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AP Calculus Summer Packet for school year 2012/2013 (email me if you have questions [email protected]) No calculator is allowed for these questions. Show all work neatly on separate paper. Due the first day of school. I will schedule review sessions in August - I will post the date on my Web Page. You can also email me if you want to get a group of people together to review these problems 1. Find the slope of 2x + 4y = 5 2. Find the equation of the line parallel to x - 2y = 12 and passing through (2,-5). Write your answer in the following forms: a. Point – slope b. Slope intercept 3. Find the equation of the line perpendicular to 3x +4y = -8 and passing through (0,-2). Write your answer in the following forms: a. Point – slope b. Slope intercept 4. Find all vertical and horizontal asymptotes of the following graphs – express asymptotes as an equation: a. y x2 x2 4 b. y= e-x +1 c. y = ln (x-3) 5. Find the domain and range of: a. e-2x +1 b. y = ln (x+2) c. tan -1 x d. cos x e. sin (arctan x) f. ln (cos x) 6. Describe the end behaviors of the following graphs: a. f(x) = x4 + 3x3 – 6x b. f(x) = -3x3 + x2 7. Find the following values: 5 ) 3 7 b. cos( )= 6 a. sin( c. arccos -1 = d. tan (arccos ( 3 ))= 2 8. Find csc θ given cosθ = 12 and tan θ < 0 13 9. The point (27,7) is on the terminal side of an angle in standard position. Determine the values of all six trig functions. 10. Find the smallest positive value x for which f(x) = sin( x ) – 1 is a maximum. 3 11. Given triangle ABC , mC 90 , mB 60 , and AC = 23, find AB. (sketch triangle – remember, no calculator) 12. Find the reference angle of = 136degrees. 13. Determine two solutions on [0, 2 ) such that sec 14. Solve the following equations in the interval [0, 2 ): a. 4sin2x -1 =0 b. tan2x + tanx = 0 c. sin 2x = .5 d. sec x -2 = 0 e. 2sin2x + sin x = 1 2 3 3 4 5 and sec(θ) = 6, find tan (θ). 9 15. Given sin(θ) = 16. Sketch the angles in standard position and state the value of all 6 trig functions 4 3 7 b. 6 c. 3 a. 17. Rewrite the angle in degree measure and find two positive co-terminal angles in radian measure: 7 6 12 5 , ), find the value of cos . 13 13 19. Sketch triangle ABC and solve given: a 13, b 18, c 26 (calculator allowed) 18. Given a terminal point of a ray ( 20. Find the x-intercepts of f(x) = x3 -2x2-x +2 21. Find the inverse ,f-1(x), of the following functions: a. f(x) = 2 x b. f(x) = 2e-x 22. If the point (5,-2) is on the graph of a function, then what point must be on the graph of its inverse, f-1(x)? 23. Given f(x) = lnx and g(x) = 4-x2, find f(g(x)) and identify the domain and range of the composite function. 24. Given f(x) = 2x2 – 3x, find f (2 h) f (2) and simplify. h 25. Solve and or simplify without a calculator: a. b. c. d. e. Log3(x-4) = 0 ln x4 = 10 e2x- ex = 6 ln(6x – 6) = 2 log42 + log48 = ? 1 3 ) =? 125 b g. logb(3b) = , b=? 2 2 2x ( x -15) h. e =e f. log3( 26. Identify the x and y intercepts of f(x)= 4ln(x-2) 27. Expand the following expression as a sum, difference, and/or constant multiple of logarithms using the log rules: ln x2 x3 1 28. Condense the following expression as a single term : 2(log5x + log57) – 1 (log5y) 3 29. Find the domain of the function: f(x) = ln( x3 ) x2 30. Find all values of x such that f(x) = g(x) given: f(x) = x2 +19x +73 g(x) = 2x +1 31. Find the roots of f(x) = 8x2 1 7 32. Determine if the following functions are odd, even , or neither: a. y = x3 +2 b. y = x3 +2x c. y = x 2 2 d. y = e x - 1 33. Use long division to divide: x 4 3x 2 4 x2 x 3 34. Use synthetic division to divide: x3 27 x 54 x 3 35. Find the following limits a. b. lim x4 lim x 0 x4 x x 12 2 x3 3 x 36. Know these graphs by heart: ex , lnx, sinx, cosx, tanx, x , x2, x3, (x-h)2+(y-k)2=r2