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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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