Midterm Exam Review
1)
Identify a pattern in the following lists of numbers. Then use this pattern to find the next
number.
1 1 1
, ___
3 9 27
a) 1, , ,
b) 125, −25, 5, −1, ___
2)
Identify the reasoning process, inductive or deductive, in each example below.
a) All books by Stephen King have made the best-seller list. Carrie is a novel by Stephen King.
Therefore, Carrie was on the best-seller list.
b) All books by Stephen King have made the best-seller list. Therefore, it is highly probable
that the novel King is currently working on will make the best-seller list.
3) Determine the following estimates without a calculator. Then use a calculator to perform the
computation necessary to obtain an exact answer. How reasonable is your estimate when
compared to the actual answer.
a) Estimate the total cost of six grocery items if their prices are $8.47, $0.89, $2.79, $0.14,
$1.19 and $4.76.
b) Estimate the salary of a worker who works for 70 hours at $9.25 an hour.
4)
Match each graph to the scenario below. Graph time on the x-axis and distance on the y-axis.
a)
b)
c)
d)
Traveling at a steady rate.
Traveling at a fast pace, then changing to a slower pace when traffic gets heavy.
Traveling at a slow pace then rapidly increasing.
Traveling at a steady pace then stopping for a while.
5) A manufacturer packages its apple juice in bottles and boxes. A 128–ounce bottle costs $5.39,
and a 9-pack of 6.75 boxes costs $3.15. Which packaging option is the better value?
6) One person earns $48,000 per year. Another earns $3750 per month. How much more does the
first person earn in a year than the second?
7) Use dimensional analysis to convert the quantity to the indicated unit. If necessary, round the
answer to two decimal places. (You should know basic conversions such as inches to feet, feet to
yards, grams to kg, mg to g, etc..) You will be given a table of English to Metric conversions.)
a)
b)
c)
d)
e)
0.75 mi to ft
21 yd to inches
12 m to yd
776 mi to km
14 in to cm
8) Convert the given square unit to the square unit indicated. (You will be given a table with
conversion units provided).
a)
b)
c)
d)
4 in.2 to cm2
14 mi2 to km2
1496 gal to ft3
150 mL to cm3
9) The prescribed dosage of a drug is 10 mg/kg daily, meaning that 10 milligrams of the drug should
be administered daily for each kilogram of a patient’s weight. How many 400-milligram tablets
should be given each day to a patient who weighs 175 pounds?
10) The average temperature of Plateau, Antarctica is -56.7 °C. The average temperature of
Amundsen-Scott, Antartica is -56.2 °F. Which location has the cooler average temperature and
by how much?
11) Tell whether the following statement makes sense or does not make sense. Be able to explain
your reasoning.
When I played high school basketball, I weighed 250 kg.
12) A man who is 6 feet tall is standing 10 feet from the base of a lamppost. The man’s shadow has
a length of 4 feet. How tall is the lamppost?
6 ft
4 ft
10 ft
13) What will it cost to place baseboard around the region shown if the baseboard costs $0.25 per
foot? No baseboard is needed for the 2-foot doorway.
14) One side of a square flower bed is 8 feet long. How many plants are needed if they are to be
spaced 8 inches apart around the outside of the bed?
15) A one-story home is being built. The floor plan is shown below. If construction costs $95 per
square foot, find the cost of building the home.
16) If carpeting costs $17.95 per square yard and is available in whole square yards only, find the cost of
carpeting the three bedroom floors. (Using the floor plan above.)
17) A stained glass window is to be placed in a house. The window consists of a rectangle, 6 feet high by
3 feet wide, with a semicircle at the top. (See below) Approximately how many feet of stripping, to
the nearest tenth of a foot, will be needed to frame the window? (Hint: to find the distance around
the top, find the circumference of the circle and then divide it by 2!)
