8 Grade & Equations Expressions - Miss Jarrelljarrellmnps.weebly.com/uploads/8/6/3/3/86337132/ee...B. 6.2×101 D. 8.8×102 4) In 2016, the population of the United States was approximately

By: Math in the Midwest

8 Grade

Expressions & Equations

Worksheets

Name: _____________________ Date: ______ Hour: _______

Expressions & Equations – 8.EE.1

Simplify 1. 𝑥5 ∙ 𝑥2 2. 𝑦3 ∙ 𝑦7 3. 𝑏4 ∙ 𝑏12

4. 𝑐3𝑐5𝑐2 5. 𝑎3𝑎1𝑎8 6. (𝑦2)4 7. (𝑚3)5 8. (2𝑥4)2 9. (3𝑦2)3 10. (𝑏7)0 11. (𝑠2)6 ∙ 𝑠5 12. 𝑡𝑥 ∙ 𝑡𝑦 Find the missing exponent in each expression. 13. 𝑥 ∙ 𝑥5 = 𝑥7 14. 𝑏 ∙ 𝑏3 = 𝑏8 15. 𝑦4 ∙ 𝑦 = 𝑦11 16. 𝑚4 ∙ 𝑚 = 𝑚5 Solve the following: 17. (𝑎2𝑏)4 ∙ (𝑎3𝑏5)2

Name: _____________________ Date: ______ Hour: _______


Simplify – Your answers must contain positive exponents 1. 𝑥7 ∙ 𝑥−2 2. 𝑦7 ∙ 𝑦4 ∙ 𝑦 3. (𝑏4)−2

4. 5𝑥−4

𝑥−9 5. 𝑏4

𝑏6 6. (𝑦−2)4

7. 𝑥3∙𝑥4

𝑥2 8. 𝑟2𝑡−3

𝑟−3𝑡5 9. 2𝑥−2

10. (𝑏7𝑥3)0 11. (𝑠2 ∙ 𝑠5)−4 12.(𝑥−2𝑦)−3

13. (𝑥4𝑦−8

𝑥−3𝑦4)2 14. 𝑥3𝑦

𝑥𝑦5 ∙𝑥2𝑦9

𝑥8 Solve the following: 15. (5𝑥7𝑦3𝑧−1)2 ∙ (2𝑥𝑦−5)3 ∙ (2𝑦−3𝑧2)3

Name: _____________________ Date: ______ Hour: _______


Evaluate the following expressions:

1. 64 = 9. 144 + 7 = 2. 92 = 10. 16 + 42 =

3. 1253 = 11. 273 + 16 =

4. 52 + 23 = 12. 643 + 43 =

5. 30 + 6 = 13. 100 + 10 = 6. 22 = 14. 72 + 42 =

7. 273 + 23 = 15. 273 + 3 =

8. 52 + 5 = 16. 4 + 16 =

Name: _____________________ Date: ______ Hour: _______


Solve each equation for the unknown variable. Round your answers to the nearest tenth if necessary.

1. 𝑥3 = 27 9. 𝑎2 = 121 2. 𝑥2 = 49 10. 𝑐3 = 150

3. 𝑚3 = 8 11. 𝑟2 = 80

4. 𝑦2 = 64 12. 𝑥3 = 125

5. 𝑏2 = 100 13. 𝑙3 = 512 6. ℎ3 = 100 14. 𝑡2 = 81

7. 𝑗3 = 64 15. 𝑘2 = 169

8. 𝑛2 = 50 16. 𝑏3 = 1000

Name: _____________________ Date: ______ Hour: _______


1) Fill in the following table:

Estimate the following values by rewriting them as a single digit times a power of ten. 2) 2,479 3) 431,056 4) 2,943,450 5) 123,488 6) 9,765,344 7) 805,465,321 8) 0.000678 9) 0.345001 10) 0.000000002 11) 0.00000418

