SAT Math Test
55 Minutes—38 Questions
CALCULATOR SECTION
1.
1. This section corresponds to Section 4 of your answer sheet.
Directions
For this section, solve each problem and decide which is the best of
the choice
...
SAT Math Test
55 Minutes—38 Questions
CALCULATOR SECTION
1.
1. This section corresponds to Section 4 of your answer sheet.
Directions
For this section, solve each problem and decide which is the best of
the choices given. Fill in the corresponding oval on the answer
sheet. You may use any available space for scratch work.Notes:
1. Calculator use is permitted.
2. All numbers used are real numbers, and all variables used
represent real numbers, unless otherwise indicated.
3. Figures are drawn to scale and lie in a plane unless otherwise
indicated.
4. Unless stated otherwise, the domain of any function f is
assumed to be the set of all real numbers x, for which f (x) is a
real number.
Information:The sum of the degree measures of the angles in a triangle is
180.
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2π.
O2c. eans, seas, and bays represent about 96.5 percent of Earth’swater, including the water found in our atmosphere. If the
volume of the water contained in oceans, seas, and bays is
about 321,000,000 cubic miles, which of the following best
represents the approximate volume, in cubic miles, of all the
world’s water?
1. 308,160,000
2. 309,765,000
3. 332,642,000
4. 334,375,000
A3n. electrician charges a one-time site visit fee to evaluate a
potential job. If the electrician accepts the job, he charges an
hourly rate plus the cost of any materials needed to complete
the job. The electrician also charges for tax, but only on the cost
of the materials. If the total cost of completing a job that takes h
hours is given by the function C(h) = 45h + 1.06(82.5) + 75,
then the term 1.06(82.5) represents
1. the hourly rate.
2. the site visit fee.
3. the cost of the materials, including tax.
4. the cost of the materials, not including tax.T4h.e figure above shows the solution set for the system of
inequalities. Which of the following is not a solution to the
system?
1. (0, 3)
2. (1, 2)
3. (2, 4)
4. (3, 3)
E5a.ch of the following quadratic equations represents the graph
shown above. Which equation reveals the exact values of the xintercepts of the graph?
1.
2.
3.
4.M6.argo surveyed all the students in the government classes at her
school to see what they thought should be the most important
concern of a national government. The results of the survey are
shown in the figure above. If the ratio of students who
answered “Foreign Policy” to those who answered
“Environment” was 5:3, what percentage of the students
answered “Environment”?
1. 16%
2. 21%
3. 24%
4. 35%
W7.hich of the following best describes the type of association
shown in the scatterplot above?1. Linear, positive
2. Linear, negative
3. Exponential, positive
4. Exponential, negative
T8h.e figure above shows the average annual gas prices in the United
States from 2003 to 2013. Based on the information shown,
which of the following conclusions is valid?
1. A gallon of gas cost more in 2008 than in 2013.
2. The price more than doubled between 2003 and 2013.
3. The drop in price from 2008 to 2009 was more than $1.00
per gallon.
4. The overall change in price was greater between 2003 and
2008 than it was between 2008 and 2013.
I9f.(x, y) is a solution to the system of equations above, what is the
sum of x and y?
1.
2. −43.
4. −3
1A0.voltage divider is a simple circuit that converts a large voltage
into a smaller one. The figure above shows a voltage divider
that consists of two resistors that together have a total resistance
of 294 ohms. To produce the desired voltage of 330 volts, R2
must be 6 ohms less than twice R1. Solving which of the
following systems of equations gives the individual resistances
for R1 and R2?
1.
2.
3.
4.
1I1f. , what is the value of x?
1. x = −2
2. x = 23. There is no value of x for which the equation is true.
4. There are infinitely many values of x for which the
equation is true.
1C2r.ude oil is being transferred from a full rectangular storage
container with dimensions 4 meters by 9 meters by 10 meters
into a cylindrical transportation container that has a diameter of
6 meters. What is the minimum possible length for a
transportation container that will hold all of the oil?
1. 40π
2.
3. 60π
4.
1T3h.e percent increase from 5 to 12 is equal to the percent increase
from 12 to what number?
1. 16.8
2. 19.0
3. 26.6
4. 28.8
1T4h.e brightness of a celestial body, like a star, decreases as you
move away from it. In contrast, the luminosity of a celestial
body is a constant number that represents its intrinsic
brightness. The inverse square law, shown above, is used to
find the brightness, b, of a celestial body when you know its
luminosity, L, and the distance, d, in meters to the body. Which
equation shows the distance to a celestial body, given its
brightness and luminosity?1.
2.
3.
4.
15.
1. Questions 14 and 15 refer to the following information.
2. Each month, the Bureau of Labor Statistics conducts a survey
called the Current Population Survey (CPS) to measure
unemployment in the United States. Across the country, about
60,000 households are included in the survey sample. These
households are grouped by geographic region. A summary of
the January 2014 survey results for male respondents in one
geographic region is shown in the table below.
