Rising Pre-Calculus student Summer Packet for 016 (school year 016-17) Dear Advanced Algebra: Pre-Calculus student: To be successful in Advanced Algebra: Pre-Calculus, you must be proficient at solving and simplifying each type of problem in this packet. This is a review of Algebra. Upon returning to school in the fall, you are epected to have completed this assignment. We will correct and review during the first week of class, and then you will have an assessment on this content during the second week of school. Please make sure to show all work for each problem to receive full credit. Calculators are NOT ALLOWED on this assignment. Furthermore, you are epected to be able to complete without a calculator on assessment. TI-84 calculators will be utilized for some units during the school year and it is highly recommended that you have one available for use at home. Pre-Calculus is a faster paced course with many units that is designed for students preparing for the AP Calculus course or preparing for college mathematics. It is important that you maintain all pre-requisite skills. We will not have time to spend re-teaching the content in this packet. Make sure you are comfortable with this material without the use of a calculator. Lots of space has been provided for you. Place final answer on line provided and include documentation in space provided. Enjoy your summer and good luck! Full Name Remember, lots of space, thus lots of pages!
Solve the equation. 5 1 4 1. 1.. 1 6 5 14 15. Solve the inequality. Use interval notation for solution set. Then graph your solution on a number line.. 7 8. 4. 6 11 4. 5. 4 8 1 00 5.
6. 6 4 or 5 8 6. 7. 4a 7 1 7. Graph the following. Show all important details: f 8. 9. f 10. 1 1 f 11. f
1. f 1 4 1. f() = ( ) Graph the following. Make sure you put all asymptotes, holes, intercepts on the graph provided. Go beyond a sketch! Guidelines for Graphing Rational Functions 1. Removable Discontinuity (hole in the graph) Occurs when p() and q() have a common factor. Non-removable Discontinuity (Vertical Asymptote) (VA) Occurs when the denominator equals zero. Horizontal Asymptote (HA) The value that the function approaches as increases without bound a.) If the degree of the numerator < the degree of the denominator y = 0 is the horizontal asymptote b.) If the degree of the numerator = the degree of the denominator; y = lead coefficient of the numerator lead coefficient of the denominator is the HA c.) If the degree of the numerator > the degree of the denominator There are NO horizontal asymptotes. 4. X-Intercepts zero(s) of the numerator 5. y-intercept the value of f(0) 6. Slant Asymptote: Occurs when the degree of the numerator is eactly one more than the degree of the denominator. Eample: f() = +1 14. 5 1 f ( ) 15. 16 f ( ) 4
16. ( ) f 17. f() = 1 4 Determine the quotient by long division: 18. ( + 8 6) ( 1) 18. 19. ( 16 + 49) ( 8) 19. Graph: 0. f() = 9
1. Evaluate and graph the function for the given value of., if 1 f 4, if 1 f = f 1 = f 0 =. Graph the function. f 1 5, 5 4, if if Factor the trinomial. (Be sure to factor completely!). 11 4. 4. 9a 56a 1 4. 5. 4 0 5.
Use square roots or factoring to solve each equation. 6. 10 1 6. 7. 8y 5y y 4 7. 8. 1 7 0 8. n 0 17n 10n 9. 9. 0. 4 0 0.
1. 1 4 1. Solve the equation by completing the square. (You will be using this in class!) STEPS TO COMPLETING THE SQUARE: 1) Take an equation in standard form: + b + c ) Rewrite as: + b = c ) Add ( b ) to both sides + b + ( b ) = c + ( b ) 4) The left side is now a perfect square trinomial ( + b ) = c + ( b ) 5) Now you can take the square root of both sides and solve for. (remember two roots + and -). 4 8 0.. 10 1. 4. 5 7 4.
Use the quadratic formula to solve the equation. (Must use quadratic formula!) 5. 8 0 5. 6. 4 6. Find the product of the polynomials. 7. 4 1 7. 8. 1 5 8. 9. This is a number cubed with a plus sign between! It does not = + 9.
Factoring is an essential skill that you will need to master without the use of a calculator. Factor the polynomials completely. 40. 56 5 81 40. 41. 7 41. 5 4. 6 45 4. 4. 5 8 40 4. 44. 18 5 45 44. Solve the equation. Check for etraneous solutions. (No calculator!) 45. 5 1 4 45.
46. 7 46. / 47. 16 47. 48. 4 48. Perform the indicated operation. Simplify the result completely. 5 0 y 49. 49. y 10 7 14 5 10 50. 5 50. 51. 0 4 15 51.
5. 4 6 1 8 5. 5. 16 4 4 16 4 m m m m m 5. 54. 5 4 1 54. Solve each equation. 55. 1 1 55. 56. 6 9 56.
57. 4 57. Find the value of each variable. Write your answers in simplest radical form. Do not change any of the values to decimals. EXACT means leave it in a radical. 58. 59. 60. 61. 6. 6.
64. Rationalize the denominator. f() = 7 + 64. 65. Use the functions f() = and g() = 1 + 1 a) f() + g() b) f() g() c) g(f()) a) b) c) 66. Find the domain of the following and use interval notation: a) f ( ) b) f( ) 5 c) f( ) 5 a) b) c) 6 d) f( ) 5 e) g ( ) 8 f) 15 h ( ) 6 d) e) f)
67. Give intervals for which f() is: Increasing Decreasing Constant (all in interval notation) 68. Give intervals for which f() is Increasing Decreasing Constant (all in interval notation) 69. f ( ), g( ), and h( ) ; Find the indicated value. a) f h 5 69a. b gb g b) bg f gb g 69b. c) h() g() 69c. d) hb g = 69d. e) g( ) R S T 1 1,. Find g() 69e.,
70. Perimeter The altitude of an equilateral triangle is 1 centimeters. Find the perimeter of the triangle. Round to the nearest tenth. 71. Area The diagonal of a square is 1 inches. Find the area. Round to the nearest tenth. 7. Bleachers A fan at a sporting event is sitting at point A in the bleachers. The bleacher seating has an angle of elevation of 0 and a base length of 90 feet. Round to the nearest tenth. 7. Canyon A symmetrical canyon is 4850 feet deep. A river runs through the canyon at its deepest point. The angle of depression from each side of the canyon to the river is 60. Round to the nearest tenth. 0 0 60 4850 ft a) Find the height CD of the bleachers. b) Find the height of the fan sitting at point A from the ground. c) Find the distance AB that the fan is sitting from the base, point B. a) Find the distance across the canyon. b) Find the length of the canyon wall from the edge to the river. c) Is it more or less than a mile across the canyon? (580 feet = 1 mile)