HSPA Review Questions

HSPA Review Questions

-1 0-2-3-4-5

1 2 3 4 5

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 ResponseThe 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.

Open Ended Response

Standard 4.1:

Number and Numerical Operations

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

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

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?

Which of the following expressions has the same value as

–3 x |4-7|?

5.2 X 102=

3.5 x 10-

2=

Which of the following results in a negative number?

Which of the following sets of numbers are equal?

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?

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?

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

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?

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1a/math_module_1a_sample1.htm

Solution:


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. http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1a/

math_module_1a_sample2.htm

Solution:


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?

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_1/1b/math_module_1b_sample1.htm

Solution:


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:


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:


Standard 4.2:

Geometry and Measurement

How many square feet of tile are needed to cover the floor?

14 ft.

12 ft.

8 ft.

7 ft.

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

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?

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?

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?

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.

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?

What must happen to triangle ABC tocreate the triangle DEF?

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.

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

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.

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.)

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?

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?

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:


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:


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:


Draw a parallelogram that has the same area as the triangle shown below. Explain and show all of your work.


Solution:


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:


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.

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2c/math_module_2c_sample1.htm

Solution:


In triangle XYZ, angles x and y are congruent. What is the length of YZ? Explain and show all your work.


Solution:


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:


Standard 4.3:

Patterns and Algebra

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?

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?

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

A

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

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.

The table below shows a pattern. Which formula represents the function shown?

0 01 -12 03 34 8

x y

A

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

A local jewelry dealer calculates the price at which he will buy back gold jewelry based on the following formula: B = .75(G - 15) + .15G, where B is the "buyback" price and G is the current market value of the gold. You bring in a gold bracelet with a current market value of $105. What will the dealer pay you for the bracelet?

D

James came home from school with 16 hours of homework. He had three times as much English homework as he had math. How much math homework did he have?

B

Roland just bought a used car that has a capacity of 1500 pounds. If he and his brother weigh 320 pounds together, which of the inequalities below could be used to find the maximum number of additional friends who can ride in his car (assume an average weight of 160 pounds).

A

In 2000, a particular technology stock dropped quickly, and then leveled off. Which of the graphs below best represents that stock's performance?

A

A bag of jelly beans includes only r red and y yellow jellybeans. If Violet removes 1 red jellybean, what fractional part of the jelly beans in the bag are red?

A

If @ is defined for all positive numbers a and b by a @ b = 2ab - b2 , then 5 @ 3 =

C

What is the inequality for the following graph?

B

A Web designer is building pages that are 600 pixels wide and 480 pixels high. She wishes to place an image on the page that is proportionate to those dimensions.The image is 320 pixels wide. How high will it have to be?

A

Belinda wants to determine the number of dots in the 30th step of the following pattern, but she does not want to actually draw all 30 steps.

·Explain how Belinda could find the number of dots in Step 30 without actually drawing them. ·What would be the number of dots in the 30th step? ·Write an algebraic expression for the number of dots in the nth step.


Solution:


Analyze the pattern below. What letter will be in the 76th position? Show your work and explain your answer.

M A T H M A T H M A T H M A …


Solution:


Judge Esther Odometer developed a formula to determine the fine for speeding on the parkway in her town. The formula she developed is:

F = 12(R – 60) + 55

In this equation, F represents the total amount of fine, R represents how fast (rate of speed) the car was going in miles per hour.·A car has been stopped for traveling 75 mph, 80 mph, 87 mph, 90 mph, and 100 mph over the course of the past year. Show the domain and range for this relation.·Judge Esther charges you a fine of $175 for speeding. Is this a reasonable fine? Why or why not


Solution:


Sharifa is offered two jobs: one at Tom’s World of Music and one at Rosie’s Café. Tom's promises her a salary of $30,000 and a raise of $500 each year. Rosie's offers her a salary of $30,000 and a raise of 4% of her current salary each year. Which job should she accept? Explain your answer. Show all work.


Solution:


Mike dropped a basketball ball from his bedroom window a height of 20 feet. Each time the ball bounced, it reached a maximum height of approximately half that of its previous height. ·Draw a graph to represent the relationship between the number of times the ball bounces and the height reached by the ball. ·What is the total of the heights the ball reached after the 4th bounce. ·What do you think this total would have been if the ball had bounced 20 times?


