Page 1
Question ID: be9cb6a2
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
The cost of renting a backhoe for up to days is for the first day and for each additional day. Which of the following equations
gives the cost , in dollars, of renting the backhoe for days, where is a positive integer and ?
Answer
A.
B.
C.
D.
Correct Answer: D
Rationale
Choice D is correct. It's given that the cost of renting a backhoe for up to days is for the first day and for each additional day.
Therefore, the cost , in dollars, for days, where , is the sum of the cost for the first day, , and the cost for the additional
days, . It follows that , which is equivalent to , or
.
Choice A is incorrect. This equation represents a situation where the cost of renting a backhoe is for the first day and for each
additional day.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Page 2
Question ID: 620fe971
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Medium
Question
A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, y, that remains to
be moved x hours after the team started working.
The graph of this equation in the xy-plane is a line. What is the best interpretation of the x-intercept in this context?
Answer
A. The team will have moved all the cargo in about 4.8 hours.
B. The team has been moving about 4.8 tons of cargo per hour.
C. The team has been moving about 25 tons of cargo per hour.
D. The team started with 120 tons of cargo to move.
Correct Answer: A
Rationale
Choice A is correct. The x-intercept of the line with equation y= 120 – 25x can be found by substituting 0 for y and finding the value of x. When y
= 0, x = 4.8, so the x-intercept is at(4.8, 0). Since yrepresents the number of tons of cargo remaining to be moved x hours after the team started
working, it follows that the x-intercept refers to the team having no cargo remaining to be moved after 4.8 hours. In other words, the team will
have moved all of the cargo after about 4.8 hours.
Choice B is incorrect and may result from incorrectly interpreting the value 4.8. Choices C and D are incorrect and may result from
misunderstanding the x-intercept. These statements are accurate but not directly relevant to the x-intercept.
Page 3
Question ID: b3abf40f
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
The function gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of kelvins. If a temperature increased by
kelvins, by how much did the temperature increase, in degrees Fahrenheit?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. It’s given that the function gives the temperature, in degrees Fahrenheit, that corresponds to
a temperature of kelvins. A temperature that increased by kelvins means that the value of increased by kelvins. It follows that an
increase in by increases by , or
. Therefore, if a temperature increased by kelvins, the temperature increased by
degrees Fahrenheit.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
Page 4
Question ID: af2ba762
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the UnitedStates from September
1, 2014, to December 1, 2014, is modeled by the function F defined below, where is the average price per gallon xmonths after September
1.
The constant 2.74 in this function estimates which of the following?
Answer
A. The average monthly decrease in the price per gallon
B. The difference in the average price per gallon from September1,2014, to December1,2014
C. The average price per gallon on September 1, 2014
D. The average price per gallon on December 1, 2014
Correct Answer: D
Rationale
Choice D is correct. Since 2.74 is a constant term, it represents an actual price of gas rather than a measure of change in gas price. To determine
what gas price it represents, findxsuch thatF(x) = 2.74, or 2.74 = 2.74 – 0.19(x–
3). Subtracting 2.74 from both sides gives 0 = –0.19(x–
3).
Dividing both sides by –0.19 results in 0 =x–
3, orx= 3. Therefore, the average price of gas is $2.74 per gallon 3 months after September 1,
2014, which is December 1, 2014.
Choice A is incorrect. Since 2.74 is a constant, not a multiple of x, it cannot represent a rate of change in price. Choice B is incorrect. The
difference in the average price from September 1, 2014, to December 1, 2014, isF(3) –
F(0) = 2.74 – 0.19(3 – 3) – (2.74 – 0.19(0 – 3)) = 2.74
–
(2.74 + 0.57) = –0.57, which is not 2.74. Choice C is incorrect. The average price per gallon on September 1, 2014, isF(0) = 2.74 – 0.19(0 – 3) =
2.74 + 0.57 = 3.31, which is not 2.74.
Page 5
Question ID: c22b5f25
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Medium
Question
In the xy-plane, the points and lie on the graph of which of the following linear functions?
Answer
A.
B.
C.
D.
Correct Answer: C
Rationale
Choice C is correct. A linear function can be written in the form , where m is the slope and b is the y-coordinate of the y-
intercept of the line. The slope of the graph can be found using the formula . Substituting the values of the given points into
this formula yields or , which simplifies to . Only choice C shows an equation with this slope.
Choices A, B, and D are incorrect and may result from computation errors or misinterpreting the given information.
Page 6
Question ID: 11e1ab81
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Medium
Question
The graph above shows the distance traveled d, infeet, by a product on a conveyor belt mminutes after the product is placed on the belt. Which
of the following equations correctly relates d and m ?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. The line passes through the origin. Therefore, this is a relationship of the form , where k is a constant representing
the slope of the graph. To find the value of k, choose a point on the graph of the line other than the origin and substitute the values of m
and d into the equation. For example, if the point is chosen, then , and . Therefore, the equation of the line is .