18) Evaluate the following functions at the given value of the variable.
a) 𝑓𝑓(𝑥𝑥) = 5 − 𝑥𝑥; find 𝑓𝑓(2) and 𝑓𝑓(−10)
b) 𝑔𝑔(𝑥𝑥) = 3𝑥𝑥 2 − 2𝑥𝑥 + 9; find 𝑔𝑔(3) and 𝑔𝑔(−4)
19) Whether on the slopes or at the shore, people are exposed to harmful amounts of the sun’s skindamaging ultraviolet (UV) rays. The quadratic function 𝐷𝐷(𝑥𝑥) = 0.8𝑥𝑥 2 − 17𝑥𝑥 + 109 models the
average time in which skin damage begins for burn-prone people, 𝐷𝐷(𝑥𝑥), in minutes, where x is
the UV index, or measure of the sun’s UV intensity. The graph of D is shown for a UV index from 1
(low) to 11 (high).
Find and interpret 𝐷𝐷(1). D(1) = 92.8.
20) Graph the following linear functions using the slope and y-intercept.
1
2
a) 𝑦𝑦 = 𝑥𝑥 + 3
b) 𝑦𝑦 = −2𝑥𝑥 + 7
21) A company that manufactures running shoes has a fixed cost of $300,000. Additionally, it costs $30
to produce each pair of shoes. They are sold at $80 per pair.
a) Write the cost function, C, of producing x pairs of running shoes.
b) Write the revenue function, R, from the sale of x pairs of running shoes.
c) Determine the break-even point. Describe what this means.
22) In 1900, Americans age 65 and over made up only 4.1% of the population. By 2010, that figure was
13% or approximately 44.6 million people. Demographic projections indicate that by the year 2050,
approximately 82 million Americans, or 20% of the U.S. population, will be at least 65. The bar
graph shows the number of people in the United States age 65 and over, with projected figures for
the year 2020 and beyond.
The graphing calculator displays an exponential function that models the U.S. population age 65 and
over, y, in millions, x years after 1899. Use this information to answer the following questions.
a) Use the graphing calculator screen to express the model in function notation, with numbers
rounded to three decimal places.
b) According to the model in part (a), how many Americans age 65 and over will there be in 2010?
Round to one decimal place. Does this rounded number overestimate or underestimate the
2010 population displayed by the bar graph?
c) According to the model in part (a), how many Americans age 65 and over will there be in 2020?
Round to one decimal place. Does this rounded number overestimate or underestimate the
2020 population projection displayed by the bar graph?
23) Exercise is useful not only in preventing depression, but also as a treatment. The graphs at the top
of the next column show the percentage of patients with depression in remission when exercise (brisk
walking) was used as a treatment. (The control group that engaged in no exercise had 11% of the
patients in remission.)
a) Find the slop of the line passing through the two points shown by the voice balloons. Express
the slope as a decimal.
b) Use your answer from part (a) to complete this statement:
For each minute of brisk walking, the percentage of patients with depression in remission
increased by ____%. The rate of change is ___% per _______.
24) In 1968, 23% of the grades for students entering college were C(C+, C, or C-). This has decreased at
an average rate of approximately 0.45% per year since then. Find a linear function in slope-intercept
form that models this description.
25) Make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables
appear to be related.
x
y
1
5
4
3
3
3
5
1
2
4
26) Use the scatter plots shown, labeled a – f, to solve the following problems.
Which scatter plot indicates a perfect negative correlation?
Which scatter plot indicates a perfect positive correlation?
In which scatter plot is r = 0.9?
In which scatter plot is r = 0.01?
27) Use the data below to answer the questions that follow.
a) Determine the correlation coefficient, rounded to two decimal places, between the percentage
of teenagers who have used marijuana and the percentage who have used other drugs.
b) Find the equation of the regression line for the percentage of teenagers who have used
marijuana and the percentage who have used other drugs. Round your values to two decimal
places.
c) What percentage of teenagers, to the nearest percent, can we anticipate using illegal drugs
other than marijuana in a country where 10% of teenagers have used marijuana?