Welcome to AP Calculus BC! I hope you are as excited as I am about Advanced Placement Calculus BC, as we start on the journey to prepare for the AP Exam on May 15th - just 288 days and counting! (For planning purposes, cost for AP Exams this year is $94 each, and students will be able to register August 15-September 15 in order to make staggered payments .) Click to download Advanced Placement Calculus A CLASSROOM POLICIES here.

#### Students received their textbook today, and have their first assignment -- which is to look through Chapter 1 to make sure they have mastered all these PreCalculus topics. (College Calculus teachers assume that you remember how to do all the math you've seen when you walk into their classroom, so this is a chance to assess yourself)

1) Read carefully Sections 1.1 and 1.2 (pages 1-18), paying particular attention to vocabulary -- all of these topics were first learned in middle school math or Accelerated Math 1. **Concepts to note specifically: absolute value inequalities, algebraic definition of symmetry, and transformations. ** Problems to examine are found on Pages 10-11: #1, 7, 21, 23, 24, 29, 37, and 61-66, and then Pages 19-20: #26, 39, 45, and 47. Remember that if you have questions on these concepts, you can always do additional problems for practice -- odd answers can be found in the back of the book.

2) Next, review Section 1.3 on the basic classes of functions and Section 1.4 on trigonometry. Read carefully through these two sections (pages 21-31), again noting vocabulary and technology issues. *Be sure you have your dozen basic unit circle values memorized, know how to use transformations to graph trig functions, and absolutely know your seven basic trig identities* -- which ones are those? Review assigned problems on Pages 23-24: #8, 33, and 36, and then Pages 32-33: #21, 25, 30, 34, 37, 49, and 50. (Remember that this is a minimum assignment for review: if you need to do more in order to be proficient, do so!)

3) Now look at inverse relations, which can be found both algebraically (exchange **x** and *y* in the equation and solve for the new **y**), graphically (reflect the graph over the identity line **y **= *x*; consider the DrawInv command on your calculator), or numerically (exchange **x** and *y* values in your table) -- think about whether or not any inverse of a function will itself be a function. What about inverses of the six basic trigonometric functions? Section 1.6 then looked at one of the most common uses of inverses, exponential and logarithmic functions. Be sure to review the laws of exponents and logarithms you learned back in Accelerated Math 2. **(Note: Hyperbolic trig functions are a new topic, and will not be on any test by name.)** Review assignment is Pages 42-43: #4, 15, 19, 22, 33, 41, 45, and then Page 52: #5, 17, 24, 35, and 37.

4) The final section in this first chapter examines the power and/or shortcomings of technology as a tool. If my graphing calculator works properly 99+% of the time, when does it fail, and why? When are window settings an issue, or pixel resolution a problem? Why does the calculator produce such different looking graphs for **y** = sin 50*x*, just because I change the window slightly? Just because we're looking at more interesting equations now, must I still think? (YES! -- your brain is about ten times the size of your calculator; don't look like a fool next to the machine!) As examples, look at Page 57: #5, 7, 11, and 16 -- and look for other instances where the calculator might lead you astray!