Study Questions for Exam

1. You randomly survey people in the mall about whether or not they regularly use text messaging. The results are shown in the tally sheets below based on the people’s ages.
a.Make a two-­way table that includes the marginal frequencies.
b.Make a two­-way table that shows both the joint and marginal relative frequencies. Round to the nearest hundredth, if necessary.
c.What is the probability that someone who is between the ages of 20-29 also texts regularly?
d.What is the probability that someone who is between the ages of 40-49 also texts regularly?
e.Does the data show a relationship between age and texting? Explain.
2. The data below represents the number of hits on your web site over 10 months.
a.Make a scatter plot of ln ?y? versus ?x?. Use the scatter plot to find the equation for the line of best fit.
b.Make a scatter plot of ln ?y? versus ln ?x?. Use the scatter plot to find the equation for the line of best fit.
c.Based on your answers in part a and b, would an exponential model or a power model be better to represent this data? Explain.
d.Use your answers from parts a and b to find an exponential model and a power model to represent this data by hand.
e.Use the regression feature on your calculator to find an exponential model and a power model to represent this data.
f.Use your answer from parts c and d to make the ?best? estimate for the number of hits your web site will have in 12 months.
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Study Questions For Upcoming Exam
1. Solve the system of equations below both algebraically and by graphing. Be sure to show all
of your work and state your solution as an ordered pair.
2. The population of a country is initially 2.5 million people and is increasing by 0.8 million
people every year. The country’s annual food supply is initially adequate for 4 million people
and is increasing at a constant rate for an additional 0.4 million people per year.
a. Based on these assumptions, in approximately how many years will the country first
experience shortages of food?
b. If the country doubled its initial food supply and maintained a constant rate of increase in the
supply adequate for an additional 0.5 million people per year, would shortages still occur? If so,
how many years would it take for shortages to occur? If not, explain.
c. If the country doubled the rate at which its food supply increases, in addition to doubling its
initial food supply, would shortages still occur? If so, how many years would it take for
shortages to occur? If not, explain.
3. Springfield will be opening a new high school in the fall. The number of underclassmen (9th
and 10th graders) must fall between 500 and 600 (inclusive), the number of upperclassmen (11th
and 12th graders) must fall between 400 and 500 (inclusive), and the number of students cannot
exceed 1000.
a. Let x represent the number of underclassmen and y represent the number of upperclassmen.
Write a system of inequalities that models the situation.
b. Graph the solution to the system of inequalities in part a.
4. A projectile is fired upward from the ground with an initial velocity of 300 feet per second.
Neglecting air resistance, the height of the projectile at any time t can be described by the
polynomial function P(t) = 16t2 + 300t
a. Find the height of the projectile when t = 1 second.
b. Find the height of the projectile when t = 5 seconds.
c. How long will it be until the object hits the ground?
5. A board has length (3×4 + 6×2 18) meters and width of 2x + 1 meters. The board is cut into
three pieces of the same length.
a. Find the length of each piece.
b. Find the area of each piece.
c. Find the area of the board before it is cut.
d. How is the area of each piece of the board related to the area of the board before it is cut?
6. A cubic equation has zeros at 2, 1, and 3.
a. Write an equation for a polynomial function that meets the given conditions.
b. Draw the graph of a polynomial function that meets the given conditions.
7. Alice was having a conversation with her friend Trina, who had a discovery to share:
Pick any two integers. Look at the sum of their squares, the difference of their squares, and
twice the product of the two integers you chose. Those three numbers are the sides of a right
triangle.
a. Write an equation that models this conjecture using the variables x and y.
b. Investigate this conjecture for at least three pairs of integers. Does her trick appear to work in
all cases, or only in some cases? Explain.
c. Use Trina’s trick to find an example of a right triangle in which all of the sides have integer
length, all three sides are longer than 100 units, and the three side lengths do not have common
factors.
If Trina’s conjecture is true, use the equation found in part a to prove the conjecture. If it is not
true, modify it so it is a true statement, and prove the new statement.
Study Questions For Exam 2
1. A label on an iced tea drink mix says to use 2 tbsp of iced tea mix to make one serving (8 oz)
of iced tea.
a. What is the ratio of drink mix to iced tea? (Hint: 1 oz = 2 tbsp)
b. Suppose you want to make a quart (32 oz) of iced tea. How many ounces of drink mix should
be used?
c. How many tablespoons of iced tea mix should be used to make a quart (32 oz) of iced tea?
2. ? RST has coordinates R(-4, -3), S(0, 5), and T(7, -3).
a. Graph ? RST in a coordinate plane.
b. Find the perimeter of ? RST.
c. Find the area of ? RST.
d. The centroid of a triangle is the intersection of its medians. Use the following steps to find the
centroid of ? RST using segment partition.
i. Find the midpoint of
. Label it N.
ii. Find the point, C, that partitions
such that SC:CN has a ratio of 2:1 .
iii. Plot point C in your graph of ? RST.
e. Find and graph the midpoints of
,
opposite each midpoint to the midpoint.
,and
. Draw a segment connecting the vertex
i. How does the intersection of the segments compare to point C from question 4?
3. Brian is renting an apartment. The floor plan of the apartment is shown below.
a. What is the total area of the apartment?
b. What are the dimensions of the master bedroom?
c. Brian wants to buy a dining room table from the local furniture store. He sees a table that is 9
ft long and 3 ft wide. Would it be reasonable to buy this table to put in the dining room? Why or
why not?
1. You randomly survey people in the mall about whether or not they regularly use text
messaging. The results are shown in the tally sheets below based on the people’s ages.
a. Make a two-way table that includes the marginal frequencies.
b. Make a two-way table that shows both the joint and marginal relative frequencies. Round to
the nearest hundredth, if necessary.
c. What is the probability that someone who is between the ages of 20-29 also texts regularly?
d. What is the probability that someone who is between the ages of 40-49 also texts regularly?
e. Does the data show a relationship between age and texting? Explain.
2. The data below represents the number of hits on your web site over 10 months.
a. Make a scatter plot of ln y versus x. Use the scatter plot to find the equation for the line of
best fit.
b. Make a scatter plot of ln y versus ln x. Use the scatter plot to find the equation for the line of
best fit.
c. Based on your answers in part a and b, would an exponential model or a power model be
better to represent this data? Explain.
d. Use your answers from parts a and b to find an exponential model and a power model to
represent this data by hand.
e. Use the regression feature on your calculator to find an exponential model and a power model
to represent this data.
f. Use your answer from parts c and d to make the best estimate for the number of hits your web
site will have in 12 months.

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