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HSPA Review Questions

-5. 5. -1. -2. 0. 3. 4. -3. 2. -4. 1. HSPA Review Questions. Open Ended Response. 3-Point Response

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HSPA Review Questions

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  1. -5 5 -1 -2 0 3 4 -3 2 -4 1 HSPA Review Questions

  2. Open Ended Response 3-Point Response The response shows complete understanding of the problem's essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made. 2-Point Response The response shows nearly complete understanding of the problem's essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences. 1-Point Response The response shows limited understanding of the problem's essential mathematical concepts. The response and procedures may be incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made. 0-Point Response The response shows insufficient understanding of the problem's essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.

  3. Standard 4.1: Number and Numerical Operations

  4. What is the product of 5.1 and 0.47 approximately equal to?

  5. Which of the following sets of numbers includes only prime numbers?

  6. Alan bought a dozen donuts. He gave half to his mother, kept a third of the remaining donuts for himself, and gave the rest to friends. How many donuts did Alan keep?

  7. Which of the following expressions has the same value as –3 x |4-7|?

  8. 5.2 X 102=

  9. 3.5 x 10-2=

  10. Which of the following results in a negative number?

  11. Which of the following sets of numbers are equal?

  12. A stereo you want is on sale at 15% off the manufacturer’s retail price of $445. You have an additional coupon for 10% off after the sale discount has been computed. How much will the stereo cost?

  13. Joe receives a weekly paycheck. He immediately puts 10% of his salary each week into a savings account. If Joe can spend everything he doesn't save and won't take any money back out of his savings account, what would Joe's minimum salary have to be so he would have $250 to spend each week?

  14. Sherise wants to raise her English grade from 83 up to a 90. Approximately what percentage increase would that represent?

  15. Ellen was tutoring Susan in mathematics at the library. Susan had to find the product of (5.3 x 1028) x (8.9 x 1016). They both forgot their calculators. How could Ellen explain how to find this product without using a calculator? Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1a/math_module_1a_sample1.htm

  16. Maurice and Aldo both go to the same library. The last time they saw each other was last Thursday. Maurice goes to the library every seven days. Aldo goes to the library every five days. · How many days, from their last meeting, will they both be at the library together? · Show how you arrived at your answer. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1a/math_module_1a_sample2.htm

  17. Jason’s Discount Store is having a Holiday Sale. During this sale, a pair of pants is reduced by 30%; then an additional 15% is taken off of the reduced price at the cash register. The original cost of the pants is $35.99. · How much would a customer pay for these pants? · How much would the pants be if they are sold at a one time discount of 45% off the original cost? · Why didn’t the store sell these pants for 45% off the original cost? Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1b/math_module_1b_sample1.htm

  18. Angela has applied for a job as a florist. She had to choose between two salary options. Plan 1: $800 a month+ 6% of monthly sales, or Plan 2: 10% of monthly sales. Sales for the prior months were: · January - $9,000 · February - $15,000 · March- $6,000 · April- $ 12,000 Based on this information, which salary option should Angela select if she decides to accept the job? Explain your answer. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1b/math_module_1b_sample2.htm

  19. Naser owns a rare stamp collection. There are 45 rare stamps in his collection. He wants to divide the stamps among his 3 children. He requested that the oldest child receive 4/5 of the collection, the middle child receive 1/10 of the collection and the youngest child receive 1/15 of the collection. His children met and tried to figure out how to distribute the stamps according to their father’s specifications. · How many stamps should each child get? · Did Naser choose the fractional parts each child was to receive in the best way? Explain why or why not. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1b/math_module_1b_sample3.htm

  20. Standard 4.2: Geometry and Measurement

  21. 7 ft. 8 ft. 14 ft. 12 ft. How many square feet of tile are needed to cover the floor?

  22. Which of the following figures has the same fractional part of its area shaded as the sample below?

  23. Each day, John attends school for 7 hours a day, watches 3 hours of television, visits with friends for 4 hours, sleeps for 8 hours, rollerblades for 1 hour, and has family time for 1 hour. What percent of his day awake is he not in school?

  24. The area of a circle 8 inches in diameter is greater than the combined areas of a circle 6 inches in diameter and a circle 2 inches in diameter by approximately how many square inches?

  25. A right triangle is constructed with points F (1,-1), G (4,5), and H (- 5,2) as its vertices. Which of the following statements is true?

  26. Parents are building a playground for the community's children. They plan to build a sandbox by using railroad ties to form a proportionally similar triangle to the one shown below. Which combination of ties should they use? 8 ft. 6 ft.

