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St. Michael’s Episcopal School Summer Math for rising 7th grade pre-algebra students 2016 Students entering pre-algebra should be proficient in working with integers, fractions and decimals and order of operations. To maintain skills through the summer, students are expected to complete the attached review problems, showing all work. The summer skills packet will be collected on the first day of school and graded. Students are also encouraged to use math throughout the summer. Suggested activities include: *Play games with other people. Board games such as Monopoly, checkers and chess require logic and/or math skills. Set, 24, Sudoku, and many card games require logic and strategy. *Worksheets, computer games, and word problems that require students to add, subtract, multiply, and divide without a calculator provide needed practice. Include operations with fractions and decimals. *Real life situations often require math. Measuring and adjusting recipes, figuring a checkbook, determining a trip’s costs and mileage are all opportunities to use math. Compare the costs of driving or flying for a vacation trip. Graph swim times or the price of gasoline each week. Determine tips, change and taxes on purchases. Summer Review 2016 Name: Attach notebook paper to show work. Number your problems. Simplify. 1. −6 + 10 15 + 12 ÷ 3 4. Express as a decimal. Show your work. 2. 3. 23 3 8 Round 538.9043 5. to the hundreds place __________ 6. to the hundredths place 7. to the nearest whole ______________ ______________ Evaluate the following expressions when 𝒋 = 𝟏𝟐 and 𝒌 = −𝟒. Watch signs. 8. 𝑗 ÷ 𝑘 10. 2𝑘 9. 11. 𝑗 − 𝑗𝑘 + 40 12. Estimate the product to the nearest whole. 4.12 × 6.8. 13. Write 7 200 as a percent. Use >, < , o r = to complete each of the following. 14. −28 ________ − 29 16. 42 ________ 24 Show work to justify your answer. 15. 0.36 _______ 𝑘 9 25 17. Express 0.375 as a fraction in lowest terms. 18. Name the parts of the circle below. SP ________________ RQ ___________________ Draw chord SQ.____________________ 19. The radius is 4½ cm. What is the diameter of the circle? ______cm What is the circumference? Use the formula, C = πd ________ 20. 21. What is the measure of ∠𝑎? What are the coordinates of the graphed point? 22. 4 − 23. 7 8 • 1 2 5 9 = 11 21 There are 12 cubes in a bag. Four are red, 3 are blue, 2 are orange, and 3 are yellow. Find the probability of drawing the following: 24. P( yellow) ____________________ 25. P (red or orange) ____________________ 26. To make 24 cookies, a recipe requires ¾ teaspoon of vanilla. How much vanilla is needed for a dozen cookies? 27. Write 6,230,000 in scientific notation. 28. Express the prime factorization of 72. 29. What is the total cost of an item priced at $12.75 if there is a 5% sales tax? Find the product and simplify if necessary. 30. 4 • 1 4 31. 8 • 3 3 4 32. 5 1 4 • 4 4 7 Find the quotient and simplify if necessary. 33. 4 ÷ 1 4 2 34. 8 ÷ 1 3 𝟑𝟓. 3 24 ÷ 1 2 36. What is 12% of 50? Show your work. 37. One centimeter on a map represents 50 miles. What is the actual distance between two cities that are 6.5 cm apart on the map? 38. Find the missing number. input output -5 20 8 -32 10 ³ = 39. -1 40. Circle the numbers that are factors of 492? Use the rules of divisibility. 2, 3, 4, 5, 6, 9, 10 41. What is the square root of 81? 42. Find the product of 4.12 × 6.8. Show your work. Go back and compare your answer to your estimate for #12. 43. To make green paint, a painter mixed yellow paint and blue paint in the ratio 3:2. If he used 12 gallons of yellow paint, how much blue paint did he use? 44. A sum of money was shared between Susan and Nancy in the ratio 2:5. Nancy received $36 more than Susan. How much money did Susan receive? You may use unit bars to solve the problem. 