10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 104 105 106

Name: _____________________ Date: ______ Hour: _______


1) Which of the following has a value greater than 200 but less than 2,000 A. 2.5 × 103 C. 7.2 × 104 B. 3.2 × 102 D. 2.8 × 101 2) Which of the following has a value greater than 500 but less than 1,000 A. 5.1 × 102 C. 9.2 × 103 B. 3.8 × 102 D. 5.8 × 101 3) Which of the following has a value greater than 450 but less than 890 A. 7.4 × 103 C. 3.8 × 102 B. 6.2 × 101 D. 8.8 × 102 4) In 2016, the population of the United States was approximately 3.24 × 108. It is expected that the population will be about 3.98 × 108 in 2050. Which shows the growth population, written in scientific notation? A. 7.4 × 10−1 C. 7.4 × 108 B. 7.4 × 107 D. 7.4 × 10−2 5) A small town in Kansas started with a population of 2,300 people 80 years ago. Now, the town has experienced significant growth and has a population of about 3,234,956 people. Approximately how many times larger is the current population in the Kansas town than it was 80 years ago?

Name: _____________________ Date: ______ Hour: _______


Write each number in scientific notation 1. 27,001 2. 0.34156020 3. 0.0089 4. 134 5. 901,034 6. 0.000004 7. There are about 270000000000000 red blood cells in the human body. 8. It is 380000000 meters from the Earth to the moon 9. 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: _______


State whether the following is in scientific notation or not. If it is not explain why. 1. 12.345 × 102 ________________________________________________ 2. 3.42 × 10−5 _______________________________________________ 3. 2 × 104 _______________________________________________ 4. 0.321 × 103 _______________________________________________ 5. 3.21 × 100 _______________________________________________ Solve the following: 6. (2 × 103) × 4 × 102 7. 3 × 105 × (5 × 104) ___________________________ ___________________________ 8. (8 × 106) ÷ (4 × 103) 9. (4 × 102) ÷ (8 × 107) ___________________________ ___________________________ 10. 9 × 102 + (1 × 104) 11. 5 × 105 + (2 × 104)

___________________________ ___________________________ 12. 5 × 103 − (8 × 102) 13. 7 × 1010 − (3.5 × 108) ___________________________ ___________________________

Name: _____________________ Date: ______ Hour: _______


Determine 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:

Week 1 2 5 10

Amount 120 140 200 300

Time (hours)

5 10 15 20

Distance (miles)

25 50 75 100

8) 9) 10)

11) 𝑦 = 5𝑥 12) 2𝑦 = 10𝑥 13) 𝑦 = 14𝑥

14) 15)

Name: _____________________ Date: ______ Hour: _______


1) Compare the following graph and table to determine which object is moving at a greater speed and explain your answer. ____________________________________________________________________________________________________________________________________________________________ ______________________________________________________________________________ 2) Compare the following equation and graph to determine which object is moving at a greater speed and explain your answer. ____________________________________________________________________________________________________________________________________________________________________________________________________________

Dist

ance

(mile

s)

Time (hours)

Time (hours)

4 8 12 16

Distance (miles)

15 30 45 60

Dist

ance

(mile

s)

Time (minutes)

𝑑 = 15𝑡 Where d = distance

(miles) and t = time (minutes)

Name: _____________________ Date: ______ Hour: _______


1. What is slope intercept form of a linear equation? _______________________ Find the slope and y – intercept of each of the following lines: 2. 𝑦 = 4𝑥 – 6 3. 𝑦 = −𝑥 – 4 4. 𝑦 = 3𝑥 m = m = m = b = ( , ) b = ( , ) b = ( , ) 5. 𝑦 = 1

2𝑥 + 2 6. 𝑦 = 2𝑥 − 5 7. 𝑦 = − 2

3𝑥 − 3

m = m = m = b = ( , ) b = ( , ) 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) 10. slope = 4

5 and y – intercept (0, -1) 11. slope = -3 and y – intercept (0, 5)

12. slope = 2 and y – intercept (0, 3) 13. slope = 2

3 and y – intercept (0, 0)

