Westland High School 146 Galloway Road Galoway, Ohio 43146 (614) 851-7000 John Rathburn, Principal Assistant Principals Lori Balough, Chad Dotson, Vincent Spirko May 29, 2014 AP Calculus Class of 2014-2015: Your AP Calculus exam in on Wednesday, May 6, 2015. That may seem like a long way away, but with snow days, exams, assemblies, school activities, ect, we can expect to have only 135-140 days of class before the exam. It is my goal that you are successful in AP Calculus, and that is why I have designed this summer assignment for you! For you to be successful in this course, it is essential that you have a firm grasp on the concepts of algebra, geometry, trigonometry, and functions. It is also imperative to be familiar with operating your graphing calculator. This summer assignment is designed to give your brain a jump-start so that you may start the year off on the right foot, and put you in a better position to take the AP exam in May. Believe it or not, with this summer assignment, we can start calculus on the 4 th day of school! The assignment is due on the first day of school Tuesday, September 2, 2014. It is to be done NEATLY and on a SEPARATE piece of paper. Additionally, all work must be shown. There will be a test over this material on Thursday, September 4, 2014. If you have any questions regarding this assignment, I would be more than happy to help you. Feel free to e- mail me at sarah.weber@swcs.us. I will be available the following dates: Tuesday, July 29, 2014 12pm 2:30pm WHS room 602 Tuesday, August 19, 2014 2pm 3:30pm WHS room 602 I also have videos on my website: http://whs.swcs.us/~sarah.weber/ I am available via email as well, sarah.weber@swcs.us My work and answers will be posted in late August on to my website as well. I will send a remind101 message when I post the answers/work. Have a great summer and I am looking forward to working with you in the fall! Sarah Weber
1. Simplify each expression a. b. c. d. 2. Simplify each expression a. b. c. 3. Solve for a. b. 4. If determine each of the following a. b. c. d. e. f. g. h. 5. Follow the directions for each problems a. Evaluate and simplify if b. Expand c. Simplify d. 6. Expand a. b. 7. Simplify a. b. c. d. e. f. g. h. i. j. k. l. m. 8. Using point slope form,, write an equation for the line: a. With slope of containing the b. Containing the points and c. With slope containing point point d. Parallel to and passes e. Perpendicular to the line in problem through, containing the point 9. Without a calculator, determine the exact value of each expression a. b. c. d. e. f. g. h. i. j. 10. For each function, determine its domain and range a. b. c. d. 11. Determine all points of intersection graphically (with a calculator)or algebraically a. and b. and in the first quadrant 12. Solve for,where is a real number a. b. c. d. e. f. g. h. i. j. k. l. 13. Graph each function by hand. Give its domain and range a. b. c. d. e. f. g. h. (use calc for table of values) i. j. (use calc for table of values) m. k. l.
AP Calculus AB 2014-2015 Summer Assignment Agreement Please review and sign below; return to Mrs. Weber before you leave for break: Summer Assignments: I agree to complete the summer assignments. Failure to complete the summer assignment does not provide grounds for removal from the course. Instead, the incomplete summer assignment will be used in the determination of the student s grade during the 1 st 9 weeks. The required summer work must be completed by the deadline specified by the teacher. The material will be distributed during the final week of the 2013-2014 school year. If you are unable to attend the meeting it is your responsibility to obtain the information/packet from your teacher. Mrs. Weber will provide support via online tutorial videos (posted during June) on her school website. She is also available during the summer via email sarah.weber@swcs.us Student Name (printed) Guardian Name (printed) Guardian phone Guardian email Student signature Guardian signature Teacher signature Please detach and keep this information for your records: Mrs. Weber Contact information sarah.weber@swcs.us http://whs.swcs.us/~sarah.weber/ 614-851-7017 Important Information for AP Calculus Summer Work: Study/Help Sessions: Website: Remind101: Tuesday, July 29, 2014 12pm 1:30pm WHS room 602 Tuesday, August 19, 2014 2pm 3:30pm WHS room 602 https://sites.google.com/a/swcsd.us/whsweber/ The site will not be live until July! What will be posted: Answer key (mid-july) Videos (mid-july) Weber s work (mid-july) Sign up for Weber s AP reminders (open to parents and students). TEXT 708-443-4283 (number) @whscalc15 (message) EMAIL Whscalc15@mail.remind101.com Subject line blank Work will be collected on Tuesday, September 4, 2014 during class. You can expect a test over the material in the summer assignment during the first week of school.
DOMAIN AND RANGE Domain all values for which a function is defined (input values) Range possible or output values Example 1 Example 2 Find the domain and range of answers in interval notation. Write DOMAIN: For to be defined This is true when (solve for ) Domain: The domain is the set of inputs of the function. Input values run along the horizontal axis. The furthest left input value associated with a point o the graph is. The furtheest right input value associated with a point on the graph is 5. So the domain is RANGE: The solution to a square root mush always be positive, thus must be greater than or equal to 0. Also, there are no vertical shifts, therefore the graph doesnot translate up/down impacting the range. Range: The range represents the set of output values for the function. Output values run along the vertical axis. The lowest output value is. The highest output value is, however, there is a gap in the graph between 3 and 4, where the range is undefined. Therefore the range is [-2, EVEN AND ODD FUNCTIONS Even Functions functions that are symmetric over the -axis. Algebraically: Odd Functions functions that are symmetric about the origin (or ). Algebraically:
Add/subtra ct to Add/Subtra ct to Multiply values by Multiply values by reciprocal of Inverses To find the inverse of a function, simply switch the and and solve for the new values. Recall is defined as the inverse of. Example: Rewrite as Switch and Solve for your new Cube both sides Solve for Rewrite in inverse notation Transformations of Functions Vertical stretches/shrinks Horizontal stretches/shrinks shrink stretch Reflection over the axis Vertical Shifts units up Vertical Shifts units down shrink stretch Reflection over the axis Horizontal shift left Horizontal shift right Vertical Asymptotes Set the denominator equal to zero to find the -value for which the function is undefined. That will b the vertical asymptote given the numerator does not equal 0 also. Write the vertical asymptotes as a line in the form Example: Find the vertical asymptote of Since when the function is in the form, then the vertical line is the vertical asymptote of the function.
To evaluate a function for a given value, simplify plug the value into the function for Functions read of of. Means to plus the inside function (in this case in for in the outside function (in this case, ). Example: Given and. Find : Equation of a Line Slope intercept form: Vertical line: (slope is undefined) Point-Slope form: Horizontal line: (slope is zero) Example: Write a linear equation that has a slope of and passes through the point Slope-intercept form Point-Slope Form Exponential & Logarithmic Functions Switch forms to solve or get same base on each side!!!!! Log Form Exponential Form Product Rule: Expand: Properties of Logarithms Example: Example: Quotient Rule: Condense: Power Rule: Expand: The Reciprocal Function & Transformations You may need to use synthetic division to get function in this form! Vertical asymptote moves with HORIZONTAL shifts Horizontal asymptote moves with VERTICAL shifts