Dear Student I Please find attached your summer review packet for Academic Calculus. The problems in this packet are taken from Precalculus and they should be familiar to you. However I if you need review I you can use the attached websites for additional information. Internet access is available at all public libraries. You will need a graphing calculator for this class and to complete portions of this packet. Please plan to have one for the coming school year. The packet is due the first day of class and will be graded. To receive full credit I you will need to show all work. This assignment will count toward your first quarter grade and your first quiz of the year will be on this material. Don't wait until the last minute!! A good overall resource for math help is: www.purplemath.com If you have any questions please do not hesitate to contact the High School at: 860-844-3014. Or you can email Mrs.Bastiaanseat:bastiaansem@granby.k12.ct.us I will be checking email every few days during the month of August. We are looking forward to seeing you on the first day of school! - The Math Team at GMHS Below is a list of topics covered in the packet with formulas and helpful websites: Functions and domain: http://www.purplemath.com/modules/fcns2.htm http://www.algebralab.org/lessons/lesson.aspx?file=algebra FunctionsRelationsEvaluation.xml Simplifying radicals: http://www.regentsprep.org/regents/math/radicals/lsimplify.htm http://www.themathpage.com/alg/simplify-radicals.htm Rational Functions: http://id.mind.net/~zona/mmts/functionlnstitute/rationaifunctions/rational http://www.themathpage.com/aprecalcirational-functions.htm Functions.htm I Logarithms: http://www.themathpage.com/aprecalc/logarithms.htm
Complex Numbers: a + bi, the number i = ~, complex conjugate of a-bi is a-bi http://www.purplemath.com/modules/complex.htm http://www.geom.uiuc.edu/-iaurence/welcome.html http://www.wtamu.edu/academic/anns/mps/math/mathlab/ col algebral col alg tut12 complexnum. htm http://regentsprep.org/regents/mathb/3c4/multlesson.htm http://library.thinkguest.org/10030/4complex.htm Linear Equations and Slope: http://www.mathwarehouse.com/algebra/linear equation/slope-intercept-form.php http://www.math.com/school/subiect2/lessons/s2u4l3gl.html Quadratic functions. parabolas, vertex, axis of symmetry: Solve by factoring - http://www.algebrahelp.com/lessons/equations/solvebyfactoringl http://www.mathwarehouse.com/guadratic/solve-guadratic-eguation-by-factoring.php Graphing Parabolas, find the vertex, axis of symmetry: http://www.mc.maricopa.edu/-pikeu/mat122/notes/graph guads/not vertex form/graph quads n ot vertex form.html http://www.purplemath.com/modules/grphguad.htm http://hotmath.com/hotmathhelp/algebral/axis of symmetry of a parabola.html Special Right Triangles: http://www.regentsprep.org/regents/math/rtritrig/ltri30.htm http://www.onlinemathlearning.com/special-right-triangles.html Exponent Rules, Rational Exponents and Radical Notation: http://www.purplemath.com/modules/exponent.htm http://www.mathwords.com/e/exponentrules.htm http://www.themathpage.com/alg/rational-exponents.htm Trigonometry: http://www.gradebook.org/trigonometryto20class.htm http://www.findingdulcinea.com/guides/education/high-school-trigonometry.pgo.html#o http://math.about.com/od/trigonometry/trigonometrytutorials Resources.htm http://www.homeschoolmath.net/online/trigonometry.php
Academic Summer Calculus Packet Name _ Date _ Please complete and turn in on the first day of class. Show all work to receive full credit. You will need a graphing calculator to complete portions of this packet. 1. If f(x) = x 3-2x, find f( -2). 1. 2. If f(x) = _2x2 + 6, find the value of i!-3). 2. 3. Solve for x: 42.,.+1 = 82.,. 3. 4. If log, X = 3, what is the value of x? 4. 5. If log, 5 =!, find the value of x. 5. 6. Find the value of x: log3(x - 2) = 2 6. 7..... 2x + 3 For which value of x ISthe function f(x) = --2- undefined? x 7. 8. 2X2 + 3x + I For which value of :r is the function g(x) = undefined? x-i 8.