14. What is the slope formula? __________________ where (𝑥1, 𝑦1) 𝑎𝑛𝑑 (𝑥2, 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, 1 18. (3, 2) (3, -2) 19. (3, -6) (2, -4) 20. (0, 4) (4, 4)

Name: _____________________ Date: ______ Hour: _______


Write the equation in slope intercept form for the following graphs: Graph the following equations:

1) ____________________ 2) ____________________ 3) ____________________

7) 𝑦 = 2𝑥 + 3 8) 𝑦 = − 13𝑥 − 4 9) 𝑦 = −𝑥 + 1

4) ____________________ 5) ____________________ 6) ____________________

Name: _____________________ Date: ______ Hour: _______


Solve the following: 1. 𝑥 − 12 + 5𝑥 = 24 2. 4𝑦 + 6 − 2𝑦 = 14 3. 2𝑥 − 8 + 3𝑥 = 7 4. 5𝑎 − 1 + 𝑎 = 11 5. −6 8𝑥 − 3 = 114 6. −3 = 4𝑥 + 6 − 𝑥 7. 1

2𝑏 + 3

2𝑏 + 7 = 21 8. 3 2𝑥 − 7 + 4 = 13

Match the following vocabulary words to the correct definition: 9. ________ Expression 10. ________ Terms 11. ________ Coefficient 12. ________ Like Terms A. Terms that have the same base, variable, and exponent B. The number in front of a variable C. A mathematical phrase that can contains numbers, variables and operators D. A constant or a variable in an expression 13. One students worked the equation below, and their work is shows. Work through the problems, and check to see if any mistakes were made. If so, state on which line the error was made and how it should be corrected. Equation #1 Line 1: 9𝑥 + 2 + 3𝑥 − 7 = 15 Line 2: 12𝑥 + 9 = 15 Line 3: 12𝑥 = 24 Line 4: 𝑥 = 2

Name: _____________________ Date: ______ Hour: _______


Solve the following: 1. 7𝑥 − 11 = −19 + 3𝑥 2. 11𝑎 + 9 = 4𝑎 + 30 3. 19𝑐 + 31 = 26𝑐 − 74 4. 10𝑎 − 37 = 6𝑎 + 51 5. 5𝑤 + 9.9 = 4.8 + 8𝑤 6. 15 − 𝑥 = 2(𝑥 + 3) 7. 4 3𝑑 − 2 = 88𝑑 − 5 8. 15𝑦 + 14 = 2(5𝑦 + 6) 9. 1

26𝑥 − 4 = 4𝑥 − 9 10. 3 2𝑥 + 1 = 5(𝑥 − 4)

11. 1

440 − 8𝑥 = 19𝑥 + 2 − 5𝑥 12. −5𝑥 + 12 − 7𝑥 = −3(5𝑥 + 8)

Name: _____________________ Date: ______ Hour: _______


Match the following examples to the correct special case 1. _________ x = x A. No Solution 2. _________ x = 5 B. Infinite Solutions 3. _________ x = y C. One Solution Solve the following equations: 4. 2𝑥 + 3𝑥 + 8 = 5𝑥 + 8 5. −7𝑥 − 3𝑥 + 2 = −10𝑥 + 9 6. 4 3𝑑 + 2 = 22𝑑 − 2 7. 9 + 8𝑥 = 8𝑥 − 9 8. 10 + 3𝑥 − 12 = −2 + 3𝑥 9. 12 𝑥 − 3 = 10 + 2(6𝑥 − 10) 10. 8 𝑥 − 3 + 15 = 55 11. 6 2𝑥 − 2 = 24

Name: _____________________ Date: ______ Hour: _______


Solve each system by graphing. 1. 𝑦 = 2𝑥 + 3

𝑦 = −2𝑥 + 3 2. 𝑦 = 𝑥 − 7𝑦 = −2𝑥 + 11 3.

𝑦 = 𝑥 − 6𝑦 = −4

5𝑥 + 3

4. 𝑦 = 4𝑥 + 1

𝑦 = 4𝑥 − 2 5. 𝑦 = 3𝑥𝑦 = 4 6.

