Math Department Math Summer Packet: Incoming 8 th -Graders, 2018-2019 Student Name: Period: Math Teacher: Important: You must show your work on a separate sheet of paper. Remember: It is important to arrive at the correct answer. Ratios, Proportions, and Proportional Relationships Write ratios for each question in fraction form. 1. There are 2 red balls and 5 green balls. Write the ratio of red to green balls. 2. There are two brown pots. The first contains 10 stones and the second 11 stones. Write the ratio of number of stones in first to the second pot. 3. A computer has two drives. The first hard drive contains 20 folders and the second has 7 folders. Write the ratio of folders in the first to the second drive. 4. In city 1, there are 3 radio stations and in city 2 there are 4. Write the ratio of the number of stations in the first to the second city. Proportion World Problems 5. A map scale designates 1 = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive to go from the first town to the second. 6. Bob is taking his son to look at colleges. The first college they plan to visit is 150 miles from their home. In the first hour, they drive at a rate of 60 mph. If they want to reach their destination in 2 ½ hours, what speed must they average for the remainder of their trip? 7. An 8-ounce glass of Orange juice contains 72 milligrams of vitamin C. How much juice contains 36 milligrams of vitamin C?
8. These two figures are similar. Use a proportion to find the length of side n. n 20 m 12 m 30 m Proportional Relationships 9. Daisy made an envelope from sheets of paper. The table below shows the number of envelopes made by the number of sheets. Do the numbers in the table represent a proportional relationship? Number of envelopes Number of sheets 1 2 2 4 3 6 4 12 10. Fred wrote notes during an examination. The table below shows number of pages written in relation to the time it took to make the notes (in hours). Does the table represent a proportional relationship? Notes (pages) Time (In Hours) 8 16 9 18 10 20 11 23
Percent Problems Solve each problem. Round to the nearest tenth or tenth of a percent. 11) What percent of 29 is 3? 12) 41% of 78 is what? 13) 58% of what is 63.4? 14) 140 ft is 97% of what? 15) What is 170% of 97 tons? Percent Word Problems 16. A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number) 17. There are 36 carpenters in a crew. On a certain day, 29 were present. What percent showed up for work (round to the nearest tenth)? Expressions and Equations Write the verbal phrase or sentence as a variable expression or equation. Let n represent the number. 18. The quotient of a number plus 6 and 3 19. 8 multiplied by the difference of 9 and a number 20. 1/ 3 of a number is equal to 8 plus the number. 21. The product of 3 and a number is twice the sum of the number and 5. Critical Thinking Question: ****Is three less than a number equivalent to the difference of three and a number? Explain your reasoning.
Properties of Real Numbers In Exercises (22 30), use the property of real numbers to fill in the missing part of the statement. 22. Associative Property of Multiplication 3 (6 y) = 23. Commutative Property of Addition 10 + (- 6) = 24. Commutative Property of Multiplication 15 (- 3) = 25. Associative Property of Addition 6 + (5 y) = 26. Distributive Property
(6 + z) 5 = 27. Commutative Property of Addition 25 + (- x) = 28. Additive Inverse Property 13 x 13 x = 29. Multiplicative Identity Property (x + 8) 1 = 30. Additive Identity Property 8 x + 0 = Solve each equation using addition and subtraction. Check your answer. 31. 27 + n = 9 32. -5 + a = 21 33. 67 = w 65 34. y 19 = 37 35. 4 = q + 13 36. 5.5 = -2 + d 37. 23 = b 1 38. 2.5 = p + 7 39. f + 9 = 20 40. c + 4 = - 9 41. g 3.5 = 10 42. j 3 = - 7 43. Which of the following best describes the solution of the inequality 1 < x + 3 < 6? A. x is greater than 2 and less than 3. B. x is greater than 2 and less than - 3. C. x is greater than - 2 and less than 3. D. x is greater than - 2 and less than - 3. 44. Identify the graph that represents x > 5 or x -2
A. Graph 3 B. Graph 1 C. Graph 2 D. Graph 4 Geometric Shapes 45. The area of a figure is 64 square centimeters. Suppose the sides of the figure are doubled. What will be the new area of the similar figure? A. 16 square centimeters B. 32 square centimeters C. 128 square centimeters D. 256 square centimeters
46. Suppose the dimensions of a rectangular prism are enlarged by a factor of 3. By what scale factor will the volume of the prism be scaled? A. 1/3 B. 3 C. 9 D. 27
47. A cone has a height of 24 inches, a slant height of 25 inches, and a diameter of 14 inches. What is the surface area of the cone? A. 1,176π in2 B. 392π in 2 C. 224π in 2 D. 178π in 2 48. What is the approximate surface area of a cylinder with a height of 12 meters and a base radius of 2 meters? Use 3.14 for π. Round to the nearest tenth, if necessary. A. 242.1 squared meters B. 175.8 squared meters C.150.7 squared meters D. 124.5 squared meters
49. The square pyramid has base side lengths of 12 centimeters and a slant height of 15 centimeters. What is the total surface area of the pyramid?
A. 720 in 2 B. 640 in 2 C. 504 in 2 D. 360 in 2 Note: None of the figures above are made to scale. The Pythagorean Theorem 50. COMPUTERS In a computer catalog, a computer monitor is said to be 19 inches. This distance is the diagonal distance across the screen. If the screen is 10 inches high, what is the width of the screen? Round to the nearest tenth. Note: Make a sketch of the situation, and remember to show you work. SUMMER! HAVE A GREAT