  27. A graphic artist designing a company's logo wants to reflect triangle LMN across the dotted line to form triangle PQR. What will the vertex of point P be?

  28. What must happen to triangle ABC to create the triangle DEF?

  29. A stone mason is repaving a school's courtyard with the following 3-color tiles. Given that he is only using these tiles, what color will the white stone in the large area be? This is one tri-colored tile.

  30. Which addition problem is represented by the following vector diagram? (Assume that the origin is the starting point.)

  31. Polygon ABCD is congruent to polygon WXYZ, where angle A corresponds to angle W. The value of angle A is 4x - 30 and the value of angle W is 2x + 10. Find angle A.

  32. A packaging company is designing various packages to hold salt water taffy, offering the customer choices in shape. All of the boxes must hold the same volume, however. Given the following two choices, what is the value of side x ? (Figures are not drawn to scale.)

  33. The water company is stacking cylindrical pipes as shown to the right. Each pipe is 30 inches in diameter. How high will the stack be?

  34. A local pizza parlor sells a special "Everything-On-It" pie in two sizes: a 12" pie for $8 and a 16" pie for $10. You want to know which pie is the better deal. What is the approximate price per square inch for the 12" pie and the 16" pie, in that order?

  35. A carpenter positions the bottom of his 45 foot ladder 5 ½ feet from the base of a building to fix a broken window. How high up on the building will the ladder reach to enable the carpenter to fix the window? Explain and show all of your work. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2a/math_module_2a_sample1.htm

  36. If a rectangular stick of butter, as shown below, measures 6 in. x 2 in. x 1 in. ·What is the volume of the stick of butter? (in square inches) ·If you take ½ (or 50%) off each side of this stick of butter, what us the volume of the new solid? (in square inches) ·What is the ratio of the volume of the original stick of butter to the volume if the second? Explain and show your work. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2a/math_module_2a_sample2.htm

  37. If you line up 30 squares in a row, side by side, as shown below, with each side equal to 6 inches, what would the perimeter of the figure be? Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2a/math_module_2a_sample3.htm

  38. Draw a parallelogram that has the same area as the triangle shown below. Explain and show all of your work. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2b/math_module_2b_sample1.htm

  39. A car starts at point A, travels 8 miles east, and then turns and travels 10 miles south to reach point B. ·Using graph paper, make a scale drawing using vectors to show the cars movement, starting from point A. ·Draw a vector that would show the direct path from point A to point B. What would be the approximate number of miles the car could have traveled along this path? ·Approximately how many degrees from north would this path be? Explain how you arrived at this answer. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2b/math_module_2b_sample2.htm

  40. A rectangular vacant lot is 100 feet long. Its area (in square feet) is twice its perimeter (in feet). How wide is the lot? Show all of your work and justify your answer. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2c/math_module_2c_sample1.htm

  41. In triangle XYZ, angles x and y are congruent. What is the length of YZ? Explain and show all your work. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2c/math_module_2c_sample2.htm

  42. Circle A has a radius of 10 inches. How much greater than its area is the area of Circle B whose radius is twice as large? Explain and show how you arrived at your answer. Solution: http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2c/math_module_2c_sample3.htm

  43. Standard 4.3: Patterns and Algebra

  44. A garden center is growing bean plants using a new fertilizer. At the end of each week, they record the number of new sprouts. Using the information above, how many sprouts should the center expect at the end of the seventh week?

  45. Jessie's business partner set a computer password on the office computer and went on vacation. Jessie remembered that the password is a simple pattern. The first few letters of the password are A Z D Y G X ____ Assuming that the pattern continues, what is the next and final letter of the password?

  46. Jose's cousin owes him $50. He offers to pay Jose $30 today, and tomorrow pay him one-third of what he paid today. If this pattern of paying one-third what he paid the day before continues, how much money will Jose's cousin have paid back in total by the end of day 4? D

  47. Kylee and Robin are racing their pet turtles. Kylee's turtle starts at 1/2 foot from the starting line and moves at 4 inches per minute. Robin's turtle starts at the starting line and moves at 6 inches per minute. Assuming they move in the same direction, where are the turtles after 5 minutes? A

  48. You find the code sheet for a secret code, but something was spilled on one row. See if you can recognize a pattern and complete the missing row. A

  49. x y 0 0 1 -1 2 0 3 3 4 8 The table below shows a pattern. Which formula represents the function shown? A

  50. Lauren goes into a music store where all CDs are marked 12% off. If she buys n CDs for 16.99 each, how much money will she need? C

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