Day 4: Systems, Algebra, Problem Solving



Algebra 1 EOC Homework Packet Name:_______________

Linear Review Day 1: Due Thursday, May 17

|Jim is selling hot dogs at a ball game. It cost Jim $250 to purchase everything |Which of the following equations describes the data in the table below? |

|to make the hot dogs. Jim sells hot dogs for $2.00 each. If he sells h hot dogs,|x (% of reduction (or increase) in dietary fat) |

|which equation models his profit (P)? |-6 |

| |-4 |

|A. [pic] B. [pic] |-2 |

|C. [pic] D. [pic] |1 |

| |5 |

| | |

| |y (weight loss (or gain) in pounds) |

| |-15 |

| |-11 |

| |-7 |

| |-1 |

| |7 |

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| |A. [pic] B. [pic] |

| |C. [pic] D. [pic] |

|The following data compares the heights and weights of 5 people. |The cost of a large pizza is given by the formula [pic], where C(t) is the cost of|

|[pic] |the pizza and t is the number of topings. What does the slope represent? |

|Which of the following equations best represents the data? | |

| |A. number of toppings |

|A. [pic] B. [pic] |B. cost per slice |

|C. [pic] D. [pic] |C. cost of each topping |

| |D. cost of the pizza with no toppings |

| | |

| |Denisha bought a car for $15,000. The value depreciates linearly. After 3 years |

| |the value is $11,250. What is the amount of yearly depreciation? |

| | |

| |A. $2,000 B. $1,500 |

| |C. $1,250 D. $750 |

| | |

|In 1977, the price of a scientific calculator was $175. In 2004, the price was |The table contains data about the cost of telephone calls to Sydney Australia. |

|$15. Assuming the change in price was linear, what was the approximate price of a|The long-distance service charges a connection fee plus a certain amount per |

|scientific calculator in 1998? |minute. What is the connection fee charged for each call? |

| | |

|A. $23.00 B. $27.00 |Time (min) |

|C. $51.00 D. $60.00 |Cost (¢) |

| | |

| |1 |

| |17.9 |

| | |

| |5 |

| |49.5 |

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| |8 |

| |73.2 |

| | |

| |11 |

| |96.9 |

| | |

| |20 |

| |168.0 |

| | |

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| |A. 5¢ B. 7.9¢ |

| |C. 10¢ D. 17.9¢ |

| | |

Linear Review Day 2: Due Friday, May 18

|Hooke’s law states that the distance a vertical spring stretches varies directly |What is “7 less than 3 times c” represented as an algebraic expression? |

|with the weight hanging from it. A spring stretches 14 inches when a 35-pound | |

|weight is hanging from it. How much weight is needed to stretch the spring 44 |A. [pic] B. [pic] |

|inches? |C. [pic] D. [pic] |

| | |

|A. 110 pounds B. 65 pounds | |

|C. 17.6 pounds D. 11.1 pounds | |

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|When x is 3, and y is 12. If y varies directly as x, which equation relates x and |For the line [pic], where [pic]and [pic], what change would occur if b is |

|y? |multiplied by -1 and m remains the same? |

| | |

|A. [pic] B. [pic] |A. The y-intercept would become negative. |

|C. [pic] D. [pic] | |

| |B. The slope would become negative. |

| | |

| |C. The resulting line would be perpendicular to the original line. |

| | |

| |D. The resulting line would be parallel to the original line. |

|Suppose that y varies directly as x, and [pic] when [pic]. What is the value of y | |

|when [pic]? | |

| | |

|A. 2.8 B. 10 | |

|C. 17.5 D. 35 | |

|Mark burns 34 calories when he plays volleyball for 10 minutes. If he plays for 15 |A line has a slope of [pic] and y-intercept of -4. Which of the following is the|

|minutes, he burns 51 calories. How fast is Mark burning calories? |equation of the line? |

| | |

|A. [pic] calories per minute |A. [pic] B. [pic] |

|B. [pic] calories per minute |C. [pic] D. [pic] |

|C. [pic] calories per minute | |

|D. [pic] calories per minute | |

| | |

|Kirin has d dimes and q quarters. Which of the following expressions gives the |Which algebraic equation represents “three less than twice a number is the same |