45. What fraction of 2 hours is 20 minutes? Simplify. 46. What fraction of one pound is12 ounces? Simplify. Write each fraction as a decimal. 47. 17 20 1 48. 2 5 1 1 49. Jane bought of a cake. She ate of it. She cut the remaining cake into 2 equal slices. What 2 4 fraction of the whole cake was each slice? 50. Divide. 70.76 ÷ 5.8 Show your work. 51. The Dark Ages ended in 1066. What is the Roman numeral for 1066? 52. Subtract 1066 from 2015. Show your work. 53. One kilometer = ______________meters. 54. One meter = ___________________centimeters. 55. 12 : 8 : 20 = 3 : ________: ________ 56. The product of two numbers is 48. The sum is 16. What are the numbers? 57. Find the perimeter of the rectangle below. Label your answer. ______________ 58. Find the area of the rectangle. Label your answer. _______________ 59. Find the perimeter of the square if one side is 8 inches in length. P = __________inches Find the area of the square. A = __________ in2 60. The stem-and-leaf plot below shows the ages of guests at a restaurant. Find the following: Mean _____ 61. 3 5 28 + 46 Median____ Mode __________ Express your answer as a mixed number in simplest form. Range __________ 62. 35% of what number is 80? 63. 45 is what percent of 60? 64. Find the sum of 0.15 + 2.46 + 3.7 65. Divide. 66. Express 8 as a decimal _______________and as a percent.______________ 67. Find the GCF of 12, 24, and 42. 4.404 ÷ 0.12 68. 7 Identify the figure. Be specific. ___________________ 69. What does regular mean in geometry? Draw a regular figure. 70. Express 71. Match: 5 16 ____ sum ____ quotient ____ product _____difference as a decimal. a. the answer to a subtraction problem b. the answer to a multiplication problem c. the answer to an addition problem d. the answer to a division problem 72. If a car is traveling at an average speed of 55m/hr. on a 330 mile trip, how long will the trip take? 73. Simplify. 74. Draw a figure with horizontal reflection. Draw the line of symmetry. 75. Draw a figure with rotational symmetry. 76. 8.52 · 0.15 77. What is the main difference between parallelograms and trapezoids? 78. Divide. 58.75 ÷ 4.7. 79. Use >, <, or =. 80. Multiply. 81. 7 14 5 8 + 14 42 8.098 _____ 8.1 · 9 10 · 2 3 John is packing his lunch. He needs a sandwich and fruit. How many different lunches can he prepare if he has the choice of cheese or peanut butter on white or whole wheat bread. His fruit selection includes grapes, an apple, or a banana. He can make ________________ different lunches. List the lunches or draw a tree diagram. 3 82. Change 57 to an improper fraction. 83. Change 84. 18 − 4 · 3 + 9 85. −7 + 18 86. −64 ÷ −16 87. −15 · 24 88. −12 · −3 89. A right isosceles triangle has angle measures of __________°, ___________°, and __________°. 90. Multiply 91. List the first twelve multiples of 7. 48 17 to a mixed number. 3.385 × 10 3.385 × 100 · −4 3.385 × 1000 0, _______ , _______, ______, ______, _______, ______, ______, ______, _____, _____, ______, ______ 2 3 = 𝑥 60 , then 𝑥 = _______ 92. If 93. Order the fractions from least to greatest. Make equivalent fractions with a common denominator. 7 11 2 3 20 33 94. Use >, <, or = to complete the statement. 116 ____________ 161 95. How many quarter pounders can Ronald McDonald make with 80 pounds of beef? 3 96. There are 125 students in the Middle School. If of them are girls, how many girls are in the 5 Middle School? _________ How many boys are in the Middle School? __________________ 97. 48 ounces = _________pounds. 98. Express 38 % as a decimal _____________ and as a fraction in lowest terms_______________. 99. List all of the factors of 24. 100. Find the sum. Simplify. 3 5 8 + 4 3 4 + 6 5 16