8 Grade & Equations Expressions - Miss Jarrell

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Grade8Expressions& EquationsWorksheetsBy: Math in the Midwest

Name:Date:Hour:Expressions & Equations – 8.EE.1Simplify1. π‘₯ 5 π‘₯ 22. 𝑦 3 𝑦 73. 𝑏 4 𝑏124. 𝑐 3 𝑐 5 𝑐 25. π‘Ž3 π‘Ž1 π‘Ž86. (𝑦 2 )47. (π‘š3 )58. (2π‘₯ 4 )29. (3𝑦 2 )310. (𝑏 7 )011. (𝑠 2 )6 𝑠 512. 𝑑 π‘₯ 𝑑 𝑦Find the missing exponent in each expression.13. π‘₯ π‘₯ 5 π‘₯ 714. 𝑏 𝑏 3 𝑏 815. 𝑦 4 𝑦 𝑦11Solve the following:17. (π‘Ž2 𝑏)4 (π‘Ž3 𝑏 5 )216. π‘š4 π‘š π‘š5

Name:Date:Hour:Expressions & Equations – 8.EE.1Simplify – Your answers must contain positive exponents1. π‘₯ 7 π‘₯ 22. 𝑦 7 𝑦 4 𝑦4.5π‘₯ 4π‘₯ 97.π‘₯ 3 π‘₯ 4π‘₯210. (𝑏 7 π‘₯ 3 )0π‘₯ 4 𝑦 8 2)π‘₯ 3 𝑦413. (3. (𝑏 4 ) 25.𝑏4𝑏66. (𝑦 2 )48.π‘Ÿ 2 𝑑 3π‘Ÿ 3 𝑑 59. 2π‘₯ 211. (𝑠 2 𝑠 5 ) 414.Solve the following:15. (5π‘₯ 7 𝑦 3 𝑧 1 )2 (2π‘₯𝑦 5 )3 (2𝑦 3 𝑧 2 )3π‘₯ 3 𝑦 π‘₯ 2 𝑦9 8π‘₯𝑦5π‘₯12.(π‘₯ 2 𝑦) 3

Name:Date:Hour:Expressions & Equations – 8.EE.2Evaluate the following expressions:1. 64 9.2. 92 10. 16 42 3144 7 33. 125 11. 27 16 4. 52 23 12. 64 43 5. 30 6 13.6. 22 14. 72 42 33100 10 37. 27 23 15. 27 3 8. 52 5 16. 4 16

Name:Date:Hour:Expressions & Equations – 8.EE.2Solve each equation for the unknown variable. Round your answers tothe nearest tenth if necessary.1. π‘₯ 3 279. π‘Ž2 1212. π‘₯ 2 4910. 𝑐 3 1503. π‘š3 811. π‘Ÿ 2 804. 𝑦 2 6412. π‘₯ 3 1255. 𝑏 2 10013. 𝑙3 5126. β„Ž3 10014. 𝑑 2 817. 𝑗 3 6415. π‘˜ 2 1698. 𝑛2 5016. 𝑏 3 1000

Name:Date:Hour:Expressions & Equations – 8.EE.31) Fill in the following table:10 6 10 5 10 4 10 3 10 2 10 1100101102103104105106Estimate the following values by rewriting them as a single digit times apower of ten.2) 2,4793) 431,0564) 2,943,4505) 123,4886) 9,765,3447) 805,465,3218) 0.0006789) 0.34500110) 0.00000000211) 0.00000418

Name:Date:Hour:Expressions & Equations – 8.EE.31) Which of the following has a value greater than 200 but less than 2,000A. 2.5 103C. 7.2 104B. 3.2 102D. 2.8 1012) Which of the following has a value greater than 500 but less than 1,000A. 5.1 102C. 9.2 103B. 3.8 102D. 5.8 1013) Which of the following has a value greater than 450 but less than 890A. 7.4 103C. 3.8 102B. 6.2 101D. 8.8 1024) In 2016, the population of the United States was approximately3.24 108 . It is expected that the population will be about 3.98 108 in2050. Which shows the growth population, written in scientific notation?A. 7.4 10 1C. 7.4 108B. 7.4 107D. 7.4 10 25) A small town in Kansas started with a population of 2,300 people 80years ago. Now, the town has experienced significant growth and has apopulation of about 3,234,956 people. Approximately how many timeslarger is the current population in the Kansas town than it was 80 yearsago?

Name:Date:Hour:Expressions & Equations – 8.EE.4Write each number in scientific notation1. 27,0012. 0.341560203. 0.00894. 1345. 901,0346. 0.0000047. There are about 270000000000000 red blood cells in the human body.8. It is 380000000 meters from the Earth to the moon9. Americans drink 145000000000 cups of coffee per year.10. A fly weighs 0.0000000000431 times as much as an elephant.11. What is 1.47 10 1? Is this the same as 147 thousandths?