Solution:


Diana had $1200 in her checking account. She withdrew the same amount each month for 5 months to pay for a car loan. At the end of 6 months, she deposited an additional $600 into her account. Her new balance was $800. ·How much money did she withdraw each month? ·What was her account balance after the 6 months before her deposit of $600? Explain and show all your work.


Solution:


John and Ellen work in a clothing store after school. John’s boss told him to reduce every item in the store for a 2-day sale by 30%. After the sale, John’s boss told her to increase every sale item’s sale price by 30%. John started marking each item with the original price. Ellen said, “That is wrong! If you increase the sale price by 30% you will not get the original price." ·Who is right? Show your work. You may wish to include a simple, specific example to support your answer.


Solution:


You are the service manager at an auto repair shop. You charge $22 per hour for labor plus the cost of any parts. A car needed $256 of new parts. The final bill for the car was $421. ·How long did it take to repair the car? Explain your answer. ·Write an algebraic equation to solve this problem. Show all work.


Solution:


Standard 4.4:

Data Analysis, Probability, Statistics & Discrete Mathematics

The 315 members of the Smithfield High School Sophomore class voted to see what kinds of movies the class liked. Their results are below. If they had an "Action Movie Night" fundraiser and sell tickets for $4 each, approximately how much money should they expect to raise? Assume that students who like the type of movie will be the only ones in attendance.

C

David is on the school's track team. This season, he has run the 400m sprint in the following times: 51.5s, 50.7s, 50.5s, 50.7s, 51.0s, and 50.0s. The coach is deciding who is going to run on the state 4 x 400 relay team. What are David's mean, median, and mode so far this season?

D

Which of the following is the most appropriate time to use a scatterplot?

A

A liquid substance in a science experiment doubles in volume every two minutes. The experiment begins at 1:00PM with a small amount of the substance being placed in a large beaker. At 2:00PM the container is full. At what time was the container one-eighth filled?

D

In the following equation C represents total car rental fee and d represents days rented. What is the slope (m) of this equation?

C = 15d + 20

B

A study recently resulted in the results shown below. Based on the data for the chart below, which choice would best help predict a reading ability at a certain age?

D

Four of Kira's six biology test scores this semester were: 95, 97, 92, and 87. If the mode for all six scores is 98, what is the mean for all six scores, to the nearest tenth?

B

How many matches will it take to determine the winner of a singles racquetball tournament with 35 players?

RideRight and CheapWheels (two automobile rental companies) are merging their businesses and, therefore, their automobile fleets. The following matrices represent the two companies' inventories, with the rows representing sub-compacts, compacts, mid-size, and full-size and the columns representing red cars, gold cars, and white cars. After the merger, how many compact cars (the most popular rental) will be in the new fleet?

D

The following table indicates the US Census Bureau's

population predictions from 1995 to 2025.

Which state shows the largest percentage growth in population from 1995 to 2025?

B

The following graph shows how Todd spends his time in the course of a day. According to this graph, how many hours a day does Todd typically spend doing homework?

A

In a school of 375 students, 225 students play on sports teams, 132 students are in the chorus, and 46 participate in both activities. How many students are in sports but not chorus

A pair of dice is thrown. What is the probability of not throwing a double?

A

A drawer contains 4 red pens, 5 blue pens, and 2 black pens. If you reach into the drawer without looking and pull out a pen for you and a pen for your work partner, what is the probability that the first pen will be blue and the second pen will be black?

You and 5 friends go on a roller coaster in which each car holds a pair. How many different pairs can you and your friends create for the ride?

In the Lucky Sevens Lottery, 100 numbered tokens (1-100) are mixed in a box. A lottery agent then picks 10 of the tokens from the box. Each time a token is removed, it remains outside the box. Thirty-four of the tokens contain the digit 7. If three numbers with the number 7 are picked in a row, you win! The agent picks 7 tokens, none of which have 7s. What is the probability that the agent will pick 3 tokens in a row with the digit 7, making you a winner?

A local man has a property that is 600 feet wide and 200 feet long. His house is 50 feet wide by 30 feet long. He is away on vacation but his neighbor just called to tell him that lightning struck his property, but he does not know where. What is the probability that lightning struck his home? (Assume that lightning is equally likely to strike anywhere on the property- there is nothing that would attract or repel lightning anywhere on his property.)

