G8 U4 Assessment
Name: ______________________________
Date:________________
Grade 8 Unit 4 Assessment Linear Equations 1. Determine if the following problem has one solution, no solutions or infinitely many solutions. If it has one solution, find it. Jack is three years older than Don. In six years, Jack will be seven years less than twice as old as Don. How old is Don? A. One solution, 4 years old B. One solution, 16 years old C. No solutions D. Infinitely many solutions 2. Determine if the following problem has one solution, no solutions or infinitely many solutions. If it has one solution, find it. 3 1 1 (π + 8) + π = 7 ( π + 1) 4 8 8 A. One solution, 4 B. One solution, 6 C. No solutions D. Infinitely many solutions
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3. Find the number of solutions graphed here: 4 3 2 1 0 -1 0 -2 -3 -4 -5 -6
1
2
3
4
5
A. One solution (4, β1) B. One solution (β1, 4) C. No Solutions D. Infinitely any solutions 4. Gordon must drive to a business meeting 360 miles away and be there by 2 pm. He intends to take a 20 minute rest near the halfway point. If he drives 72 mi/hr the whole way, what time should he leave by? Round to the earlier half-hour, so he is sure not to be late. A. 9:00 am B. 8:30 am C. 8:00 am D. 7:30 am Copyright Β© Swun Math Grade 8 Unit 4 Assessment, Page 2
5. Graph the two lines below to determine the number of solutions to the system and if it is consistent or not. If there is one, find it. 1 4
1
π₯ β π¦1 = 2 2
π¦ = 2π₯ + 4
A. One solution, consistent (0, 4) B. One solution, consistent (-2, 0) C. No solutions, inconsistent D. Infinitely many solutions, consistent 6. Jacob has a pocketful of quarters and dimes. His daughter counts them, and says, βYou have 29 coins worth $5.15.β Find out how many more quarters he has than dimes. A. 7 B. 1 C. 5 D. 3 Copyright Β© Swun Math Grade 8 Unit 4 Assessment, Page 3
7. Solve the system below by linear combination or substitution. Once you have found the coordinates of the solution add the x value to the y value. What is the sum of x+y? 3π₯ + 2π¦ = β2 π¦ = β2π₯ β 3 14. 4 15. 2 16. 1 17. β1 8. Solve the system below by linear combination or substitution. Once you have found the coordinates of the solution, add the x value to the y value. What is the sum of x+y? 2π₯ + 7π¦ = 1 π₯ β 3π¦ = 33 A. β5 B. 13 C. 3 D. β2
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9. Find the intersection point of β‘π΄π΅ and β‘πΆπ· , if A is (β1, β3), B is (2, 0), C is (β3, β4) and D is (5, 0). A. (3, β1) B. (0, β2) C. (1, β1) D. (3.5, 0) _________________________________________________________________________
10. A relief plane is flying water and food into a region hit by a natural disaster. The water containers weigh 60 pounds and take up 1 cubic foot of space. The food containers weigh 40 pounds and take up 10 cubic feet of space. The plane can carry 7200 pounds, and it can hold 680 cubic feet of containers. Figure out how many water and food containers will fill the plane optimally. Add the number of food and water containers together. What is that sum? A. 120 B. 140 C. 160 D. 180
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11. Graph the two equations below and find their point of intersection, if any. If not, tell if they are consistent or inconsistent. 1
π¦=β 2 π¦ = β3π₯ + 5
Answer: __________________________ 12. The sum of four consecutive integers is 20 more than three times the largest integer. What is the largest integer? Check if each statement about the problem is correct. A. The equation that represents this problem is: π₯ + (π₯ β 1) + (π₯ β 2) + (π₯ β 3) = 20 + 3π₯
Y
N
B. The largest integer is equal to
Y
N
C. The equation that best represents this problem is: 4π₯ = 20 + 3π₯
Y
N
D. The largest integer is equal to 26.
Y
N
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13. Jen has red and blue gumballs. If she triples the number of red gumballs she has, she will have 145 gumballs total. On the other hand if she doubles her blue gumballs, she will have 140 gumballs total. How many more blue gumballs than red does she have? A. 20 B. 5 C. 15 D. 25 14. If you add six to this number and triple the sum, the result is the same as if you quadruple the number, add 18 and subtract the original number from that sum. What is the number? Which of the following statements is true about the problem? A. There is one solution equal to 0.
T
F
B. The equation that best represents the problem is (6 + π₯ )3 = (4π₯ + 18) β π₯
T
F
C. There is no solution.
T
F
D. There are infinitely many solutions.
T
F
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15. Bill buys cashews and chocolate chips for his snack. The cashews cost $2.40 per pound, and the chocolate chips $1.80 per pound. Together the nuts and chips weigh 1.1 pounds and cost $2.28. How much of each did he purchase? Show your work in detailed and organized steps.
Answer: _____________________ ________________________________________________________________________
16. Fyodor encounters the following problem on a test: βFind the point of intersection between π¦ + 2π₯ = 5 and π₯ β 2π¦ = β10.β When he added the equations up, he got 2π₯ = β5. Explain what he did wrong, and the correct answer he should have gotten. Give your explanation in complete sentences.