|value of Kirin’s money in pennies? |as nine more than five times the number”? |

| | |

|A. [pic] B. [pic] |A. [pic] B. [pic] |

|C. [pic] D. [pic] |C. [pic] D. [pic] |

Matrices Review: Due Monday, May 21

|The Baltic Sea covers 147,500 square miles of area and has an average depth of 180|Matrix G shows the number of students at a gym in the year 2000. Matrix M shows |

|feet. The North Sea covers 164,900 square miles of area and has an average depth |the number of students at the same gym in 2005. |

|of 308 feet. The Red Sea has an area of 174,900 square miles and has an average |[pic] [pic] |

|depth of 1,764 feet. The East China Sea has an area of 256,600 square miles and | |

|an average depth of 620 feet. Which matrix displays this information organized by|Which matrix represents the change from 2000 to 2005? |

|area and depth of each sea? | |

| |A. [pic] B. [pic] |

|A. [pic] | |

| |C. [pic] D. [pic] |

|B. [pic] | |

| | |

|C. [pic] | |

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|D. [pic] | |

|The matrix below displays the average SAT scores of eleventh- and twelfth-grade |This matrix shows the cost of cell phone service offered by several different |

|students over a three-year period at a high school. |companies. |

|[pic] | |

| |[pic] |

|What was the change in average SAT scores of the twelfth-graders from 1998 to | |

|2000? |What is the cost of 320 minutes with Company 4? |

| | |

|A. Scores increased by 225 points. |A. $37.20 B. $45.00 |

|B. Scores increased by 89 points. |C. $49.20 D. $75.00 |

|C. Scores decreased by 225 points | |

|D. Scores decreased by 89 points. | |

|Given the matrices |

|[pic] |

| |

|What is 4J – 2K? |

| |

|A. [pic] B. [pic] C. [pic] D. [pic] |

Systems of Equations & Inequalities Review: Due Tuesday, May 22

|A region is defined by the following system. |Amy is 35 years older than her daughter Sarah. In five years Amy will be twice as|

|[pic] |old as Sarah will be. How many years old is Sarah now? |

|In which quadrants of the coordinate plane is the region located? | |

| |A. 15 B. 30 |

|A. I, II, III B. II, III |C. 25 D. 20 |

|C. III, IV D. I, II, III, IV | |

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|The perimeter of a rectangular garden is 42 feet. The length of the garden is 5 |Joan bought a total of 30 cans of cola and root beer. There were twice as many |

|feet more than twice the width. Which system of equations will determine the |cans of cola as cans of root beer. Which system of equations will determine the |

|length (l) and the width (w) of the garden? |number of cans of cola (c) and the number of cans of root beer (r) that Joan |

| |bought? |

|A. [pic] B. [pic] | |

| |A. [pic] B. [pic] |

|C. [pic] D. [pic] | |

| |C. [pic] D. [pic] |

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|Chris bought 2 chicken sandwiches and 3 bowls of vegetable soup for $16.50, not |Solve: [pic] if [pic] |

|including tax. Jim bought 1 chicken sandwich and 2 bowls of vegetable soup for | |

|$9.50, not including tax. What was the cost of a bowl of soup? |A. [pic] |

| |B. {1, 2, 3} |

|A. $5.50 B. $4.50 |C. {-2, -1, 0, 1, 2, 3} |

|C. $3.25 D. $2.50 |D. {-3, -2, -1, 0, 1, 2, 3} |

Exponential Functions Review: Due Wednesday, May 23

|The distance, d, from Earth to the sun is approximately [pic]miles. The speed of |The population of a town is 345,000. The function [pic]gives the predicted |

|light, c, is approximately [pic] miles per second. The equation [pic]can be used |population of the town in t years. Approximately what will the population be in 3|

|to find the time, t, for light to reach Earth from the sun. How long, in seconds,|years? |

|does it take light to travel from the sun to the Earth? | |

| |A. 350,000 B. 600,000 |

|A. [pic] seconds B. [pic]seconds |C. 700,000 D. 1,250,000 |

|C. [pic] seconds D. [pic] seconds | |

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|A chemist presented this graph to local government officials who needed to know |Each year, Cathy invests $1,200 in her account. The account pays an interest rate|

