I wish you a solid majority of your summer to take a healthy break from school matters. This assignment should not demand an unreasonable amount of time, but on the other hand, please don't save it until the last minute. It's glaringly apparent whenever incoming AP Calc AB students have waited too long to start the textbook assignment. If you have any concerns at all about picking up where we left off in the final weeks of Mr. W's PreCalcH class, resolve to start the textbook assignment no later than mid July. Leave yourself time to follow up with questions. No question about this assignment is "too small" to answer before we start our AP Calc travels. Also consider starting a routine of just 5 minutes per day of Unit Circle Practice by mid-late July.
I will be in New Orleans all June and July except as follows:
Scoring AP Exams in Kansas City: June 5 - June 18
Personal travel: July 2 - July 9
Other than those dates, my schedule is flexible. Contact me and I'll be glad to schedule a help session. (Really... I actually start to miss students and I enjoy these summer sessions.) Any assistance from me must be sought before August 4, when teachers return to campus. If too many students wait until the last minute to seek help, my schedule may not accommodate everyone.
In return for me generously offering my time to help you over the summer as needed, I fully expect every student on my roster to show up on day #1 with big and small questions answered, confident in their skills, and ready to hit the ground running.
Textbook exercises below due (Day #1)
Assessment on Limits/Derivatives and Ugly Algebra (Day #1 or #2)
There will be 17 questions that you need to finish within 60 minutes. Fifteen questions will be very similar to those on the textbook assignment below. Two of the questions will be on "Ugly Algebra," as we learned at the end of PreCalcH.
CALCULATOR NOT ALLOWED on the entire test. While practicing Ugly Algebra, you should continue the habit of checking your answers on your graphing calculator even though this will not be an option on our non-calculator written test.
Unit Circle Assessment (Day #2 or #3)
Practice your Unit Circle skills here. This is also the same website/app that will be used for the in-class assessment. For that assessment, you will keep all the default settings except that you may change the timer to 30 seconds/question (as usual). Still, while practicing over the summer, I encourage you to strive for the default timing of 20 seconds/question. Pencil and paper are also prohibited during the in-class assessment. Calculator prohibited too. (Did I even need to say that?)
You may take the assessment multiple times within the allotted half-hour of class, and I will record your best score.
All videos from our PreCalc course are available to help jog your memory if necessary, but this Trig Functions on the x-y Plane video gives the best summary of my suggested way of learning this skill. There are slightly different approaches to mastering the Unit Circle that some people prefer. If you find another approach that you like better, go for it, but be wary of any suggestions that you merely memorize something without understanding why.
Your assigned summer assignment exercises are listed in blue below. Throughout, you are to USE A CALCULATOR ONLY FOR CHECKING PURPOSES! Since you will not be allowed a calculator (nor book/notes) on the assessment, avoid any temptation to depend on it while doing the assignment. I will be collecting the assignments on the first day of class, so all questions need to be addressed and all work needs to be completed during the summer.
Note that there are 56 exercises total. If you know that you need more practice on a particular skill, there's nothing stopping the responsible student from trying a few more exercises in the relevant section. Pace yourself accordingly.
Here are a bunch of worked-out solutions to questions very similar to the assigned exercises. You may find these helpful as examples of how a solution and all its supporting work may be presented.
Please contact me via email if you have any questions or would like to arrange for a help session.
Ugly Algebra (link to PreCalcH packet)
We've spent enough time on this in PreCalcH, so officially I'm not assigning any new work on this topic. However, there will be two such questions on the first-day test, so you determine how much practice is necessary to master this skill.
You don't need to turn in any work on this topic for the summer assignment that I collect. I leave it completely up to you to determine how much you need to practice this skill and ensure that you can demonstrate your skills on day #1.
Here's a single PDF with ALL textbook pages required for Summer Assignment (a bit large at 20 Mb). Be sure to take advantage of the bookmarks that help you navigate through the pages. Alternately, click on the individual chapter links below. Note that answers to odd-numbered questions are included at the end of the PDF.
Chapter 1.1 – A Preview of Calculus
no exercises assigned
Chapter 1.2 – Finding Limits Graphically and Numerically
you already did assignments from this section in PreCalculusH
Chapter 1.3 – Evaluating Limits Analytically
p65: 19, 21, 29, 31, 37, 39, 49-57 odd (without calculator; note “indeterminate form”)
p66: 68-76 even, and 77 (check even answers graphically)
You should already have a sense of how to interpret limits graphically and numerically from the introduction in the last days of PreCalculus Honors. Here we learn some algebraic (a.k.a. analytic) techniques for evaluating limits. Affirm your algebraic results graphically and numerically (i.e. examining graph on calculator and tracing to values close to the "hole").
With limits involving trig expressions, it's easy to make sloppy trig errors. Even if you get lucky and arrive at the right final answer, you may not consider yourself successful if you used faulty reasoning along the way. Especially make sure you can CORRECTLY obtain the right answer to exercise 77 in your assignment. Recall, for example, that sin(2x) is NOT equal to 2sin(x).
ERROR: At 10:54 I write on the screen that the limit =1 (which is correct), but then I say that as the x value approaches 0 the y value also approaches 0 (oops, that's wrong, meant to say 1).
Chapter 1.4 – Continuity and One-Sided Limits (and Intermediate Value Theorem)
p76: 1-17 odd, 37-47 odd, 75, 77, 83, 85
In Chapters 1.3-1.4 the book assigns "Does Not Exist" (or DNE) to limits that approach ∞ or -∞. In Chapter 1.5 the book switches to the common convention of allowing ∞ or -∞ as an answer. I invite you to go ahead and put ∞ or -∞ as your answer instead of DNE when applicable. Because of this, your answer to #9 on this assignment may differ from the book's.
In this video, Calculus definition of Continuity is discussed and worked-out exercises include p77: 42, 46
In this video, concept of One-Sided Limits if summarized and worked-out exercises include p76: 10, 12, 16
ERRORS: At 5:26 I say "right" instead of "left." Later on, we should never write "=0/0." Instead say "gives 0/0" or even "→0/0." See YouTube description for more.
In this video, Intermediate Value Theorem (IVT) is discussed and worked-out exercises include p78: 76, exercise similar to 85. Pay close attention to what's required for a complete answer. Students often skimp on the details and lose credit accordingly.
Chapter 1.5 – Infinite Limits
p85: 33-47 odd
How do we algebraically/numerically determine when a limit approaches positive infinity or negative infinity?
Worked-out exercises include p85: 38, 44, 48.
This was a difficult topic to explain via video -- in the midst of a school year I would've saved this for a classroom discussion. Do your best to keep your brain engaged and think of what "makes sense," and be sure to contact me or any other resources if you're having trouble.
Chapter 2.1 – The Derivative and the Tangent Line Problem
p102: 25-36 all
Note: I'll never discourage you from looking ahead in the book or engaging with Math you encounter on the streets if you are so inclined, but you are NOT allowed to use any of the derivative "shortcuts" that have not been officially introduced yet. For now, every derivative you calculate must involve the limit process. (I have my reasons... don't fight me on this one!)
This video summarizes the connection of the derivative to the definition of slope that you learned years back and the usefulness of limits in finding the exact slope of the tangent line. The video concludes with a very simple example.
The derivative is used in finding the equation of the tangent line to a function at a given point. A couple calculator features regarding derivatives are introduced. We'll need to become confident in BOTH such technological means AND algebraic means for finding derivatives. The example in this video is p102: 32.
The derivative is used in finding the equation of a tangent line that satisfies given conditions. Warning: The algebra gets ugly (or beautifully complex, depending on your perspective). The example in this video is p102: 36.