Dear AP Calculus Student, Welcome to AP AB Calculus!

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Allen Hart
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1 Dear AP Calculus Student, Welcome to AP AB Calculus! The main objective of this course is to develop your understanding of the concepts of calculus and provide experience with its methods and applications. The course emphasizes a multi-representational approach to calculus with concepts being expressed graphically, numerically, analytically, and verbally. In order to be successful in this course you need the proper foundation, i.e. knowledge of algebra, geometry, trigonometry, and elementary functions. You will also need to be able to carry out certain computational tasks with ease. These include manipulations of functions, solving algebraic equations, interpreting numerical values given by formulas, graphs, and tables, using and manipulating data, and knowing how and when to use your calculator. This is a rigorous college course. The curriculum and pace of the course is intense. Since this is a college class you can expect to spend approximately 1-2 hours completing homework and/or studying for every hour that you are in class learning. This packet will be due at the end of second week of school, and there will be an assignment on this material. The assignment covers all concepts and skills from algebra, geometry, trigonometry, and functions. It is in your best interest to review the sample questions provided on the subsequent pages. Feel free to contact me with any questions or concerns that you may have. I will check at least once a week in June and July, and almost every day during the month of August. Have a restful summer and be ready for an exciting time in AP Calculus next year! Sincerely, Your AP Calculus Teacher Mrs. Ligatti elizabeth_ligatti@ccpsnet.net

2 The following Trigonometric Identities MUST be memorized Reciprocal Identities Quotient Identities Pythagorean Identities Co-Function Identities Odd/Even Identities Odd Even Double Angle Identities Half Angle Identities

3 The Radian Measures and Coordinates MUST be memorized Remember :,, and

S A T C a reminder of what trig functions are

be completed without the use of a calculator.

If I cannot read your work and answers, I

4 S A T C a reminder of what trig functions are positive in each quadrant All questions are to be completed without the use of a calculator. Your answers need to be legible. If I cannot read your work and answers, I cannot grade the problem. I. Algebraic Manipulation Simplify the expression: Simplify: 3. (hint: rationalize the denominator) 4. Simplify completely: 5.

5 II. Solving Equations Solve for x III. Exponents and Logarithms 8. Solve for x: 9. Solve for x : 10. Solve for x : 11. Condense and Simplify: 12. Given A. Find the line parallel through (6,1) B. Find the line perpendicular (normal) through (6,1)

6 IV. Functions / Graphs If you can t remember the parent graph, just make a table and plot points. 13. Sketch the graph of 14. Sketch the graph of (find zeros) (find VA, HA, x & y intercepts, label) 15. Sketch the graph of 16. Sketch the graph of

7 17. Sketch the graph of 18. Graph shifted right 2 and up 3. Write the equation. 19. Sketch the graph of 20. Find the Domain / Range: (Use proper notation.) Domain: Range:

8 21. Given Identify the hole and all asymptotes. Holes: Asymptotes : 22. Find the Domain / Range: (Use proper notation.) Domain: Range: 23. Find the Domain / Range: (Use proper notation.) Domain: Range: V. Evaluation and Combination of Functions (These are NOT multiple choice questions.) 24. Given:, find: a. f(4x) b. f(g(x)) c. f(x)g(x) d. f(x)-g(x) e. g(f(x)) f. f(g(2)) 25. Given:, find: (NO decimals.) a. f(0) b. c. 26. Given:, find: a. f(-2) b. c. f(t-1) d.

9 27. Given:, find: a. f(-1) b. f(0) c. f(2) 28. If, find 29. If, find VI. Trigonometry (Use Unit Circle.) 30. Find: (No decimals) 31. Evaluate: (No decimals) 32. Find 2 solutions over the interval for x if: 33. Solve for x: 34. Solve:

10 VII. Limits Find the limit

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a