|the rate at which trash decays inside a landfill. |of 6.3%. The formula to calculate the balance in her account is |

|[pic] |[pic], where |

|Which is the correct interpretation of the rate of decay? |A is the amount invested per year, |

| |r is the interest rate, and |

|A. Half of the trash will decay every year. |n is the number of years investing. |

|B. Half of the trash will decay every two years. | |

|C. Half of the trash will decay every three years |Approximately how much will Cathy have in her account after 45 years? |

|D. Half of the trash will decay every six months. | |

| |A. $217,000 B. $248,000 |

| |C. $279,000 D. $297,000 |

| | |

|Local scientists have been asked to study the population of gnats around a lake. |Alan won $2,000 in an essay contest. He invested the money in a savings account |

|After five days, the scientist generated these results: |which pays 6% interest compounded annually. Consider the formula: |

| |[pic], where |

|Day | |

|1 |A(t) is the accumulated amount at time t |

|2 |Ao is the amount of invested at time t = 0, |

|3 |r is the interest rate, and |

|4 |t is the time in years. |

|5 | |

| |What is Alan’s investment worth after two years? |

|Gnats | |

|4 |A. $240 B. $247 |

|16 |C. $2,240 D. $2,247 |

|64 | |

|256 | |

|1,024 | |

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|How can the data best be described? | |

| | |

|A. The population doubles daily. | |

|B. The population quadruples daily | |

|C. The population increases by 4 daily | |

|D. The population increases daily by squaring. | |

Quadratic Functions Review: Due Thursday, May 24

|Multiply: [pic] |The length of a rectangle is 2 units greater than the width, w. What is the area |

| |of the rectangle? |

|A. [pic] B. [pic] | |

|C. [pic] D. [pic] |A. [pic] B. [pic] |

| |C. [pic] D. [pic] |

| | |

|What are the vertex and y-intercept of the quadratic function [pic]? |The height of an object dropped from a hot-air balloon can be determined by the |

| |formula [pic], where h is the height of the object in feet, t is the elapsed time |

|A. vertex [pic] y-intercept: -2 |in seconds, and s is the height of the balloon. |

|B. vertex [pic] y-intercept: -2 | |

|C. vertex [pic] y-intercept: [pic] |If the balloon is 400 feet from the ground, how long will it take for an object |

|D. vertex [pic] y-intercept: [pic] |dropped from the balloon to hit the ground? |

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| |A. 2.5 seconds B. 5 seconds |

| |C. 7.5 seconds D. 10 seconds |

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|Which is an x-intercept of [pic]? |Which binomial is a factor of [pic]? |

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|A. [pic] B. [pic] |A. [pic] B. [pic] |

|C. -3 D. [pic] |C. [pic] D. [pic] |

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|Which of the following statements best describes the solution(s) of [pic]? |Given [pic], what is the range of the function? |

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|A. no solution |A. all real numbers less than or equal to 5 |

|B. 1 negative solution |B. all integers less than or equal to 5 |

|C. 1 positive solution and 1 negative solution |C. all nonnegative real numbers |

|D. 2 positive solutions |D. all nonnegative integers |

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|An object is shot upward from ground level with an initial velocity of 64 feet per second. Its height after t seconds is given by [pic]. Which graph best represents|

|this function? |

|[pic] [pic] [pic] [pic] |

Reading Comprehension Review: Due on Review Day (first period due exam day)

|UNRAAVEL: Reading Strategy |Shirley needs data to find an equation relating the number of hours that students |

|U - Underline the Question |spent per day working at a part-time job and their grade point average (GPA). She|

|N - Now Predict - what do you need to do to solve the problem? |found that the top GPA was 3.90 if the student did not work at all, and for every |

|R - Read the problem |hour a student worked, 0.10 points were lost. Which of the following best |

|A - Are the important words circled? |describes the relationship Shirley found between the number of hours a student |