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Date:________________
Grade 8 Unit 4 Assessment Linear Equations 1. Determine if the following problem has one solution, no solutions or infinitely many solutions. If it has one solution, find it. Jack is three years older than Don. In six years, Jack will be seven years less than twice as old as Don. How old is Don? A. One solution, 4 years old B. One solution, 16 years old C. No solutions D. Infinitely many solutions 2. Determine if the following problem has one solution, no solutions or infinitely many solutions. If it has one solution, find it. 3 1 1 (π + 8) + π = 7 ( π + 1) 4 8 8 A. One solution, 4 B. One solution, 6 C. No solutions D. Infinitely many solutions
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3. Find the number of solutions graphed here: 4 3 2 1 0 -1 0 -2 -3 -4 -5 -6
1
2
3
4
5
A. One solution (4, β1) B. One solution (β1, 4) C. No Solutions D. Infinitely any solutions 4. Gordon must drive to a business meeting 360 miles away and be there by 2 pm. He intends to take a 20 minute rest near the halfway point. If he drives 72 mi/hr the whole way, what time should he leave by? Round to the earlier half-hour, so he is sure not to be late. A. 9:00 am B. 8:30 am C. 8:00 am D. 7:30 am Copyright Β© Swun Math Grade 8 Unit 4 Assessment, Page 2
5. Graph the two lines below to determine the number of solutions to the system and if it is consistent or not. If there is one, find it. 1 4
1
π₯ β π¦1 = 2 2
π¦ = 2π₯ + 4
A. One solution, consistent (0, 4) B. One solution, consistent (-2, 0) C. No solutions, inconsistent D. Infinitely many solutions, consistent 6. Jacob has a pocketful of quarters and dimes. His daughter counts them, and says, βYou have 29 coins worth $5.15.β Find out how many more quarters he has than dimes. A. 7 B. 1 C. 5 D. 3 Copyright Β© Swun Math Grade 8 Unit 4 Assessment, Page 3
7. Solve the system below by linear combination or substitution. Once you have found the coordinates of the solution add the x value to the y value. What is the sum of x+y? 3π₯ + 2π¦ = β2 π¦ = β2π₯ β 3 14. 4 15. 2 16. 1 17. β1 8. Solve the system below by linear combination or substitution. Once you have found the coordinates of the solution, add the x value to the y value. What is the sum of x+y? 2π₯ + 7π¦ = 1 π₯ β 3π¦ = 33 A. β5 B. 13 C. 3 D. β2
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9. Find the intersection point of β‘π΄π΅ and β‘πΆπ· , if A is (β1, β3), B is (2, 0), C is (β3, β4) and D is (5, 0). A. (3, β1) B. (0, β2) C. (1, β1) D. (3.5, 0) _________________________________________________________________________
10. A relief plane is flying water and food into a region hit by a natural disaster. The water containers weigh 60 pounds and take up 1 cubic foot of space. The food containers weigh 40 pounds and take up 10 cubic feet of space. The plane can carry 7200 pounds, and it can hold 680 cubic feet of containers. Figure out how many water and food containers will fill the plane optimally. Add the number of food and water containers together. What is that sum? A. 120 B. 140 C. 160 D. 180
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11. Graph the two equations below and find their point of intersection, if any. If not, tell if they are consistent or inconsistent. 1
π¦=β 2 π¦ = β3π₯ + 5
Answer: __________________________ 12. The sum of four consecutive integers is 20 more than three times the largest integer. What is the largest integer? Check if each statement about the problem is correct. A. The equation that represents this problem is: π₯ + (π₯ β 1) + (π₯ β 2) + (π₯ β 3) = 20 + 3π₯
Y
N
B. The largest integer is equal to
Y
N
C. The equation that best represents this problem is: 4π₯ = 20 + 3π₯
Y
N
D. The largest integer is equal to 26.
Y
N
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13. Jen has red and blue gumballs. If she triples the number of red gumballs she has, she will have 145 gumballs total. On the other hand if she doubles her blue gumballs, she will have 140 gumballs total. How many more blue gumballs than red does she have? A. 20 B. 5 C. 15 D. 25 14. If you add six to this number and triple the sum, the result is the same as if you quadruple the number, add 18 and subtract the original number from that sum. What is the number? Which of the following statements is true about the problem? A. There is one solution equal to 0.
T
F
B. The equation that best represents the problem is (6 + π₯ )3 = (4π₯ + 18) β π₯
T
F
C. There is no solution.
T
F
D. There are infinitely many solutions.
T
F
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15. Bill buys cashews and chocolate chips for his snack. The cashews cost $2.40 per pound, and the chocolate chips $1.80 per pound. Together the nuts and chips weigh 1.1 pounds and cost $2.28. How much of each did he purchase? Show your work in detailed and organized steps.
Answer: _____________________ ________________________________________________________________________
16. Fyodor encounters the following problem on a test: βFind the point of intersection between π¦ + 2π₯ = 5 and π₯ β 2π¦ = β10.β When he added the equations up, he got 2π₯ = β5. Explain what he did wrong, and the correct answer he should have gotten. Give your explanation in complete sentences.
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