𝑦 = 4𝑥 − 2𝑦 = −3𝑥 + 5

Tell whether the ordered pair is a solution of the given system.

7. −2,−4 𝑦 = 12𝑥 − 3

𝑦 = −2𝑥 − 8 8. 6, 4 𝑦 = 𝑥 + 2

𝑦 = 2𝑥 − 2

Name: _____________________ Date: ______ Hour: _______


Solve each system by graphing. 1.

3𝑥 + 𝑦 = 5−1

2𝑥 + 𝑦 = 5 2. 𝑥 + 𝑦 = 6

−𝑥 + 𝑦 = −2 3. 𝑦 = 3𝑥 − 12𝑥 + 𝑦 = −6

4. 3𝑥 + 𝑦 = −8−2𝑥 + 𝑦 = 7 5. 6𝑥 + 3𝑦 = 9

8𝑥 − 2𝑦 = 18 6. −2𝑥 + 4𝑦 = 125𝑥 − 2𝑦 = 10

Fill 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: _______


Solve each system by substitution.

1. 𝑥 = 8 2𝑥 + 𝑦 = 12 2. 𝑦 = 6

𝑥 + 𝑦 = −2 3. 𝑦 = −1𝑥 + 2𝑦 = −6

4. 𝑦 = 2𝑥𝑥 + 𝑦 = 9 5.

𝑥 = 𝑦 2𝑥 + 2𝑦 = 8 6. 𝑥 = −2𝑦

𝑥 − 𝑦 = 9

7. 𝑦 = −4𝑥 + 2𝑦 = 6𝑥 − 8 8. 𝑦 = 2𝑥 + 4

𝑦 = 2𝑥 + 4 9. 𝑦 = 6𝑥 − 1𝑦 = 6𝑥 + 3

10. 3𝑥 + 𝑦 = 4−4𝑥 + 𝑦 = −10 11. 𝑥 + 5𝑦 = 13

2𝑥 − 4𝑦 = −16 12. 3𝑥 + 𝑦 = 42𝑥 − 𝑦 = 6

Name: _____________________ Date: ______ Hour: _______


Solve each system by elimination. 1. 𝑥 + 𝑦 = 8

𝑥 − 𝑦 = −4 2. 𝑥 + 𝑦 = 6𝑥 − 𝑦 = −4 3. 𝑥 + 𝑦 = 6

−𝑥 + 𝑦 = −10

4. −𝑥 + 𝑦 = 2𝑥 + 𝑦 = 8 5. 2𝑥 + 𝑦 = 4

3𝑥 − 𝑦 = 11 6. 2𝑥 − 3𝑦 = −4𝑥 + 3𝑦 = 7

7. −3𝑥 − 6𝑦 = −126𝑥 + 12𝑦 = 11 8. 2𝑥 + 2𝑦 = 14

−4𝑥 + 3𝑦 = −7

9. 4𝑥 − 3𝑦 = 9−2𝑥 + 𝑦 = −5 10. 8𝑥 − 5𝑦 = −18

4𝑥 − 4𝑦 = 0

Name: _____________________ Date: ______ Hour: _______


Solve 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 $5 and 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 hamburgers and hotdogs did they sell? 3) The basketball team scored 89 points in just two- and three-point baskets. The number of two-point baskets was 27 more than the number of three-point baskets. How many two-point and three-pointers did the team make? 4) For dinner, Jerry had a double cheeseburger and two medium fries totaling 1200 calories. Joe has two double cheeseburgers and one medium fry totaling 1260 calories. How many calories are in one double cheeseburger and one order of medium fries? 5) A farmhouse shelters 16 animals. Some of them are chickens and the others are cows. Altogether these animals have 60 legs. How many chickens and how many cows are in the farmhouse?

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8 Grade & Equations Expressions - Miss Jarrelljarrellmnps.weebly.com/uploads/8/6/3/3/86337132/ee...B. 6.2×101 D. 8.8×102 4) In 2016, the population of the United States was approximately