AP Calculus BC Summer Assignment 2015-2016 Mrs. Comeau Please complete this assignment DUE: the first day of class, SEPTEMBER 2nd. Email me if you have questions, or need help over the summer. I would be happy to meet with you at PHS and work on problems for which you have questions. First day of class: Turn in this assignment. Bring questions/concepts from this assignment that you would like to review further. You will earn a grade in your Test/ Quizzes category for this summer assignment. The types of questions from the summer assignment will appear on the first in class exam. If you have any questions over the summer, please email me and I will get back to you as soon as I can. ccomeau@pittsfield.net I WILL CONTACT YOU VIA YOUR SCHOOL EMAIL ADDRESS to let you know when there will be a summer EXTRA HELP session in August. Required Materials Textbook: (Given to you) CALCULUS, 8 th ed, Anton, Bivens, Davis ISBN: 0-471-48238-2 Graphing Calculator: TI 84 (preferred), recommended TI-84 Plus with or without color Notebook with folders, dedicated to AP Calculus: Spiral notebook or 3-ring binder, your choice SUMMER ASSIGNMENT HANDOUT Complete all problems on the following pages; SHOW Your WORK AND BOOK - Chapter 1 - Use most of this chapter to support your work in the handout AND DO PROBLEMS: CH 1.5 - Page 62 Exercises #1 4, 19 23, 24, 27 CH 1.6 Read, notes to support your logarithmic and exponential problems CH 1.8 Read & NOTES, DO Exercises on page 93 Try #3 6 (do not panic if you have trouble with this, we will learn it in class - the prereading and pre-trying will help) IMPORTANT NOTES: When given fractions in a problem, keep your work and solution in fractions (improper are fine), do NOT convert to mixed numbers or decimals See NEED TO KNOW attachment STUDY the Unit Circle and Trig Identities 1
SECTION 1: HANDOUT Using the point-slope form y y 1 = m(x x 1 ) write an equation for the line 1. with a slope of 2 containing the point (3, 4) 1. 2. containing the points (1, -3) and (-5, 2) 2. 3. with a 0 slope, containing the point (4, 2) 3. 4. perpendicular to the line in problem #1, containing the point (3, 4) 4. SECTION 2: If f(x) = x 2 5x + 4, find the following: 1. f(2) 1. 2. f(- 2) 2. 3. f(x + 3) 3. f(x+h) f(x) 4. f (x) = lim h 0 h, h 0 4. SECTION 3: Simplify each expression & Show the work that leads to your answer: 1. 1 x+h 1 x 2. 2 x 2 10 x 5 1. 2. 3. 1 3+h 1 3 x 4. 2x 1 + 8 x 2 6x+9 x+1 x 2 2x+3 5. x2 4x 32 x 2 16 3. 4. 5. 6. sin2 x+ cos 2 x cot x 7. cot x sec x 2
SECTION 4: Solve each equation or inequality. 1. 4x + 10yz = 0 2. y 2 + 3yz 8z 4x = 0 1. 2. 3. x 2 x 6 > 0 4. x 2 2x 5 3 5. x 2 4x < 0 3. 4. 5. 6. (x 2) 2 (x + 1) 3 (x 5) 0 7. 3x 2 x+4 0 8. (2x+5)(x 1)2 (x+2) 3 0 6. 7. 8. SECTION 5: Complete the following identities: (Reminder study ALL identities given!) 1. sin 2 + cos 2 = 2. 1 + tan 2 = 3. sec 2 + 1 = 4. sin x cos x = 5. 1 csc x = 6. 1 cos x = SECTION 6: Without a calculator, determine the exact value of each expression (Reminder KNOW UNIT CIRCLE 1. sin 0 = 2. sin π 2 = 3. sin 3π 4 = 4. cos = 5. cos π 3 = 6. cos 5π 4 = 7. tan 2π 3 = 8. tan π 6 = 9. tan 7π 4 = 10. csc 5π 3 = 11.cot π 2 = 12. sec = 13. sin -1 1 2 = 14. cos -1 2 2 2 = 15. arctan 1 = 3
SECTION 7: Without a calculator, Solve each expression (Reminder KNOW UNIT CIRCLE Solve for x (in radians) on the interval [-2, 2 ] Show your work. 1. 2sin x 1 = 0 2. tan x = - 1 3. cos 2 x sin x cos x = 0 4. cos 2 x + 3cos x + 2 = 0 SECTION 8: Continuity 1. Write the THREE conditions for a function to be CONTINUOUS & 2. Create a Sketch two different functions: (be sure to label each graph) a. A function f(x), that IS continuous at x = 3 b. A function g(x), that is NOT Continuous at x = 3 SECTION 9: Points of Intersection Find the point(s) of intersection, algebraically, of each set of functions below. SHOW your WORK. Use calculators only to check your answer. Write your answer as an exact answer ( leave your answer in radicals, no rounding) 1. y = x 4 + 4 and y = 10 x 2 1. 2. f(x) = 3x + 3 and g(x) = - 4x 2 2. 3. h(x) = x 2 5x + 2 and s(x) = 3 2x 3. 4. f(x) = x and g(x) = x 5 4. 5. y = x 2 + 3x - 4 and y = 5x + 11 5. 6. 2x 3y = 13 and 5x + 3y = 1 6. 4
SECTION 10: Limits Evaluate each limit below Show your algebraic work to solve, also include a sketch of the graph if you would like, for each limit problem. 15. lim x3 2x+3 x 6 4x 2 3x 3 16. lim x 2 7 x 5+x 2 9x 3 17. lim x 3 x 1 8x 2 18. Use: f (x) = lim p f(x+h) f(x) h 0 h to find f (x) when f(x) = 3x 2 - x + 5 SECTION 11: ln & e Simplify or Solve each below: (Use the properties of Exponents & Logarithms - no calculator) 1. ln e 2 = 2. ln e = 3. ln 0 = 4. ln x = 5. ln e 4 ln e 2 = 6. Rewrite as a single logarithm: ln 8x 4 ln 4x 2 = 7. e x = 7 8. e 2x+3 = 8 9. 4e x 12 = 1 5
SECTION 12: GRAPHS - Domain & Range Find the x- and y-intercepts and the domain & range, sketch the graph for each function below. Please try to sketch with -No calculator, then double check /correct with a calculator. I would like to see your first try AND the correction! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. SECTION 13: FACTOR each expression COMPLETELY Factor each expression completely. 1. f(x) = 6x 5 + 21x 3 81x 2 + 9x 1. 2. y = 4x 3 (x + 5) 3 x(2x-7) 2 (x + 5) 6 2. 3. g(x) = x 3/2 w 4 y 6 + x -1/2 w 5 y 3. 6
SECTION 14: Solve the real-world problems & use the graph to determine the limits Answers need to be in a sentence! 1. a. b. 2. a. b. 3. 4. 5. 6. 7. 8. 7
8
9
10
11
12
13
14
15