|A - Apply steps to solve the problem |worked and the student’s GPA? |

|V - Verify your answer. Is it reasonable? Does it make | |

|sense? |A. As the number of hours worked decreased, |

|E - Eliminate any wrong answers |the GPA decreased. |

|L - Let the answer stay or rework the problem. Double | |

|check your work! |B. As the number of hours worked increased, |

| |the GPA increased. |

| | |

| |C. As the number of hours worked decreased, |

| |the GPA increased. |

| | |

| |D. No apparent relationship between the number of |

| |hours worked and the GPA. |

|To find the image length L of a 40 foot tall object in a spherical mirror with a | |

|focal length of 2 feet, [pic]can be used, where o is the distance, in feet, of the| |

|object from the mirror. What is the image length of the object when it is 1.5 | |

|feet away from the mirror? | |

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|A. 266 feet B. 128 feet | |

|C. 64 feet D. 32 feet | |

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|The value, [pic], of a particular car is related to the previous year’s value, |Jill uses data to find an equation relating the number of hours (h) that students |

|[pic], by the function [pic]. Which statement best describe the change in the |spent working per day at after-school jobs with their last math test grade (G). |

|car’s value from one year to the next? |If her equation is [pic], what is the dependent variable in the relationship? |

| | |

|A. The value is decreasing by 15%. |A. the test grade B. the student |

|B. The value is increasing by 15%. |C. after-school jobs D. the hours worked |

|C. The value is decreasing by 85%. | |

|D. The value is increasing by 85%. | |

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|Mailing a letter costs 37¢ for the first ounce and 23¢ for each additional ounce. |In the equation [pic] if an x-value is increased by 2, what would be the effect |

|Suppose that we want to write a cost function to describe this situation. Which |on the corresponding y-value? |

|of the following is an independent variable? | |

| |A. The value of y will be 3 times as large. |

|A. The letter’s weight B. The mailing cost |B. The value of y will decrease to be [pic]as large. |

|C. 37¢ D. The number of stamps |C. The value of y will increase by 6. |

|needed |D. The value of y will decrease by 6. |

Polynomials Review: Due Exam Day (bring your text book)

|The endpoints of [pic] are G(-3, 7) and H(2, 9). What are the coordinates of the |What is the greatest common factor of [pic]? |

|midpoint of [pic]? | |

| |A. [pic] B. [pic] |

|A. [pic] B. [pic] |C. [pic] D. [pic] |

|C. [pic] D. [pic] | |

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|What is the quotient when [pic] is divided by 3x? |Simplify: [pic] |

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|A. [pic] B. [pic] |A. [pic] B. [pic] |

|C. [pic] D. [pic] |C. [pic] D. [pic] |

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|On a map’s coordinate grid, Panthersville is located at (-3,2), and Heel City is |Which expression is the greatest common factor of |

|located at (4, 8). Falconton is the midpoint between Panthersville and Heel City.|[pic]? |

|What is the approximate distance from Panthersville to Falconton? (One map unit | |

|equals one mile.) |A. [pic] B. [pic] |

| |C. [pic] D. [pic] |

|A. 3.25 miles B. 4.61 miles | |

|C. 5.00 miles D. 9.22 miles | |

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|What is the perimeter of [pic] |

|[pic] |

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|A. [pic] B. [pic] |

|C. [pic] D. [pic] |

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|Good Luck on your EOC tomorrow. Remember, go to bed early, EAT BREAKFAST, take a deep breath and relax. You will be great!!! ( ( ( Your Algebra 1 Teacher |

Answers

Linear Day 1

1. B

2. D

3. A

4. C

5. C

6. C

7. C

Linear Day 2

8. A

9. D

10. D

11. D

12. C

13. D

14. D

15. C

16. B

Matrices

17. C

18. B

19. A

20. A

21. B

Systems of Equations & Inequalities

22. B

23. B

24. C

25. D

26. D

27. C

Exponential Functions

28. A

29. B

30. A

31. D

32. B

33. D

Quadratic Functions

34. C

35. D

36. B

37. B

38. B

39. C

40. C

41. A

42. B

Reading Comprehension

43. C

44. C

45. A

46. A

47. A

48. D

Polynomials

49. B

50. D

51. D

52. D

53. B

54. A

55. D

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