2017 AP Calculus AB Summer Assignment

Transcription

1 07 AP Calculus AB Summer Assignment Mrs. Peck ( kapeck@spotsylvania.k.va.us) This assignment is designed to help prepare you to start Calculus on day and be successful. I recommend that you take off the rest of June and start this during the month of July. These topics are essential pre-requisite skills that you will need for AP Calculus. These are all topics you have learned either in Advanced Algebra II or Math Analysis/ Dual Enrollment Pre-calculus. Assignment You can choose to do one of the following two options:. Attend an AP Calculus Bootcamp a. Tuesday, August, 4 pm b. Friday, August 5, 9 am pm. Complete the Summer Assignment Problem Set individually. Due the first day of class. You must complete one of the two options. You will receive a grade for the summer assignment. Material Covered on Summer Assignment: o Trig o Eponential and Logarithmic Functions o Rational Eponents Additional Material (that would be beneficial for you to review) Helpful Review Website: You must be logged into your GApps account to access the website. Modules on website o Rational Functions Holes and Asymptotes o Transformation Approach to Graphing Absolute Value, Eponential, and Logarithmic o Piece-wise Functions o Even/Odd Functions o Composition of Functions o Trig Graphs o Linear Function Review o Inverse Trig If you have questions, I will be periodically checking their this summer. Please feel free to contact me with questions.

2 Adapted from Right Angle Trigonometry Trigonometry is an integral part of AP Calculus. Students must know the basic trig function definition in terms of opposite, adjacent and hypotenuse as well as the definitions if the angle is in standard position. Given a right triangle with one of the angles named (theta), and the sides of the triangle relative to names opposite (y), adjacent (), and the hypotenuse (r) we define the 6 trig functions to be: Also vital to master is the signs of the trig functions in the four quadrants. A good way to remember this is A- S-T-C where All trig functions are positive in the st quadrant, Sin in positive in the nd quadrant, Tan is positive in the 3 rd quadrant and Cos is positive in the 4 th quadrant. Special Angles Students must be able to find trig functions of quadrant angles (0, 90, 80, 70 ) and special angles, those based on the and triangles. First, for most calculus problems, angles are given and found in radians. ALWAYS CHECK YOUR CALCULATOR FOR THE RIGHT MODE. Angles are assumed to be in radians so when an angle of 3 is given, it is in radians. It may be easier for you to think of angles in degrees than radians, but realize that unless specified, angle measurements must be written in radians. For instance, sin. 6 The trig functions of quadrant angles (0, 90, 80, 70 or 3 0,,, ) must be quickly found.

3 Trig Identities: Reciprocal Identities csc A sin A Quotient Identities: sin A tan A cos A sec A cos cot A A cos A sin A cot A tan A Pythagorean Identities: sin A cos A tan A sec A cot A csc A

4 Eponential Functions and Logarithms Calculus spends a great deal of time on eponential functions in the form of b. Students must know the definition of a logarithm is based on eponential equations. If y b and log b y to find the value of log 3, state that log 3 and 3 and therefore = 5.. So when you are trying If the base of a log statement is not specified, it is defined to be 0. When we asked for log 00, we are solving the equation: 0 00 and =. The function y log has domain ( 0, ) and range (, ). In calculus, we primarily use logs with base e, which are called natural logs (ln). So finding ln5 is the same as solving the equation e 5. Students should know that the value of e There are a few basic facts that students should know about eponential functions and logarithms: log( ) 0 ln( ) 0 e 0 a 0 ln( e ) There are three rules that students must keep in mind that will simplify problems involving logs and natural logs. These rules work with logs of any bases including natural logs. log a log b log( ab) a log a log b log b log a b blog a Eamples:

5 Negative and Rational Eponents In calculus, you will be required to perform algebraic manipulations with negative eponents as well as rational n eponents. You should know the definition of a negative eponent:, 0. Note that negative powers n do not make epressions negative; they create fractions. Typically, epressions in multiple-choice answers are written with positive eponents and students are required to eliminate negative eponents. Rational eponents create roots. The definition of a b. b a b and a a b a b As a reminder: when we multiply, we add eponents: a a b When we divide, we subtract eponents:, 0 b a ab When we raise powers, we multiply eponents: b In your algebra course, leaving an answer with a radical in the denominator was probably not allowed. You had to rationalize the denominator: changed to. In calculus, you will find that it is not necessary to rationalize and it is recommended that you not take the time to do so.

6 Assignment

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8 Simplify. Your answer should only contain positive eponents.

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