Age
Group Employed Unemployed N Foortcien the Labor Total
16–19 8 5 10 23
20–24 26 7 23 56
25–34 142 11 28 157
35–44 144 8 32 164
45–54 66 6 26 98
Over 54 65 7 36 152
Total 451 44 155 650
A3c. cording to the data in the table, for which age group did the
smallest percentage of men report that they were
unemployed in January 2014?
1. 20 to 24 years
2. 35 to 44 years
3. 45 to 54 years4. Over 54 years
I4f.one unemployed man from this sample is chosen at random
for a follow-up survey, what is the probability that he will
be between the ages of 45 and 54?
1. 6.0%
2. 13.6%
3. 15.1%
4. 44.9%
1W6.hich of the following are solutions to the quadratic equation
?
1.
2.
3.
4.
1D7a. mien is throwing darts. He has a total of 6 darts to throw. He
gets 5 points for each dart that lands in a blue ring and 10 points
for each dart that lands in a red ring. If x of his darts land in a
blue ring and the rest land in a red ring, which expression
represents his total score?
1. 10x
2. 10x + 5
3. 5x + 30
4. 60 − 5x
1R8e.d tide is a form of harmful algae that releases toxins as it breaks
down in the environment. A marine biologist is testing a new
spray, composed of clay and water, hoping to kill the red tidethat almost completely covers a beach in southern Florida. He
applies the spray to a representative sample of 200 square feet
of the beach. By the end of the week, 184 square feet of the
beach is free of the red tide. Based on these results, and
assuming the same general conditions, how many square feet of
the 10,000-square-foot beach would still be covered by red tide
if the spray had been used on the entire area?
1. 800
2. 920
3. 8,000
4. 9,200
1I9f.(a, b) is a solution to the system of equations above, which of the
following could be the value of b?
1. −3
2. −2
3. 1
4. 2
2G0i.ven the function , what domain value corresponds to
a range value of 3?
1. −6
2. −2
3. 6
4. 9
2A1.landscaper buys a new commercial-grade lawn mower that costs$2,800. Based on past experience, he expects it to last about 8
years, and then he can sell it for scrap metal with a salvage
value of about $240. Assuming the value of the lawn mower
depreciates at a constant rate, which equation could be used to
find its approximate value after x years, given that x < 8 ?
1. y = −8x + 2,560
2. y = −240x + 2,800
3. y = −320x + 2,800
4. y = 240x − 2,560
2A2. microbiologist is studying the effects of a new antibiotic on a
culture of 20,000 bacteria. When the antibiotic is added to the
culture, the number of bacteria is reduced by half every hour.
What kind of function best models the number of bacteria
remaining in the culture after the antibiotic is added?
1. A linear function
2. A quadratic function
3. A polynomial function
4. An exponential function
2A3n. airline company purchased two new airplanes. One can travel at
speeds of up to 600 miles per hour and the other at speeds of up
to 720 miles per hour. How many more miles can the faster
airplane travel in 12 seconds than the slower airplane?
1.
2.
3. 2
4. 30
State Minimum Wage per HourIdaho $7.25
Montana $7.90
Oregon $9.10
Washington $9.32
2T4h.e table above shows the 2014 minimum wages for several states
that share a border. Assuming an average workweek of between
35 and 40 hours, which inequality represents how much more a
worker who earns minimum wage can earn per week in Oregon
than in Idaho?
1. x ≥ 1.85
2. 7.25 ≤ x ≤ 9.10
3. 64.75 ≤ x ≤ 74
4. 253.75 ≤ x ≤ 364
2I5n. the United States, the maintenance and construction of airports,
transit systems, and major roads is largely funded through a
federal excise tax on gasoline. Based on the 2011 statistics
given below, how much did the average household pay per year
in federal gasoline taxes?
The federal gasoline tax rate was 18.4 cents per gallon.
The average motor vehicle was driven approximately
11,340 miles per year.
The national average fuel economy for noncommercial
vehicles was 21.4 miles per gallon.
The average American household owned 1.75 vehicles.
1. $55.73
2. $68.91
3. $97.52
4. $170.632F6o.llowing the catastrophic oil spill in the Gulf of Mexico in April
of 2010, more than 900 bottlenose dolphins were found dead or
stranded in the oil spill area. The figure above shows the weight
of a rescued dolphin during its recovery. Based on the quadratic
model fit to the data shown, which of the following is the
closest to the average rate of change in the dolphin’s weight
between week 2 and week 8 of its recovery?
