Name Summer Work Packet AP Calculus AB

Transcription

1 Name Summer Work Packet AP Calculus AB Welcome to AP Calculus AB! Advanced Placement courses are designed to expose you to college level curriculum. This requires a great amount of planning from your teacher and a greater amount of responsibility and commitment from you. One of the responsibilities you have accepted in taking an Advanced Placement course is this summer work packet. Completing this packet before the first day of school is the best way to prepare for the new school year. Calculators are used sparingly within the course and should not be used in this packet unless instructed otherwise. I encourage you to complete as much of this packet as you can without assistance. If you are stuck, consult your peers, Khan Academy, tutorial YouTube videos, older siblings, parents, tutors, or whatever/whoever else might help you remember these topics. You may also me at mgraham@hannasd.org if you are truly stuck. Your ability to complete these topics without assistance from anyone or anything else is imperative for your success in this course. Good luck and see you August 28 th! Mrs. Graham Page 1 of 14

2 Factoring Review: Factor out a GCF: 1. 7xx 2 14xx 4. xx xx ee 2xx ee xx 5. ssssssss + tttttttt 3. 2xx + 3xx aa bb aaaaaa Page 2 of 14

3 Factor Trinomials: 1. nn 2 4nn xx 2 7xx bb bb yy 2 + 4yy Factor differences and sums of cubes: 1. xx 3 + yy ww Factor differences of squares: 1. xx aa 2 bb ww 2 81xx 4 4. xx 4 *not a typo. Page 3 of 14

4 Equations of Lines: Write the equations of the following lines in all three forms: Page 4 of 14

5 1. Write the equation of the line parallel to 2xx + 4yy = 1 that passes through the point ( 3,5). 2. Write the equation of the line parallel to 3xx 5yy = 7 that passes through the point (2, 4). 3. Write the equation of the line perpendicular to 2yy + 5 3xx = 0 that passes through the points ( 1, 3). 4. Write the equation of the line that goes through the point (2,4) and is perpendicular to the line that contains the points ( 1,3) and (0,0). Page 5 of 14

6 Solving Equations: Solve all of the following equations algebraically: 1. 4xx xx + 3 = xx + 1 = 5 xx xx + 2 = xx+1 = 25 Page 6 of 14

7 5. llllll 2 xx = 3 6. llll(xx + 1) = ee 2xx = xx 3 xx = 0 Page 7 of 14

8 Complex Fraction and True/False Statements: Simplify each expression (answers will have only positive exponents): 1. aa 1 (bb 1 ) aa 2. 9 xx 2 3+xx xx+h 1 xx h 4. 1 xx 2 1 yy 2 1 yy 1 xx Page 8 of 14

9 Decide if the following statements are true or false: 1. 2kk 2xx+h = kk xx+h 2. 1 pp+qq = 1 pp + 1 qq 3. xx+yy 2 = xx 2 + yy aa bb = 3aa 3bb 5. xx 2 + yy 2 = xx + yy Page 9 of 14

10 Radicals, Logarithms and Exponents: Rationalize the denominator using the conjugate: Write as a single logarithm: 1. 2llllll xx + 3llllllxx llllll llllll 2 (xx 2 1) llllll 2 (xx 1) Expand the logarithm completely: 3. llllll bb 4xx5 xx 1 xx 7 3 xx 2 +1 Page 10 of 14

11 Evaluate the following expressions (do not use a calculator): 1. 2llll 1 ee 3 2. llllll llllll bb 1 4. llllll 10 (10 3xx ) llllll Determine the value of kk if 4xx 2 36 = kk xx 2 aa 2 and kk Rewrite xx2 3xx+2 xx as a sum using rational exponents. Page 11 of 14

12 Trigonometry: You must memorize all values of basic trig function values. ALL TRIGONOMETRY IN CALCULUS IS DONE IN RADIANS! 1. sin 0 2. cos 0 3. tan 0 4. sec 0 5. csc 0 6. cot 0 7. sin ππ 6 8. cos ππ 6 9. tan ππ sec ππ csc ππ sin ππ cos ππ tan ππ sec ππ csc ππ cot ππ cot ππ sin ππ sin ππ cos ππ cos ππ tan ππ tan ππ sec ππ sec ππ csc ππ csc ππ cot ππ cot ππ sin ππ 32. cos ππ 33. tan ππ 34. sec ππ 35. csc ππ 36. cot ππ 37. sin 3ππ cos 3ππ tan 3ππ sec 3ππ csc 3ππ cot 3ππ 2 Page 12 of 14

13 More Trigonometry 1. Let θθ be an acute angle of a right triangle. Find the values of the other five trigonometric functions of θθ if the ss(θθ) = (SOHCAHTOA) 2. What is the general solution of: (factor/difference of squares) ssssss 3 xx 36ssssssss = 0 3. List the following identities: a. All 3 Pythagorean Identity for Trigonometry b. Reciprocal Identities c. Quotient Identities Page 13 of 14

14 Functions: 1. Find the inverse of ff(xx) = 2xx Simplify ff(xx+h) ff(xx) h where, a. ff(xx) = 2xx + 3 b. ff(xx) = 2 xx c. ff(xx) = 2 xx Page 14 of 14