Page 2 9. Which of the following could be the graph of f(x) = Y - 5? 9. a) b) y c) Y 9 6..1-' 3 6-3 3 6 a: -6-3 6..1-' -6-3 3-3 -6-3 d) y e) Y 9-6 3 3 6 :1.; 6-3 3 6 a: -3 6 10. Which of the following is an approximate zero of y = 10x 3-9x + 4? 10. a) -1.4597 b) -l.2201 c) -l.1211 d) -0.5280 e) l.3265 11. Which of the following is an approximate root of y = 12x 5 + 15x 4-8x 3? 11. a) -0.3791 b) -0.1020 c) 0.2253 d) 0.4032 e) 0.6238 12. What is the slope of the line which contains (-3,2) and (6,7)'7 12. 13. What is the slope and y-intercept for the line y = ~x + 5? 13. 14. Find the slope and y-intercept for the line 6y + 2x = 9. 14. 15. What is the slope of all lines parallel to 2y - 3x = 5? 15. 16. What is the slope of all lines perpendicular to 4y + 9x = 6? 16.
Page 3 Write the equation of the line in slope/intercept form. 17. slope = -4, y-intercept = 6 17. Write the equation of the line in standard form. 18. passes through (6,5) and (3, -1) 18. 19. The given graph has what slope? 19. a) m -1 b) Tn = 3 c) m d) m -3 e) Tn. = 1-3 1 3 y 20. Which of the following lines has a positive slope? 20. a) / ""43...;......;--(;.....,....,.. b) ;'l;'}j,,......~...~. ~.ft11 ' ' ' ' ' 1 ''61 ; ;,, ; 1.. ;~I ;,'. ; ; I...;...,...,.... ;,I,, '.x,,,1 J:) -s -s ~ ""!I ~I -+e ~ i9 "'J) ~ ~ ~ ~ :.....;...~......?~... "':43 l...~...~...:...~...~.. c) -~~ ~ ~~I : :. 1......~. "';-2....... "+43...;........;--(; ~I -e -+;3 '!I ~,"'....~.... ;.. +............. ;.. d) ':'l;~li,, "':H... +~I ; ;, ; ; I,~I ;,. ; ; I e) none of these -!I ~I"'~ -+;3 ":4 ~ "~"1...............~ ;002......,.., "+43....;.....;...;--(;.
Page 4 21. Which of the following lines has a negative slope? 21. a)..,...,.,,,, ;"ll ',,,,. b)... ~...,;... : ~... ':-+2 Jj -::I ;3 ~-:I...,...,...,...,.,-'I ;: ' :~ ;:, 1. ;-3,.....:- 1 ',,...i.. 1 :t~..:, Jj --; -;3 -)1 -:1 -tfi...,...,,..,,-, ~'...., ' ;-21.. ;.. '.. ;.. ; ',.,.. 1 :+- 1.. ;..,..-:.. ;,.. 1 ; ;~II.. ;...;..,.. ;,.. I ' ;-61.. ;..,.. -!..,.. ~, ~-~ -q "';J...~..:...:..., '!l'1' l'..~...~....,.~..;.,... ;"2..,.....~... +..:-......;...,....,!'.,,...;-6.i ~........~-..; ; ~.. l d) e) none of these ~.~7Yf 7 ~l ~~ +).l~4 -tfi............... 22. Kristina is scaling one of the cliffs in Yosemite National Park. At 11:00 am, she had 22. climbed 120 feet. By 3:00 prn, she had reached an altitude of 300 feet. Find the average rate of change in Kristina's altitude during the four hours. a) -45 ft/hr b) - ft/hr c) ~ ft/hr d) 45ft/hI' e) 90ft/hr 23. An air conditioner is switched on at 1:00 pm. By 3:30 pm, the room temperature had 23. dropped from 82 F to 72 F. Find the average rate of change in the temperature of this room over this period. a) -5 F O /hr e) 5 F O /hr 24. On January 1, Andrew had a balance of $2,280 in a savings account. On April 30, he 24. had a balance of $2,900. What is the average rate of change in the balance? a) 6~O dollars per month c) - 3~O dollars per month b) 3~O dollars per month d) - 6~O dollars per month 25. On June 1, Bonnie's car had 23,825 miles. On September 1, her car had 24,385 miles. 25. What is the average rate of change? a) 2~O miles per month c) - 5~O miles per month b) - 2~O miles per month d) 5~O miles per month
