ࡱ> 8:7 Ubjbj \jjQ[l(2(2(28`2\2_hd3D5555޽$ǿ 55#~@Z55޽޽NS~ʽ5X3 `O(+(2߸ʽ/0_,y߸&yʽ|Math Analysis Name: ____________________________ Review Packet Problems Date: ______________ All work is to be done in the space provided. Be neat. Illegible work will not be accepted. SOLVING EQUATIONS and INEQUALITIES __________ 1.  EMBED Equation.DSMT4  __________ 2.  EMBED Equation.DSMT4  __________ 3.  EMBED Equation.DSMT4  __________ 4.  EMBED Equation.DSMT4  __________ 5. Solve: 4x3 + 8x = 12x2 __________ 6. Find all zeros, real and imaginary. f(x) = x3 2x2 + 4x 8 SOLVING SYSTEMS Solve each of the following systems of equations. Write your final answer as a coordinate point. __________ 7. Solve by substitution 3x + y = 1 -2x + y = -5 __________ 8. Solve by elimination 5x + y = 5 9x 4y = -20 __________ 9. Solve by matrices 4x + 5y = -7 y = 3  EMBED Equation.DSMT4  x Solving Quadratic Equations __________ 10. Solve by factoring. f(x) = x2 x 6 __________ 11. Solve by quadratic formula. f(x) = 2x2 + 3x 1 __________ 12. Solve by completing the square. x2 + 6x = 5 POLYNOMIAL FUNCTIONS __________ 13. Find the rational zeros: f(x) = x3 + 3x2 5x 15 __________ 14. Find the rational zeros: f(x) =x4 -  EMBED Equation.DSMT4 x3 7x2 + 9x + 6 __________ 15. Write the function given the zeros: -1, 2, 3 + i, 3 i RATIONAL EXPRESSIONS __________ 16. Simplify:  EMBED Equation.DSMT4  __________ 17. Simplify:  EMBED Equation.DSMT4  __________ 18. Simplify:  EMBED Equation.DSMT4  SIMPLIFYING COMPLEX FRACTIONS __________ 19. Simplify:  EMBED Equation.DSMT4  __________ 20. Simplify:  EMBED Equation.DSMT4  EXPONENTS AND RADICALS Simplify # 21-28. __________ 21.  EMBED Equation.3  __________ 22.  EMBED Equation.3  __________ 23.  EMBED Equation.3  __________ 24.  EMBED Equation.3  __________ 25. x2 ( x3 ( x4 __________26.  EMBED Equation.3  __________ 27. Evaluate without a calculator  EMBED Equation.3  __________ 28. Evaluate without a calculator  EMBED Equation.3  LOGS __________________ 29. Expand log 4  EMBED Equation.DSMT4  __________________ 30. Expand log 3  EMBED Equation.DSMT4  __________________ 31. Condense 7 log 4 y + 3 log 4 2 2 log 4 x __________________ 32. Condense: log 7 5 + log 7 9 + 6 log 7 x + 3 log 7 y (3 log 7 2 + 2 log 7 x) For #33 and #34, evaluate using the change of base formula. Use both common and natural logs for each. __________ 33. log 4 81 __________ 34. log2 19 GRAPHING Some parts may not have an answer. In that case, write the symbol for the empty set, (. 35. y = x2 + 3x 4 vertex _________ Axis of symmetry: _________ zeros: _________ domain: _________  range: _________ 36. y = (x + 2( 3 vertex _________ domain: _________ range: _________  37. y =  EMBED Equation.DSMT4  domain: _________ range: _________ 38. y = ln (x + 2) x intercept: _________ y intercept: _________ vertical asymptote: _________ domain: _________ range: _________ 39. y =  EMBED Equation.DSMT4  x intercept: _________ y intercept: _________ horizontal asymptote: _________ domain: _________ range: _________ 40. y =  EMBED Equation.DSMT4  vertical asymptote: _________ horizontal asymptote: _________ slant asymptote: _________ x intercept: _________ y intercept: _________ domain: _________ range: _________ 41. f(x) = -x4 2x3 + 3x2 + 3x + 4  (just give a rough sketch of this graph) rel max: _____________________ rel min: _____________________  abs max: _____________________ abs min: _____________________ zeros: _____________________ describe the end behavior: give the intervals where f(x) is increasing and decreasing: TRIGONOMETRY __________ 42. What quadrant does the angle  EMBED Equation.DSMT4  lie in? __________ 43. What quadrant does the angle -320( lie in? __________ 44. Sketch the angle  EMBED Equation.DSMT4  in standard position below. __________ 45. Give two coterminal angles (one pos, one neg) for -150(. __________ 46. Change 144( to radians (no calculator!) __________ 47. Change  EMBED Equation.DSMT4  to degrees (no calculator!) 48. Find the 6 trig functions (if possible) that correspond to the graph below.  sin t _____ csc t_____ cos t_____ sec t_____ tan t_____ cot t_____ 49. Evaluate (if possible) the 6 trig functions that correspond to t =  EMBED Equation.DSMT4 . sin t _____ csc t_____ cos t_____ sec t_____ tan t_____ cot t_____ __________ 50. If cos t =  EMBED Equation.DSMT4 , then find cos ( t + ( ) __________ 51. Evaluate the trig function sin  EMBED Equation.DSMT4  using the period as an aid. __________ 52. Simplify using the trig identities: cos x tan x __________ 53. Simplify using the trig identities:  EMBED Equation.DSMT4  CONICS __________ 54. Write an equation of the parabola whose vertex is at (-4, -1) and whose focus is at (-4,2). 55. Identify and graph the following conic:  EMBED Equation.DSMT4  center: _________ a-value: _________ b-value: _________ domain: _________ range: _________ 56. Identify and graph the following conic:  EMBED Equation.3   __________ 57. Classify the given conic and graph the equation.  -9x2 + 16y2 + 54x + 64y - 161=0 __________ 58. Graph the hyperbola with foci (-5, 0) and (5, 0) and vertices (2, 0) and (-2, 0).     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