The following diagram represents an airline's direct travel routes between 6 cities. Which matrix below can represent this direct-route air network? (A 0 indicates no direct route between the two cities, or no travel needed; a 1 indicates a direct route.)

How many different ways can you put 6 books in a row so that one specific book is always in the 4th position?

You and a group of 9 friends are playing pickup basketball in a local park. At the end of the game, if each player shakes hands with every other player, how many handshakes will there be?

The Orchid Orchard has 5,000 orchid plants to sell. Each month the orchard plans to sell 12% of its orchids and start 600 new plants. Which of the following statements is true?

A design follows this pattern: a square is divided in half by drawing another square inside of it on a 45 degree rotation. The outer area is then shaded. Then, the unshaded area is divided again in the same manner. Assume that the pattern stays the same, what is the ratio of the shaded area to the unshaded area in Stage 3?

Cass has $4,000 that she is saving to buy a $7,000 car. She has decided to invest this money in an investment that will return 12% each year. . She makes no withdrawals but she doesn't deposit any more money. If all of her earnings are reinvested, how many years will it be until she can buy her car? (Assume that the price of $7,000 includes all extras: license plates, taxes, etc.)

You have a watch collection of 10 watches. Three of the watches have timers. One beeps every 5 minutes; one beeps every 12 minutes; one beeps every 15 minutes. They just beeped together at 3:00PM. When will they beep together again?

Your science class’ pet mice Mickey and Minnie just gave birth to 6 babies: 3 males and 3 females. The teacher informs you that the baby mice can breed when they are 6 weeks old and the babies are born 3 weeks later. If each female mouse has a litter of 6 babies, half males and half females, how many mice will you have 12 weeks from now?

Which of the following types of numbers would solve the equation x² = 15?

a. Whole number b. Fraction c. Terminating decimal d. Irrational number

d

Which of the following is an irrational number?

a. 3.01 b. 3.010010001... c. 3.01 d. 3 1/100

b

Scientists record data from experiments with hope of eventually finding patterns that will enable them to predict future results. For example, in testing an antibacterial ointment, a chemist might record the number of bacteria present in a tissue culture after using the ointment for different periods of time. The table below shows a record of the number of hours and the number of bacteria.

·Make a scatter plot of this data. ·Does there appear to be a relationship between time and the effectiveness of the ointment? Use the scatter plot to support your answer. ·After how many hours do you expect one-half of the bacteria to be terminated? Do you expect that all the bacteria will be terminated?


Solution:


The data in the table shows the age, t ( in weeks) and the number of hours, h, slept in a day by 24 infants who are less than 1 year old.

·Draw a scatter plot to represent the data. ·Using your scatter plot, what type of correlation do t and h have? Explain how you arrived at your answer. ·Using the scatter plot, predict the number of hours a 65 week old child would sleep. http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4b/

math_module_4b_sample2.htm

Solution:


New Jersey’s population, p (in millions) from 1900 to 2000 is shown in the table below.

·Sketch a scatter plot Let t = 0 represent 1900. Label your graph with appropriate values for time and population. ·Using your scatter plot, what type of correlation do p and t have? Explain how you arrived at your answer. ·Predict what the population of New Jersey will be in the year 2010. Explain the strategy that you used to make the prediction. http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4b/

math_module_4b_sample3.htm

Solution:

A group of friends attending college in Jersey City decide that, during spring vacation, they will visit the following cities by car: Atlantic City, NJ, Philadelphia, PA, and the Delaware Water Gap, NJ. There are many choices as to the order of visiting the cities and returning to Jersey City. The friends want to design a route that minimizes the distance they will be traveling while maximizing the time visiting their friends.

·Describe the route for the minimum length trip for the friends to take to visit the three cities and to return to Jersey City. ·Explain why you think this is the minimum distance and the method you used to find it.http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4c/math_module_4c_sample1.htm

Solution:

Study the information in each of the following charts.

Based on the different sets of data displayed by the each of the charts, describe the type of graph that should be used to display each set of data. Explain why you selected each type of graph.


Solution:

The chart below shows the gross income (in millions) of Company ABC for the years 1990 to 1999.

·Find the mean, median, mode and range of the Company’s yearly gross income for the years indicated in the table.·Predict what the Company’s gross income will be for the year 1999 - 2000.