Name:Date:Hour:Expressions & Equations – 8.EE.4State whether the following is in scientific notation or not. If it is not explain why.1. 12.345 1022. 3.42 10 53. 2 1044. 0.321 1035. 3.21 100Solve the following:6. (2 103 ) 4 1028. (8 106 ) (4 103 )10. 9 102 (1 104 )12. 5 103 (8 102 )7. 3 105 (5 104 )9. (4 102 ) (8 107 )11. 5 105 (2 104 )13. 7 1010 (3.5 108 )

Name:Date:Hour:Expressions & Equations – 8.EE.5Determine if the following graphs have a slope that is positive, negative, zero, or undefined.1)2)3)4)Determine if the following statements are true or false. If false make the statement true.5) A proportional relationship has a constant rate of change.6) A proportional relationship has a graph that is linear or non-linear.7) A proportional relationship always passes through the point (1, 1).Find the slope or unit rate of the proportional relationships shown:8)11) 𝑦 5π‘₯14)10)9)13) 𝑦 12) 2𝑦 rs)51015Distance(miles)25507520100

Name:Date:Hour:Expressions & Equations – 8.EE.5Distance (miles)1) Compare the following graph and table to determine which object is moving at agreater speed and explain your e (hours)𝑑 15𝑑Where d distance(miles)and t time (minutes)Distance (miles)2) Compare the following equation and graph to determine which object is movingat a greater speed and explain your answer.Time (minutes)

Name:Date:Hour:Expressions & Equations – 8.EE.61. What is slope intercept form of a linear equation?Find the slope and y – intercept of each of the following lines:2. 𝑦 4π‘₯ – 63. 𝑦 π‘₯ – 4m m m b ( , )b ( , )b (15. 𝑦 π‘₯ 22m b ( , )4. 𝑦 3π‘₯,)26. 𝑦 2π‘₯ 5m b ( , )7. 𝑦 π‘₯ 33m b ( , )Write an equation in slope intercept form for the following problems:8. slope 6 and y – intercept (0, -8)9. slope -1 and y – intercept (0, 2)410. slope and y – intercept (0, -1)11. slope -3 and y – intercept (0, 5)12. slope 2 and y – intercept (0, 3)13. slope and y – intercept (0, 0)52314. What is the slope formula? where (π‘₯1 , 𝑦1 ) π‘Žπ‘›π‘‘ (π‘₯2 , 𝑦2 )Find the slope of the line that passes through each pair of points.Show all your work!15. (8, 7) (3, 6)16. (3, 2) (5, 4)17. (-2, -2) (-4, 118. (3, 2) (3, -2)19. (3, -6) (2, -4)20. (0, 4) (4, 4)

Name:Date:Hour:Expressions & Equations – 8.EE.6Write the equation in slope intercept form for the following graphs:1)4)2)5)3)6)Graph the following equations:7) 𝑦 2π‘₯ 3138) 𝑦 π‘₯ 49) 𝑦 π‘₯ 1

Name:Date:Hour:Expressions & Equations – 8.EE.7Solve the following:1. π‘₯ 12 5π‘₯ 242. 4𝑦 6 2𝑦 143. 2π‘₯ 8 3π‘₯ 74. 5π‘Ž 1 π‘Ž 115. 6 8π‘₯ 3 1146. 3 4π‘₯ 6 π‘₯13227. 𝑏 𝑏 7 218. 3 2π‘₯ 7 4 13Match the following vocabulary words to the correct definition:9. Expression10. Terms11. CoefficientA.B.C.D.12. Like TermsTerms that have the same base, variable, and exponentThe number in front of a variableA mathematical phrase that can contains numbers, variables and operatorsA constant or a variable in an expression13. One students worked the equation below, and their work is shows. Work through theproblems, and check to see if any mistakes were made. If so, state on which line the error wasmade and how it should be corrected.Equation #1Line 1: 9π‘₯ 2 3π‘₯ 7 15Line 2: 12π‘₯ 9 15Line 3: 12π‘₯ 24Line 4: π‘₯ 2

Name:Date:Hour:Expressions & Equations – 8.EE.7Solve the following:1. 7π‘₯ 11 19 3π‘₯2. 11π‘Ž 9 4π‘Ž 303. 19𝑐 31 26𝑐 744. 10π‘Ž 37 6π‘Ž 515. 5𝑀 9.9 4.8 8𝑀6. 15 π‘₯ 2(π‘₯ 3)7. 4 3𝑑 2 88𝑑 58. 15𝑦 14 2(5𝑦 6)9.16π‘₯ 4 4π‘₯ 9211.1440 8π‘₯ 19π‘₯ 2 5π‘₯10. 3 2π‘₯ 1 5(π‘₯ 4)12. 5π‘₯ 12 7π‘₯ 3(5π‘₯ 8)