1. 4 pounds per week
2. 16 pounds per week
3. 20 pounds per week
4. 40 pounds per week
2A7s. shown in the figure above, a lifeguard sees a struggling
swimmer who is 40 feet from the beach. The lifeguard runs 60
feet along the edge of the water at a speed of 12 feet per
second. He pauses for 1 second to locate the swimmer again,and then dives into the water and swims along a diagonal path
to the swimmer at a speed of 5 feet per second. How many
seconds go by between the time the lifeguard sees the
struggling swimmer and the time he reaches the swimmer?
1. 16
2. 22
3. 50
4. 56
2W8.hat was the initial amount of gasoline in a fuel trailer, in gallons,
if there are now x gallons, y gallons were pumped into a storage
tank, and then 50 gallons were added to the trailer?
1. x + y + 50
2. x + y − 50
3. y − x + 50
4. x − y − 50
2T9h.e figure above shows the net change, as a percentage, for U.S.
import and export prices from January to July 2014 as reported
by the Bureau of Labor Statistics. For example, U.S. import
prices declined 0.2 percent in July while export prices remained
unchanged for that month. Based on this information, which ofthe following statements is true for the time period shown in the
figure?
1. On average, export prices increased more than import
prices.
2. Import prices showed an increase more often than export
prices.
3. Import prices showed the greatest change between two
consecutive months.
4. From January to July, import prices showed a greater
overall decrease than export prices.
3T0h.e Ironman Triathlon originated in Hawaii in 1978. The format of
the Ironman has not changed since then: it consists of a 3.86-
kilometer swim, a 180.2-kilometer bicycle ride, and a 42.2-
kilometer run, all raced in that order and without a break.
Suppose an athlete bikes 10 times as fast as he swims and runs
5 times as fast as he swims. The variable x in the expression
above represents the rate at which the athlete swims, and the
whole expression represents the number of hours that it takes
him to complete the race. If it takes him 16.2 hours to complete
the race, how many kilometers did he swim in 1 hour?
1. 0.85
2. 1.01
3. 1.17
4. 1.87
2.
1. Directions
For questions 31–38, enter your responses into the appropriate grid
on your answer sheet, in accordance with the following:
1. You will receive credit only if the circles are filled incorrectly, but you may write your answers in the boxes above
each grid to help you fill in the circles accurately.
2. Don’t mark more than one circle per column.
3. None of the questions with grid-in responses will have a
negative solution.
4. Only grid in a single answer, even if there is more than one
correct answer to a given question.
5. A mixed number must be gridded as a decimal or an
improper fraction. For example, you would grid as 7.5 or
15/2.
(Were you to grid it as , this response would be
read as .)
6. A decimal that has more digits than there are places on the
grid may be either rounded or truncated, but every column in
the grid must be filled in order to receive credit.W2.hat value of x satisfies the equation ?
S3o.me doctors base the dosage of a drug to be given to a patient on
the patient’s body surface area (BSA). The most commonly
used formula for calculating BSA is , where w is the
patient’s weight (in kilograms), h is the patient’s height (in
centimeters), and BSA is measured in square meters. How tall
(in centimeters) is a patient who weighs 150 kilograms and has
a BSA of square meters?
A4. college math professor informs her students that rather than
grading the final exam on a curve, she will replace each
student’s lowest test score with the next to lowest test score,
and then re-average the test grades. If Leeza has test scores of
86, 92, 81, 64, and 83, by how many points does her final test
average change based on the professor’s policy?
I5n.the figure above, , , and are diameters of the circle. If y =
2x − 12, and the shaded area is of the circle, what is the value
of x?
I6f.the slope of a line is and a point on the line is (4, 7), what is
the y-intercept of the line?
R7o. ry left home and drove straight to the airport at an average speed
of 45 miles per hour. He returned home along the same route,
but traffic slowed him down and he only averaged 30 miles per
hour on the return trip. If his total travel time was 2 hours and
30 minutes, how far is it, in miles, from Rory’s house to the
airport?
3.
1. Questions 37 and 38 refer to the following information.
2. Chemical Makeup of One Mole of Chloroform
Element Number of Moles Mass per Mole (grams)Carbon 1 12.011
Hydrogen 1 1.008
Chlorine 3 35.453
A chemical solvent is a substance that dissolves another to form a
solution. For example, water is a solvent for sugar. Unfortunately,
many chemical solvents are hazardous to the environment. One
ecofriendly chemical solvent is chloroform, also known as
trichloromethane (CHCl3). The table above shows the chemical
makeup of one mole of chloroform.
C3a.rbon makes up what percent of the mass of one mole of
chloroform? Round your answer to the nearest whole percent
and ignore the percent sign when entering your answer.
I4f.a chemist starts with 1,000 grams of chloroform and uses 522.5
grams, how many moles of chlorine are left?
If you finish before time is called, you may check your work on this section
only. Do not turn to any other section in the test.Answer Key
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