017 018 Summer Math Program Course: Honors Pre-Calculus NAME: DIRECTIONS: Show all work in the packet. Make sure you are aware of the calculator policy for this course. No matter when you have math, this packet is due on the first day of your math class. This material will be graded, and points awarded at the discretion of each teacher A test on this material will be administered during the first week of the class. An additional resource for help with this packet is http://www.khanacademy.org. It provides videos of about 10 minutes in length on hundreds of different math topics. Math Teachers will be available in C-1 the following dates/times if you need help. Date Time Wednesday, July 6 th 8-9:30am Monday, July 31 st t 8-9:30am Tuesday, August 1 st 8-9:30am
Simplify using the order of operations: 9 8 8 1. 156 3 5 8.. 3. 3 5 10 ( 3 ) Evaluate the following algebraic expressions: 4. (x y ) (x 3 + y ) for x = -3 and y = 5. x xy + 5; when x = 4 and y = 3 Simplify the following expressions: 6. /3(6x + 9y 1 ) + 4 (x y + 7 ) 7. 6(x + ) 4(4 x ) Solve the following equations. 8. 6x (x 4 ) = (x + 5 ) + (x + 3 ) 9. 5 + 3 (x 4 ) = 7x (4x 1 ) Solve for the indicated variable: 10. Solve for y 11. Solve for y 1 x 3 4 y 3 3x5y 10
Solve and graph the following inequalities. 1. -3x 1 or 5(x ) + 3 > 3x + 5 13. 6 x 1 17 3 Use a table of values to graph the following linear equations: 14. x 3y = 6 15. x y = 5 Use the x- and y- intercepts to graph the following linear equations: 16. -5x + 6y = 30 17. x y = 6 Use any method to graph the following: 18. a line through (5, -3) which has a slope of -4/5 19. x + 3y = -9 Graph the following linear inequalities: 0. 3x y 8 1. x
Write the equation of the line in slope-intercept form:. With a slope of /3 and y-intercept of 5 3. That passes through (-5, 4) and (, -3) Write the equation of the line in standard form: 4. that has a slope of -3 and passes through (5, -7) 5. that passes through (-, 3) and (7, 10) 6. The horizontal line through (6, -3) 7. The vertical line through (5, -4) 8. The line parallel to y = 4x 6 through (-1, -) 9. The line perpendicular to x y = 3 through (4, 7) Solve the following systems of equations by substitution. 30. 3 x y 16 x3y 10 31. 7 x y 0 x y 1
Solve the following systems of equations by the linear combination method (also called the addition method or the elimination method). x3y 11 3. 33. 4 x 5 y 0 x y 13 8x 5y 60 Simplify using the Laws of Exponents: 34. (x y)(-3x 4 y 3 ) 35. (-5xy z 4 )(-x 5 y 7 z )(3x yz 3 ) 36. 5 4 3 3 ( ) 37. 4 5 3 3x y 8x y 3 xy 9xy Simplify using the Laws of Exponents. Do not leave negative or zero exponents. 1 6x y z 38. 39. ( -4x - y 3 ) - 4 5 3x y z
Simplify. 40. 56 41. 4 50 4. 48 6 43. 8 9 44. 6 3 45. 5 5 46. 4 96 6 47. 10 Simplify. 48. (x 3x + 5) + (x 7x 9 ) 49. (x 5x + 9) (x + 3x + 1 ) 50. 3x (4x 7x ) 51. 3x y ( 4x + 5xy 3y ) 5. (x + )(x ) 53. (3x + 5y)(3x 5y) 54. (y + 3) 55. (x 7 )
Solve and graph each inequality. 56. x + 3 > 8 57. x + 5 6 Solve the equation. 58. x 1 +3 = 4 Factor out the greatest common factor. 59. 3x + 6x 60. 9x 4-18x 3 + 7x Factor each polynomial completely. 61. x + 5x + 6 6. 36x 49 Solve each quadratic equation. You may use any method, but the most appropriate is written next to the problem. 63. x 13x + 36 = 0 (factoring) 64. 3(x 4) = 7 (square root) 65. 3x 3x 4 = 0 (quadratic) 66. Solve the radical equation: 6x1 x 1
Perform the indicated operation and simplify if possible. 67. x x6 3x9 x4 68. x x x x x 4x 5 5 10 5 68. 3 6 x4 x5 69. 4 3 x x 3 Determine whether the following functions are even, odd, or neither. 70. f(x) = x 5 x 71. f(x) = x 6-8x + 4 1 Given f( x) and g( x) x 5, find the following: x 5 7. f( g (7)) 73. ggx ( ( )) Find all intercepts and asymptotes of the following: x 3x x 4 74. y 75. y (3x 1) x x1 3x 1 76. y x x6
If h( x) 1x and k( x) 1 x, find the following: 77. kh ( (1)) 78. k( h( a )) If 79. f x ( ) x 3 f 1 ( x), find the following: Quick Graphs: Graph each of the following functions on graph paper without a calculator. If you do not remember, use your graphing calculator to help you determine patterns. But you need to be able to graph these functions without your calculator. 80. y x 3 81. y ( x3) 8. y x 1
Solve the following exponential and logarithmic equations: 83. 5 65 84. 5 85. e 5.7 15 x x 1 x 86. log ( x ) 87. ln x 3 1 88. log(5x+1) = log(x+3) + log 7 Evaluate the following expressions without using a calculator. 1 3 89. log3 90. log33 91. 3 7 log 19 Use properties of logarithms to expand the logarithmic expression as much as possible. 9. 3 x log 3( ) 8 y Use properties of logarithms to condense the logarithmic expression as much as possible. 93. 5log m log b b n