Name:Date:Hour:Expressions & Equations – 8.EE.7Match the following examples to the correct special case1. x xA. No Solution2. x 5B. Infinite Solutions3. x yC. One SolutionSolve the following equations:4. 2π‘₯ 3π‘₯ 8 5π‘₯ 85. 7π‘₯ 3π‘₯ 2 10π‘₯ 96. 4 3𝑑 2 22𝑑 27. 9 8π‘₯ 8π‘₯ 98. 10 3π‘₯ 12 2 3π‘₯9. 12 π‘₯ 3 10 2(6π‘₯ 10)10. 8 π‘₯ 3 15 5511. 6 2π‘₯ 2 24

Name:Date:Hour:Expressions & Equations – 8.EE.8Solve each system by graphing.1.4.𝑦 2π‘₯ 3𝑦 2π‘₯ 3𝑦 4π‘₯ 1𝑦 4π‘₯ 2𝑦 π‘₯ 62.𝑦 π‘₯ 7𝑦 2π‘₯ 113.5.𝑦 3π‘₯𝑦 46.4𝑦 5π‘₯ 3𝑦 4π‘₯ 2𝑦 3π‘₯ 5Tell whether the ordered pair is a solution of the given system.17. 2, 4𝑦 2π‘₯ 3𝑦 2π‘₯ 88. 6, 4𝑦 π‘₯ 2𝑦 2π‘₯ 2

Name:Date:Hour:Expressions & Equations – 8.EE.8Solve each system by graphing.1.4.3π‘₯ 𝑦 51 2π‘₯ 𝑦 53π‘₯ 𝑦 8 2π‘₯ 𝑦 72.π‘₯ 𝑦 6 π‘₯ 𝑦 25.6π‘₯ 3𝑦 98π‘₯ 2𝑦 183.6.𝑦 3π‘₯ 12π‘₯ 𝑦 6 2π‘₯ 4𝑦 125π‘₯ 2𝑦 10Fill in the following blanks about the steps to graphing a system of equations:7. Make sure both equations are in form.8. Graph both lines on the same .9. Find the of .10. your answer.

Name:Date:Hour:Expressions & Equations – 8.EE.8Solve each system by substitution.1.π‘₯ 82π‘₯ 𝑦 122.𝑦 6π‘₯ 𝑦 23.𝑦 1π‘₯ 2𝑦 64.𝑦 2π‘₯π‘₯ 𝑦 9π‘₯ 𝑦5. 2π‘₯ 2𝑦 86.π‘₯ 2𝑦π‘₯ 𝑦 97.𝑦 4π‘₯ 2𝑦 6π‘₯ 88.𝑦 2π‘₯ 4𝑦 2π‘₯ 49.𝑦 6π‘₯ 1𝑦 6π‘₯ 310.3π‘₯ 𝑦 4 4π‘₯ 𝑦 1011.π‘₯ 5𝑦 132π‘₯ 4𝑦 1612.3π‘₯ 𝑦 42π‘₯ 𝑦 6

Name:Date:Hour:Expressions & Equations – 8.EE.8Solve each system by elimination.1.π‘₯ 𝑦 8π‘₯ 𝑦 42.π‘₯ 𝑦 6π‘₯ 𝑦 43.π‘₯ 𝑦 6 π‘₯ 𝑦 104. π‘₯ 𝑦 2π‘₯ 𝑦 85.2π‘₯ 𝑦 43π‘₯ 𝑦 116.2π‘₯ 3𝑦 4π‘₯ 3𝑦 77. 3π‘₯ 6𝑦 126π‘₯ 12𝑦 118.9.4π‘₯ 3𝑦 9 2π‘₯ 𝑦 510.2π‘₯ 2𝑦 14 4π‘₯ 3𝑦 78π‘₯ 5𝑦 184π‘₯ 4𝑦 0

Name:Date:Hour:Expressions & Equations – 8.EE.8Solve the following word problems. Be sure to label your variables and write a system of equations then solve.1) Ms. Jones took her family and friends to the movies. There were a total of 12 people. Children tickets cost 5and adult tickets cost 10. She spent a total of 95. How many children went to the movies?2) The Roosevelt Middle School band is having a fundraiser. They sold a total of 300 hotdogs and hamburgers.Hotdogs sold for 2 and hamburgers sold for 3. They made a total of 780. How many individual hamburgersand hotdogs did they sell?3) The basketball team scored 89 points in just two- and three-point baskets. The number of two-point basketswas 27 more than the number of three-point baskets. How many two-point and three-pointers did the teammake?4) For dinner, Jerry had a double cheeseburger and two medium fries totaling 1200 calories. Joe has two doublecheeseburgers and one medium fry totaling 1260 calories. How many calories are in one double cheeseburgerand one order of medium fries?5) A farmhouse shelters 16 animals. Some of them are chickens and the others are cows. Altogether theseanimals have 60 legs. How many chickens and how many cows are in the farmhouse?

Write an equation in slope intercept form for the following problems: 8. slope 6 and y – intercept (0, -8) 9. slope -

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