Page 5 Graph. 26. y=-tx+1 27. y = ~x - 1 2. f(x) = x 3-2
Page 6 29. g(x) = x 3-4x 29. L 30. y = _x 2-3, 31. y = -3x 2-3 t- ~
Page 7 3 32. g(x) = - x 3 33. g(x) = - x 34. In a certain 30 _60 _90 triangle, the sides are in the ratio 1, 2.. a) 1 b) Vi c) J3 d) 2 e) 3 35. In a certain 45 _45 _90 triangle, the sides are in the ratio 2, 2,. 35. a) 1 b) 2 c) Vi e) 4
Page 8 36. Find the value of x. a) 1 b) V3 c) 3 d) 3v2 e) 18 36. 3 x 37. Solve for x. a) 1 b) v2 c) V3 d) 2 e) 3 37. :1: y 38. Find the exact value of y. 38. a) v2 b) J6 c) 3 d) 2V3 e) 3v2 6 y 39. Solve for a. 39. a) 3 b) 3v2 c) 3V3 d) 6v2 e) 6V3 40. Determine the value of x in the diagram. a) 7v2 b) 7V3 7v2 c) 3 7v2 d) 2 7V3 e) 3 40. X 7
Page 9 Simplify. 41. For problems 36-52 Simplify - No decimals!'!!i08 41. 42. -Ji44 42. 43. J9y16 43. 44. 2J1452 44. -5JU7 45. 9 45. 46. JPll 46. 47. 48. J(2a + 3b)2 48. 49. JU. JU 49. 50. (-2J7)(3J35) 50. 51. 52. fo M 52. 53. J3T li. J48T 7 53.
Page 10 54. 54. 55. 55. 56. 56. 57. 5n v'15n 57. Rewrite using exponents. 58. J7 58. 59. -Y4 59. 60. \Y83 60. 61. v? 61. Rewrite without any exponents. :1 62. a'i 62. :1 63. y4 63. 64. (2m-k)2 1 64.
Page 11 Simplify. 65. 65. 66. 66. Solve. 67. Vk= 4 67. 68. 2vn-10=0 68. 69. 13 = 3 + 15m 69. 70. 3 (hint: rationalize) Express --- as a fraction with a rational denominator. 3 - v's 70. 71. 4 Express 3 + j2 as an equivalent fraction with a rational denominator. 71. 72. (hint: factor first) Perform the indicated operation and express in simplest form: 72. x 2 - x 6-3- x2-1
Page 12 Solve. 73. }-900 73. 74. }-20 74. 75. -}-48 75. 76. (2 + 3i) + (4 + 2i) 76. 77. (15 + 9i) - (8 + 6i) 77. 78. (2i)(3i) 78. 79. 2i(4 + 7i) 79. 80. 7 + i 80. 81. 3 + 2i 81. 82. -2 3 + 2i 82. 83. -4-5 + i 83.
Page 13 84. Find sin LA. 84. A 85. Find cos LA. 85. 6. Find tan LA. 86. Simplify. 7. sin e. esc e 87.. tan e cos e 88. 89. cote sine 89. 90. sin 2 e + cos 2 e 90. 91. 92. 1 + cot 2 e 92.
COMPLETE the KEY TRIGONOMETRIC RATIOS IN THE FIRST QUADRANT FOR THE SPECIAL ANGLES o and 30 HAS BEEN COMPLETED FOR YOU.9.9 (Degrees) (Radians) x r r x Sin.9=Y Cos=.9 - Tan.9=Yor Csc.9 =- or Sec.9 =- or Cot.9=- or r r x Y x Y sin.9 1 1 -- 1 - - - cos.9 SIn cos tan 0 0 0 1 0 undefined 1 undefined 30 7r 1 fj fj 2 2fj fj - - - - - 6 2 2 3 3 45 60 90 1 r Cosecant (esc) = -.- or SIn.9 Y 1 r Secant (sec) = -- or - cos.9 x x Cotangent (cot) = or - tan gent S Y
Sketch the Trig Function Graphs (Use the values from your unit circle or trig table to help) y = sinx 1, 1,,_- ' 1, ' _ -n - 2 3n a - - 2n 2 2-1 _ y = cosx 1 1,,_- ' ' _ -n 3n - a - - 2n 2 2 2-1, _ y = tanx (Draw vertical lines where it is undefined) 2 _ 1, _ -n 3n - a - - 2 2 2 2n -1, _ -2, _
Fill in The Unit Circle Positive: Negative: o (-,-) Positive: Negative: (-,-) - o _0 _ (_,_) o (-,-) - (-,-) (-,-) o Positive: Negative: (-,-) Positive: Negative: