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Name: __________________________________ HSPA OPEN-ENDED PRACTICE PROBLEMS Pay particular attention to the rubric supplied for each problem. A score of 0 points means the response shows insufficient understanding of the problem’s essential mathematical concepts. The procedures may contain major errors or the explanation may be missing or confusing. 1) Tom and Jerry were offered similar jobs at competing companies. Sony offered Tom a starting salary of $32,000 per year with a 7% raise at the end of each year. Panasonic offered Jerry a $35,000 annual starting salary with a 5% raise at the end of each year. A) What is the raise for each of them at the end of the first year with their respective company? B) What will their new salaries be at the end of the first year? C) Generate a table to show each of their salaries for the first 5 years. D) Does Tom’s salary ever exceed Jerry’s salary? Explain your answer. Scoring Assessment: 3: Correctly calculates salaries, generates the correct table, and answers part D correctly. 2: Calculates salaries and generates table; may contain computational flaws. 1: Attempts to calculate salaries and generate table; may contain major calculation errors and incorrect solution to part D. Scores # of students 30 – 50 3 2) MATH TEST 51 – 64 8 65 – 75 22 76 – 90 32 91 – 100 25 A) In order to pass, a score of 65 must be achieved. To the nearest percent, what percent of the students failed the test? B) What interval contains the median score? Why? C) Construct a graph to display the data. What statement can be made based on your graph? D) From the data shown, can you determine the mean score? The median? The mode? Explain your reasoning and show all work. Scoring Assessment: 3: Correctly calculates percentage, generates a correct graph, and answers part D correctly. 2: Calculates percent and generates graph; may contain computational laws. 1: Attempts to calculate percent and generate graph; may contain major calculation errors and incorrect solution to part D. 3) On a TV game show, a contestant first chooses 1 of 3 doors and then chooses 1 of 4 boxes behind that door. Only one of the boxes contains a prize. If a contestant chooses a box that doesn’t contain a prize, the box is removed and the next contestant gets to choose 1 of 3 doors and a box. A) Draw a tree diagram showing the possible choices for the first contestant. B) What is the probability that the first contestant will choose the box containing the prize? Show how you determined your answer. C) If the first 4 contestants all picked a box behind door #1 and did not win, what is the probability that the fifth contestant will choose the box containing the prize? Explain. Scoring Assessment: 3: Correct answers to all 3 parts of the question with tree diagram and work or explanation as required. 2: Correct answer to part A and one other part. 1: Correct answer to one part with supporting work. 4) An auditorium has 20 rows. The first row has 14 seats; each row thereafter has 2 seats more than the previous row. A) How many seats are there in row 10? Explain. B) How many seats are there in the auditorium? Explain. C) The school would like to enlarge their auditorium. If they increase the first row by 6 seats and each row thereafter has 2 seats for than the previous row, can they double the seating capacity without adding additional rows? Justify your answer. Scoring Assessment: 3: Correct answers to all 3 parts of the question with supporting work. 2: Two of 3 parts are completely and correctly done; a computational error in part B that leads to incorrect values in part C will count as one error and part C will be considered correct as long as the process shown is correct. 1: One part is correct with supporting work OR the work shown may not be correct but demonstrates some understanding of the math concepts OR 3 correct answers but supporting work is unclear or incomplete. 5) Jacy, a busy college student who has two part-time jobs, wants to buy a cell phone. She considers the following two plans: Plan A Plan B $20 per month + $26 per month + 12 cents per minute 8 cents per minute A) Based on this information, what is the cost of 130 minutes of phone calls under each plan? B) What length phone call will cost the same under plan A and Plan B? What is that cost? Show your work. C) The cell phone company is considering introducing a third plan. The new plan is based on per-minute charges only. If a phone call of the same length and cost as the call in part 2 is made under this new plan, what must the per-minute charge be? Show work. Scoring Assessment: 3: Correct answers to all 3 parts of the question with supporting work. 2: Two of 3 parts are completely and correctly done; a computational error in part B that leads to incorrect values in part C will count as one error and part C will be considered correct as long as the process shown is correct. 