Solution:

Continental Airlines advertises that its flights are on time. The chart below displays a consecutive 12 day period and is representative of most 12 day periods for the last 3 months. Study the chart, which shows the touchdown times for Flight 288 which had on-time departures at 10:00 A.M. for the 2 hour and 40 minute flight to Florida from Newark.

·Explain why the advertising claim of on time arrivals is incorrect for this flight. ·Determine the probability of arriving in Florida late if this flight is taken. ·If Flight 288 is late, predict how many minutes late the flight will be and explain how you made the prediction.


Solution:

For a probability experiment, Mr. Rivas placed 6 red, 8 blue, 4 white, and 6 yellow marbles, all of which were the same size into a bag. Eighteen students each made 30 random selections from the bag of marbles, making sure to record each pick before replacing the marble. The chart below shows each student’s picks.

·Give the theoretical probability for selecting each color marble. ·Compare the experimental probability for each color to the theoretical probability for each color. ·Describe what should happen if the class conducted the same experiment for 5 days and examined the total results for each color for the 3,000 picks. http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4a/math_module_4a_sample2.htm

Solution:

At Johnny’s Burger Place, a customer can get a customized meal by ordering either a turkey burger, chicken burger, hamburger, or garden burger with a side order of potato chips or french fries with a choice of either juice, milk, or soda. ·Use a tree diagram to list all the different combinations of a burger, side order and a drink. ·Describe ways and give examples of how Johnny could change his menu so that a customer would have 30 different choices.

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4d/math_module_4d_sample1.htm

Solution:

Before Jason pays 25% tax on the 8% commission he makes on every house he sells at Top Notch Real Estate Agency, he deducts 12% of the commission for expenses to determine the amount of taxes to be paid. ·Write a set of steps that any Top Notch employee could follow, using the same procedure as Jason. ·Test out your steps by computing the amount of taxes Jason would pay on a $250,000 home.

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4e/math_module_4e_sample1.htm

Solution:

The picture below shows stages 1 and 2 of a geometric progression that follows this rule: In a triangle, a line is drawn from the middle of each leg to the middle of the hypotenuse. The legs of the new triangles are 1/2 the length of the previous triangle's legs. Stage 1 and Stage 2 of an right triangle are shown below:

·Find the area of the triangle in Stage 1. ·Draw stage 3 and Stage 4 ·Find the total area of the all shaded triangles in Stage 3 and Stage 4. ·Will the total area of the shaded triangles in any stage ever exceed the area of the triangle in Stage 1? Explain your answer.

http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4e/math_module_4e_sample2.htm

Two cars are driving around a two-mile track. One car makes a lap every 80 seconds, and the other every 60 seconds. At these rates, how long will it take the faster car to gain exactly one lap on the slower car?

(Answer: 4 min.)

Use the clues to determine the number.

Clue 1. I am an integerClue 2. When squared, I remain less than 1000Clue 3. When cubed, I become greater than 20,000Clue 4. When raised to the 4th power, I remain less than 700,000

(Answer: 28)

In the compound interest formula A = P(1 + r/n)nt, A represents the value of the investment in the future, P is the amount of the original investment, r is the annual interest rate, t is the number of years of the investment, and n is the number of times the interest is compounded each year. Find the total amount after $2500 is invested for 18 years at a rate of 6%, compounded quarterly.

(Answer: $7302.89)

A bank offers an interest rate of r compounded n times per year. The formula for the amount of money, A, in an account at the end of t years, is:

where P is the amount of money in the accountat the beginning of the year (assuming no deposits or withdrawals).

A) If at the beginning of the year Joe had $1,000 in an account with 2% interest compounded semiannually, how much money would he have in the account at the end of the year? Show your work or provide an explanation for your answer.

B) The effective interest rate, R, is the percent increase in the account over one year. What is the effective interest rate for Joe's account? (Do not round your answer.) Show your work or provide an explanation for your answer.

C) Joe had x dollars in his account at the beginning of the year. Describe how to determine the amount of money Joe would have in his account after 1 year using the effective rate you found above.

A = P ( 1 + r ) nt n

Date post:	14-Jan-2016
Category:	Documents
Upload:	abby
View:	26 times
Download:	3 times

HSPA Review Questions

Documents