016 017 Summer Math Program Course: NAME: DIRECTIONS: Show all work in the packet. You may not use a calculator. No matter when you have math, this packet is due on the first day of 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 7 th 8-9:0am Monday, August 1 st 8-9:0am Tuesday, August nd 8-9:0am
Name SUMMER MATH PACKET Students entering in Fall or Spring Directions: Use a pencil and SHOW ALL work!! Calculators are permitted only on the sections that are marked. This will be turned in on your first day of math class. ORDER OF OPERATIONS: 1. Do operations that occur within grouping symbols (parentheses, brackets, absolute value bars, radicals).. Evaluate powers if there are any.. Then do multiplications and divisions as you see them, in order, from left to right. 4. Finally, do additions and subtractions as you see them, in order, from left to right. EXAMPLES: 16 + 4 Since there are no grouping symbols or exponents, do the division first 16 + From left to right, do the addition next 18 15 ( ) ( ) 10 6 7 4 + + 1 Since there are grouping symbols, do inside them first. ( ) [ ] ( ) ( ) ( ) 10 6 + + 1 Next do the powers 10 6 9 + + 1 Now do inside the brackets 10 6 1 + 1 Time to multiply 10 7 + From left to right, do the subtraction 6 + 60 Simplify each expression. (This will require order of operations) 1. + 8 6. 8 + 6. 5 + (1 ) 4. 0 4 + ( + ) 5. (1 7) 6 6. 8 8+ 6
EVALUATING VARIABLE EXPRESSIONS: 1. Substitute values for the variables.. Simplify using the order of operations. EXAMPLES: x + 5x 4; x= x + xy y ; x=, y= = ( ) + 5( ) 4 = ( ) + ( )( ) ( ) = (4) 10 4 = 4 ( ) 18 ( 7) = 1 10 4 = 8 18 + 7 = 4 = 10 + 7 = 6 = 17 Evaluate when x =, y =1, and z= 7. 1 ( ) z y 8. x 8x+ 1 9. y z+ y Write the mixed number as an improper fraction. Write each fraction as a mixed number. 10. 7 9 11. 4 9 Evaluate. Express answer in simplest form. 1. + 4 1. + 14. + 1 + 5 9 9 5 4 6 15. 1 + 8 16. 10 5 1 1 1 17. 5 1 9 9 4
18. 4 g 0 19. 5 g 0. 9 8 1 6 g 1 7 1. 8 6. 9 6 5 1. 5 7 1 10 4. 9.18 + 6.45 5. 0.9 + 15.67 6..8 + 1.45 + 7.08 7. 8..58 Evaluate. Express fractional answers in simplest form. 8.. 7.4 9. (.)( 7.16) 0.. 8 1. 480.006. 48 1. 1 4
Evaluate. 4. 1 18 5. ( 17) 1 6. ( 8) ( 6) 7. ( 14) + ( ) 8. ( 7) + 11 9. 9 + ( 5) Write each percent as a decimal. 40. 54% 41. % 4. 50% Write each percent as fraction in simplest form. 4. 64% 44. 0% Write each fraction as a percent. 45. 10 46. 17 5 Solve. (You may use a calculator on these but you must show how you set the equations up!!) 47. What number is 5% of 186? 48. What number is 75% of 19? 49. What percent of 5 is 0? 50. 5% of what number is 6?
COMBINING LIKE TERMS: Like terms have the same variables and the same exponents. You can add and subtract like terms by combining the coefficients (the numbers in front) and leaving the variables and exponents the same. EXAMPLES: ( x+ y) x( y) 4 = x+ y 4x+ xy = x+ y+ xy ( a b) ( a b) + 4 = 6a 1b a+ b = 9a 10b ( ) ( ) 4x x 5 x 4 x = 4x 0x 8x+ x = 6x 8 x Simplify. Use the distributive property when necessary. 51. x+ 7 + 8x 1 5. 18a 1b+ a 15b 5. c d 10c+ 8d 54. a b 5a 7b 55. c d 9d 1c+ 5d 56. 4e+ 10f + 10e f 57. (8 5 g) + 6( + g) 58. (r v) 4( r 5 v) 59. (x 9) (x 1) 60. (a 4 b) + (4a 6 b) (9a b) 61. (x+ 5 d) 5(8c d)
SOLVING EQUATIONS: *Distribute and combine like terms as needed. *Get the variable by itself by moving across the equal sign, again always looking for like terms to combine. *If a variable drops out, look at the remaining part of the equation. If you are seeing a true statement, then the solution is all real numbers. If you see a false statement, then the solution is the empty set. EXAMPLES: ( ) 7 a 6= a+ 8+ a 7a 14 6= a+ 8+ a 7a 0= a+ 8 4a = 8 a = 7 Solve. ( Make sure you show work and not just an answer!) Leave answers as fractions, not decimals. 6. x 6 = 1 6. a + 18 = 64. c ( ) = 65. 7n = 56 66. 0 5 n = 67. 8 x = 68. 1 0 x = 69. 1x = 18 70. 1 x = 5 a n 1 71. n = 10 7. 4 = 8 7. = 4
74. m [4 ( m)] = 9 75. 5( p 6) = p 76. (5a ) a= (4a ) 77. 5( x) ( x 5) = 6x+ 5 78. 4 [( m ) ( m 9)] = ( m ) Write an equation for each sentence. Use n for the variable. (You do NOT have to solve) 79. Half of a number increased by six is 1. 80. Four less than three times a number is 9. 81. The quotient of a number and 6 is two-thirds of the number. 1 x < 10 x < x > 1
Solve and graph each inequality (on a number line) 8. x < 14 8. r 8 10 84 x 1 Using the graph paper below, graph the following points and label them. 85. A (,) 86. B( -, 1 ) 87. C(, 0) 88. D ( -, -) 89. E ( 0, ) 90. F ( 1, -) Express answer in simplified radical form. (NOT a decimal answer) 91. 6 9. 0 9. 108