HSPA Review Questions
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.
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 expression
has the same value as
–3 x |4-7|?
2
5.2 X 10 =
-2
3.5 x 10 =
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
28
16
10 ) x (8.9 x 10 ). 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
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
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
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
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
Standard 4.2:
Geometry and Measurement
How many square feet of tile are needed to cover the floor?
7 ft.
8 ft.
14 ft.
12 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 to
create the triangle DEF?
A stone mason is repaving a school's courtyard with the following 3color 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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2a/math_module_2a_sample1.
htm
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
f 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?
I
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_2/2a/math_module_2a_sample3.
htm
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
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
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
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
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
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
AZ
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
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.
A
The table below shows a pattern.
Which formula represents the function shown?
x
0
1
2
3
4
A
y
0
-1
0
3
8
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3a/math_module_3a_sample1.
htm
Analyze the pattern below. What letter will
th
be in the 76 position? Show your work
and explain your answer.
MATHMATHMATHMA…
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3a/math_module_3a_sample2.
htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3b/math_module_3b_sample1.
htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3b/math_module_3b_sample2.
htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3b/math_module_3b_sample3.
htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3c/math_module_3c_sample1.
htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3c/math_module_3c_sampl
e2.htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_3/3c/math_module_3c_sampl
e3.htm
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 propertythere 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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4b/math_module_4b_sampl
e1.htm
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
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4b/math_module_4b_sampl
week
old child would sleep.
e2.htm
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.
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4b/math_module_4b_sampl
e3.htm
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.
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4c/math_module_4c_sampl
e1.htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4c/math_module_4c_sampl
e2.htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4c/math_module_4c_sampl
e3.htm
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:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4a/math_module_4a_sampl
e1.htm
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.
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4a/math_module_4a_sampl
e2.htm
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.
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4d/math_module_4d_sampl
e1.htm
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.
Solution:
http://www.state.nj.us/education/njpep/assessment/hspa/hspa_math/module_4/4e/math_module_4e_sampl
e1.htm
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 integer
Clue 2. When squared, I remain less than 1000
Clue 3. When cubed, I become greater than 20,000
Clue 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:
A = P ( 1 + nr ) nt
where P is the amount of money in the account
at 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.