, homework is due the next class day.