Seven Hills Summer 2017 Math Packet for Rising 7 th Graders

Transcription

1 Seven Hills Summer 2017 Math Packet for Rising 7 th Graders How well does your child know his or her math facts (addition, subtraction, multiplication, and division of whole numbers from 0-12)? Being able to retrieve these quickly and from memory is key to your child s success in middle school math and beyond. This is the most important math preparation your child can do this summer. In addition, the Middle School Mathematics Department is asking your child to work on the attached summer math review packet. This packet reviews key concepts that your child has already learned. Teachers will collect the packets on the first day of school. In working on this packet, students should display their work neatly in the space provided. All computations should be done without a calculator. A ruler will be needed for some problems. Answers to review problems are attached. Here are some helpful websites you may find useful if your child gets stuck on the summer packet or would like to do some additional work online. Please have your child check out at least two of these and list these at the end of this packet. (The 7 th and 8 th Grade sections will be most helpful.) (try the hardest level) ( basketball game that reviews onestep equations) (integer games) (integer games) (problem solving) Enjoy your summer. We look forward to working with your child in the fall! 1

2 Seven Hills Summer 2016 Mathematics Packet for Rising 7 th Graders Directions. Please show all work in the space provided. No calculator unless otherwise indicated! Use order of operations to determine each answer. 1) = 2) 8(3 + 4) 2 * 8 (5 3) = 3) (13 3) 2 5 = Insert parentheses to make the following equation true. 4) = 1 Determine the answer for each problem. 5) 94 ( 87) = 6) = 7) = 8) (-801) = 2

3 9) -10 (-2 18) = 10) - ( ) = 11) = 12) -183/-61= 13) = Simplify. 14) -2(x + 3) = 15) 3(2x 3) + (x 5) = 3

4 2 16) (3x + 9) = 3 Write in simplest form. 17) = 2 18) = 19) = 20) = 1 21) = 4

5 22) = 23) = Write as a decimal ) 25) 26) Write as a percent. 4 27) 28) ) Write as a decimal. 30) 51% = 31) 102% = 32) 0.75% = Write as a simple fraction or mixed number in lowest terms. 33) 125% = 34) 3% = 35) 50% = 5

6 Write as a percent AND as a simple fraction or mixed number. 36) 0.25 = = 37) 1.2 = = 38) = = Solve each equation below and check your answers. 39) x + 22 = ) 184 x = 51 41) x 6 = ) 30x = ) 4y 8 = 20 44) 17 = x 3 45) x 24 =

7 For each of the following, write an algebraic equation. Then solve each equation. 46) Eight times a number, increased by 6, is 62. What is the number? 47) Number C divided by 0.4 is 10. What is C? 48) One half of a number is equal to 14. What is the number? For each of the following, write an equation or set up a proportion. Then solve these percent problems. Calculators allowed here. 49) What number is 15% of 60? 50) 66 is 11% of what number? 51) 308 is what percent of 350? 7

8 52) A $150 leather jacket is going on sale for a 25% discount. How much will the jacket cost on sale? 53) Jim bought 3 CDs at a cost of $14.99 each. What will he pay including 7% sales tax? Evaluate each expression given that a) x = 4 and b) x = -3 54) 2x a) b) x 2 55) a) b) 56) x + 6 a) b) 57) 5x 3 a) b) 8

9 Basic Geometry and Using Formulas. 58) Find the perimeter of the following rectangle. 59) Find the area of the rectangle in the previous question. 60) Find the perimeter of the following right triangle. 61) Find the area of the triangle above. 9

10 62) Find the circumference to the nearest tenth. Use π ) Find the area of a circle with diameter 5 cm. Round answer to the nearest tenth. Calculator allowed. Simplify. 64) 4(x + 3) = 65) -2(3x 5) = 66) 2(3b + 1) 5 = 67) 2(x + 3) 5(2x + 1) = 10

11 Plot each of the following points on the grid below. Use the letter to label the point on the graph. 68) A(3,0) B(5,5) C(-1,2) D(-3,-2) E(0,-3) 69) The perimeter of the figure below is equal to 150 cm. What is the length of the missing side? 11

12 70) Taylor is participating in a new fitness program in which he is required to report his weight at the end of each week. The table below shows some of his results. a) Graph the data from the table on the grid provided. Use a straight edge to sketch the trend. Put number of weeks along the x-axis, weight along the y-axis. 12

13 b) Explain the mathematical relationship between the number of weeks in the fitness program and the weight in pounds. c) Using information from the graph and table, predict Taylor s starting weight and weight after 25 weeks in the fitness program. 2 math websites I tried this summer: 1) 2) 13

14 Answer Key 1) 72 2) 48 3) 84 4) (8 + 12) (4 5) = 1 5) 181 6) ) -71 8) 24 9) ) -1 11) ) 3 13) ) -2x-6 15) 7x-14 16) 2x+6 17) 9 3/5 18) 2 1/8 19) 6 2/3 20) 6 7/12 21) 1/4 22) -2/9 23) -1/2 24) ) ) ) 80% 28) 140% 29) 66 2/3% 30) ) ) ) 1 1/4 34) 3/100 35) 1/2 36) 25%=1/4 37) 120% = 6/5 or 1 1/5 38) 12.5% = 1/8 39) x= ) x=133 41) x=48 42) x=16 43) y=7 44) x=51 45) x=10 46) 8n+6=62; n=7 47) C/0.4=10; C=4 48) ½ n = 14; n=28 49) 9 50) ) 88% 52) $ ) $ ) a) 8; b) -6 55) a) 16; b) 9 56) a) 10; b) 3 57) a) 17; b) ) 110 cm 59) 726 sq cm 60) 12 cm 61) 6 sq cm 62) 18.8 in 63) 19.6 sq cm 64) 4x+12 65) -6x+10 66) 6b-3 67) -8x+1 68) graph 69) x=27 cm 70) graph; As the weeks increase, Tyler s weight decreases. Tyler s weight was approximately 185 pounds at the start of the fitness program. After 25 weeks Tyler would weigh approximately 135 pounds if the relationship between number of weeks in the fitness program and weight continued. Adapted from Timberlake Middle School summer review math packet. 14