1: One part is correct with supporting work OR the work shown may not be correct but demonstrates some understanding of the math concepts OR 3 correct answers but supporting work is unclear or incomplete. 6) A) Given points A(3,1), B(7,4) and D(8,1) on a coordinate plan, find point C such that a parallelogram is formed. B) Find the slope of each diagonal. Label your responses and show all work. C) Is this parallelogram (from Part A) a rhombus? Use mathematical statements to justify your answer. Scoring Assessment: 3: Correct answers to all 3 parts of the question with supporting work shown and justified for part C; A process error in Part C is a major error. 2: Correct answer to any 2 parts with supporting work as required. 1: Correct answer to part A and correctly determines slope for one diagonal, but supporting work and justification are missing, incorrect, or incomplete. http:///www.census.gov/popest/states/tables/NST-EST2004-01.xls 7) As of October 2005, it is estimated that there are approximately 6,472,000,000 people in the world. In the United States, there are approximately 297,400,000 people. In July 2004, it was estimated that Puerto Rico had 3,895,000 people and New Jersey had 8,699,000. A) Write the current populations of the following in scientific notation: the world: the U.S.: Puerto Rico: B) How much greater is the population of the world than that of the U.S.? How much greater is the U.S. compared with Puerto Rico? Write these answers in scientific notation. Show all work. C) As of July 1, 2004, there were approximately 293,700,000 people living in the United States. Other approximations for July 2004 populations are: New York, 19,227,000; Connecticut, 3,504,000; Pennsylvania, 12,406,000; Maryland, 5,558,000. Including New Jersey, what is the total population for the five states? Write your answer in scientific notation. Show your work. D) Smarty Pants claims that the total population of the states listed in part C is at least 20% of the total population of the U.S. Is Smarty Pants correct? Show your work to explain your answer. Scoring Assessment: 3: Correct answers to all 4 parts of the question with supporting work shown; minor error OK 2: Correct answer to any 2 parts with supporting work as required. 1: Correct answer to 1 part 8) Every Monday at Capri Pizza, lucky customers can get free slices of pizza and free soda. Every 10 th customer gets a free plain slice of pizza and every 12th customer gets a free cup of soda. On the first Monday of the month, Capri pizza had 211 customers. A) How many free slices of pizza were given? How many free cups of soda? B) Jackie was the first person to get a free soda and a free slice. What number customer was she? How many other of the 211 customers got both pizza and soda free? C) Suppose the owner also decides to give away a free bag of potato chips to every 7th customer. Would any of the 211 customers be lucky enough to get all three free items? Explain. Scoring Assessment: 3: Correct answers to all 3 parts of the question with supporting work shown 2: Correct answer to any 2 parts with supporting work as required. 1: Correct answer to 1 part 9) The local A & P offers two brands of cheeses sticks: Brand A = 12 oz. package for $2.49 Brand B = 15 oz. package for $3.19 A) Which is the better buy? Show how you arrive at your answer. B) Suppose the one that is a better buy now has a 10% price increase. Is it still the better buy? Explain. Scoring Assessment: 3: Correct answers to both parts of the question with supporting work shown and justified. 2: Correct answer to part A with supporting work as required and attempt at part B, with plausible explanation OR incorrect answer in part A leading to error in part B, but processes for both parts are correct. 1: Correct process but arithmetic error in part A leads to incorrect answers in both parts. 10) WCHS, announces weather updates every 30 minutes. Another station, WWET, announces weather updates every 25 minutes. A) WWET claims they give weather updates over 50 times a day. Is the station’s claim true? Explain your answer. B) If both stations announce weather at 8 a.m., when is the next time the will both announce weather at the same time? Explain. C) WBOR announces weather every 17 minutes. If all 3 stations start announcing the weather updates at the same time, will there ever be another time during the first 24 hours when all 3 stations announce the weather at the same time again? Explain. D) If all 3 stations start announcing the weather updates at the same time, when is the next time they will all announce weather together? Explain. Scoring Assessment: 3: Correct answers to all parts of the question with supporting work shown and justified. 2: Correct answer to 2 of the 4 parts with supporting work as required. 1: Correct answers to all 4 parts with no work OR inadequate explanations for 3 parts OR correct answers for 2 of the 4 parts with incomplete explanations.

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posted: | 6/18/2012 |

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