Harmony Public Schools



2018-2019 AP Calculus AB Summer AssignmentWelcome to AP Calculus! You are now at the highest point of all high school math courses. This is not going to be easy but it will be totally worth it! Get ready to challenge yourself, work hard and have some fun in the meantime!One of the main keys to success is early preparation. So, I need you to complete below assignment while enjoying the summer. The goal here is to make you ready for this challenging fast-paced AP course that is taught at the college level. Questions in this assignment will help you refresh your memory, strengthen your math skills, and identify topics that you might have problems with before the course begins. Please do not get overwhelmed by the number of questions. The more you practice during the summer, the more you feel ready when the school starts! Besides, summer is long! I suggest you solve no more than three or four questions in a week and complete the assignment the week right before school starts. Please do not finish the whole packet in the beginning of the summer or wait until the last day of your summer vacation.This assignment is DUE ON THE FIRST DAY OF SCHOOL. You may use reference materials to help you out and refresh your memory (old notes, textbooks, online resources, etc.). Use your discretion as to whether you should use a calculator or not. All work must be neatly shown for each problem. Use graph paper for the problems that needs to be sketched. Please show all work! Have a great summer and I am looking forward to seeing you in August. Algebra Skill:Identify the following statements as true or false (Questions 1-3).4. Solve xz+y+1=z for z. 5. Solve for . 6. Solve V = 2(ab + bc + ca) for a.7. Factor: 8. Factor: 9. Factor: 4x3 - 8x2 - 25x + 5010. Factor: x3 ? xy2 + x2y ? y3 11. Simplify 12. Simplify 13. Simplify 3xx+1-2(2x+1)x-12 Equations and Inequalities:Find all real solutions, if any, of each equation. Use Quadratic formula if necessary.14. 15. 16. 17. 18. y = x2 + 4x - 3Solve each inequality. Then graph the solution set. 19. –9 20. 21. x2-4x-4x2+1>022. Solve the system of equations: 23. Graph the system of inequalities: 3x-y-6<05y+2x-10≥0Functions:362394565405000For the following function, find, (questions 24-31)24. The graph of f(x) (no calculator)? 25. Domain? 26. Range?27. Intercepts? 28. Zeros? 29. Asymptotes?30. Determine if the function is even, odd, or neither.31. f-1(x) = ?If fx=x2+1 and g(x) =, then find (questions 32-37)32. fof(x) __________33. fog(x) __________34. gof(x) __________35. gog(x) __________36. f-1(x) __________37. g-1(x) __________34575753403600038. Convert the function to a piecewise function.39. Graph the piecewise function. (No calculator)342900228600040. 41. A piece of wire 5 inches long is to be cut into two pieces. One piece is x inches long and is to be bent into the shape of a square. The other piece is to be bent into the shape of a circle. Find an expression for the total area made up by the square and the circle as a function of x.Geometry:Find an equation of the line having the given characteristics. Express your answer in both general form and the slope-intercept form of the equation of a line.42. Parallel to the line 2x – 3y = -4; containing the point (-5, 3)43. Perpendicular to the line x + y = 2; containing the point (4, -3).Consider the equations: 4x +14y = -28 and 2x + ky = 21.44. In order for lines to be parallel, k= ________________45. In order for lines to be perpendicular, k= ________________Exponents and Logarithm:46. Solve for x: 47. Solve the equation (Hint: Treat like a quadratic, do a temporary substitution.Do algebraically and use calculator at the end.)48. Solve for x. 49. Solve for x. e[2lnx-lnx2+x-3]=150. Simplify log12 2 + log12 9 + log12 8 = ? (no calculator)51. Simplify log4(2)5 = ? (no calculator)52. Solve for x. lnx3-lnx2=1253. Solve for x. lnx-lnx+1=154. Write the expression as a single logarithm.2377440228600055. Draw a sketch the function y = -e–x Trigonometry:Find two solutions to the inverse trig equations in 50 and 41. 56.57.58. Solve for y. 59. Solve for x. 3sin2x=cos2x where 0≤x≤2π60. Verify the following identity: 11+tanx+11+cotx=161. Write the given expression in algebraic form: tan(arccosx3) (Hint: Use right triangle)31775406305550062. Determine the exact value of the other 5 trigonometric functions (sin, cos, cot, csc, and sec) of ? given that tanθ=247 and ? is in quadrant I. Do not use your calculator. (Hint: Use right triangle)63. Draw a sketch the function y=3-2sinx 64. Solve for x. 2cos2x-1-cosx=0 where 0≤x≤2π (Hint: Treat like a quadratic and factor)65. Write the expression x2+4 in terms of θ whenx=2tanθ ................
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