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Review Packet for AP Calculus I. Simplify each expression below in #1-3. 1. 5 9 8 16 2. 24 3 4 3. 12 63 21 84 II. Exponent Review. Simplify leaving no negative exponents in #4-6. Evaluate in #7-9. 4 x 1 y 3 5. 5 x 4 y 2 4. (2 x ) (3x ) 3 4 7. (27) 2 3 2 3 8. (64) 1 2 2 6. 4 x 1 y 3 2 ( 4 2 ) 5x y 3 9. (16) 4 1 32 +( ) 9 1 (64) 2 III. Polynomial Review. Perform the given operation for each problem in #10-14. 10. ( x 3) 2 (2 x 1) 13. Divide ( (3 x 3 11. x 2 7 x 6) (3x 2)( x 2 4 x 5) by ( x 2) 12. (8 x 2 3 x) (4 x 2 5 x 3) using long division. Do the same problem using synthetic division. 14. Cube the binomial (2 x 3) . IV. Radicals. Simplify the following radical expressions in #15-20, removing all possible factors from each radical. Rationalize when necessary. (That is, leave no radicals in a denominator). Solve the radical equation for x in #21. 6 15. 32x y 19. 2 3 6 9 16. 5b 10b 4 17. m 2 n5 12m 4 20. (8 3 2)(8 3 2) 18. 5 27 2 48 7 12 21. x2 3 x 1 V. Factoring/Solving quadratic equations. Completely factor the following polynomials in #22-25. Check for greatest common factors first. 22. z2 – 81 23. 2x2 + 13x – 24 24. 8z5 – 4z4 + 20z3 25. b4 – 81 Solve the problems in #26-31 by factoring completely. 26. r3 + 3r2 – 54r = 0 29. 27. x3 3x 2 x 3 = 0 8 x 4 32 x 2 0 30. 10 x 2 9 x 28. 4 x 2 4 x 35 = 0 31. 8 x 4 32 x 2 0 VI. Simplifying rational expressions. Common denominators are needed to add/subtract. Perform the operations as required in #32-37. 5 y 5 y2 32. 2 x2 8x2 x 2 13x 40 33. x 2 2 x 35 y2 2 y y 2 81 34. 2 y 7 y 18 y 2 11y 18 3 4 35. 2 7 x y 21xy 2 4 3 36. 2 x 3x 3x 9 2 x 37. 6 4 x 1 VII. Solving equations/inequalities. This is a mixture of all types of equations/inequalities, from as easy as linear, to quadratic, to rational, to logarithmic, to exponential . 38. 4 3 ( x 10) ( x 30) 39. 3x 8 14 5 10 42. 2x2 5x 11 0 43. 8 x 2 40 x 0 40. 2 x 5 9 41. 6 (2 x 7) 15 3x (1 x ) 44. x3 216 0 45. 2 5 6 2 x2 x2 x 4 46. 42 x3 6 14 47. log 4 x log 4 ( x 1) 1 2 48. 2ln x ln3 2 49. x 4 4 x 2 45 0 VIII. Linear Equations/Slope. In #50-52, find the slope of a line joining the two points. 50. (3, 8) and ( 5, 2) 51. (4,3) and (6,3) 52. (-2,5) and (-2,4) In #53-55, find the equation of the line described. Use point-slope form when necessary, but pupt your final answer in slope-intercept form. 53. A line that passes through (0,4) and (-2,3) 54. A line with x-intercept of 3 and y-intercept of 9. 55. A line parallel to x 3 y 6 that passes through the point (-9,6) 56. A line perpendicular to y=2/3x + 4 that passes through the point (-2,-4). 57. A line that passes through (4,3) and (7,3). 58. A line that passes through (-2,-5) and (-2,-1). IX. Trig Review. 59. Determine two coterminal angles to each of the following angle measures: a) 5/4 b) 60º 60. Determine the values of all six trigonometric functions for the angle whose terminal side lands on the ordered pair (-5, 12). 61. Without using a calculator, find the value of the six trig values for each given angle measure below. t quadrant 7/6 Reference Terminal number point Sin t Cos t Tan t Csc t Sec t Cot t 8/3 -3/4 -3/2 62. Solve the following trig equations for values between 0 2 . a) 4sin x 2 3 0 b) tan 2 x 1 0 c) 2sin 2 x sin x 0 d) 2 cos 2 x 3cos x 1 0 63. Use trig identities (including reciprocal, quotient, and Pythagorean) to prove the following identities. Do not move terms from one side to the other nor should you multiply/divide each side by anything to prove the identities. a) cos x sin x tan x sec x b) (tan 2 x 1)(1 cos 2 x) tan 2 x c) tan 2 x sec2 x tan 2 x tan 4 x