Choice B is incorrect and may result from calculating the slope of the line as the change in time over the change in distance traveled instead of
the change in distance traveled over the change in time. Choices C and D are incorrect because each of these equations represents a line with a
d-intercept of 2. However, the graph shows a line with a d-intercept of 0.
Page 7
Question ID: a309803e
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
One gallon of paint will cover square feet of a surface. A room has a total wall area of square feet. Which equation represents the total
amount of paint , in gallons, needed to paint the walls of the room twice?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. It's given that represents the total wall area, in square feet. Since the walls of the room will be painted twice, the amount of
paint, in gallons, needs to cover square feet. It’s also given that one gallon of paint will cover square feet. Dividing the total area, in
square feet, of the surface to be painted by the number of square feet covered by one gallon of paint gives the number of gallons of paint that
will be needed. Dividing by yields , or . Therefore, the equation that represents the total amount of paint , in gallons, needed to
paint the walls of the room twice is .
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from finding the amount of paint needed to paint the walls once rather than twice.
Choice D is incorrect and may result from conceptual or calculation errors.
Page 8
Question ID: 0b0fa68b
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
For the function , for all values of , where is a positive constant. If , what is the value of ?
Correct Answer: .0465, 2/43
Rationale
The correct answer is . It's given that for all values of , where is a positive constant, and . Therefore, for the
given function ,
. Dividing both sides of this equation by yields
. Substituting for in the equation yields
, or . Since it’s given that , substituting for yields . Adding to both sides of this
equation yields . Multiplying both sides of this equation by yields . Dividing both sides of this equation by yields .
Note that 2/43, .0465, 0.046, and 0.047 are examples of ways to enter a correct answer.
Page 9
Question ID: 6989c80a
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
The function gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of kelvins. If a temperature increased by
kelvins, by how much did the temperature increase, in degrees Fahrenheit?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. It’s given that the function gives the temperature, in degrees Fahrenheit, that corresponds to
a temperature of kelvins. A temperature that increased by kelvins means that the value of increased by kelvins. It follows that an
increase in by increases by , or
. Therefore, if a temperature increased by kelvins, the temperature increased by
degrees Fahrenheit.
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
Page 10
Question ID: a7e2859a
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
The cost of renting a large canopy tent for up to days is for the first day and for each additional day. Which of the following
equations gives the cost , in dollars, of renting the tent for days, where is a positive integer and ?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. It’s given that the cost of renting a large canopy tent is
for the first day and for each additional day for up to
days. For days of renting the tent, the cost includes for the first day and for each of the additional days. It follows that the
cost , in dollars, of renting the tent can be expressed as , which is equivalent to , or
. Therefore, the equation gives the cost of renting the tent for days, where is a positive integer and .
Choice B is incorrect. This equation represents a situation where the cost of renting the tent for the first day is , not , and the cost for
each additional day is , not .
Choice C is incorrect. This equation represents a situation where the cost of renting the tent for the first day is , not , and the cost for
each additional day is , not .
Choice D is incorrect. This equation represents a situation where the cost of renting the tent for the first day is , not .
Page 11
Question ID: 023c0a8d
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
For the function f, if for all values of x, what is the value of ?
Answer
A.
B.
C. 0
D. 2
Correct Answer: B
Rationale
Choice B is correct. It’s given that for all values of x. If , then will equal . Dividing both sides of by
3 gives . Therefore, substituting 2 for x in the given equation yields , which can be rewritten as .
Choice A is incorrect. This is the value of the constant in the given equation for f. Choice C is incorrect and may result from substituting ,
rather than , into the given equation. Choice D is incorrect. This is the value of x that yields for the left-hand side of the given
equation; it’s not the value of .
Page 12
Question ID: bbf9e5ce
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Hard
Question
For groups of or more people, a museum charges per person for the first people and for each additional person. Which function
gives the total charge, in dollars, for a tour group with people, where ?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. A tour group with people, where , can be split into two subgroups: the first people and the additional
people. Since the museum charges per person for the first people and for each additional person, the charge for the first people
is and the charge for the additional people is . Therefore, the total charge, in dollars, is given by the function
, or .
Choice B is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect and may result from conceptual or calculation errors.
Page 13
Question ID: 41fdc0b8
Assessment Test Domain Skill Difficulty
SAT Math Algebra Linear functions Medium
Question
The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010. If the relationship between population and year is linear,
which of the following functions P models the population of Greenleaf t years after 2000?
Answer
A.
B.
C.
D.
Correct Answer: A
Rationale
Choice A is correct. It is given that the relationship between population and year is linear; therefore, the function that models the population t
years after 2000 is of the form , where m is the slope and b is the population when . In the year 2000, . Therefore,
. The slope is given by . Therefore, , which is
equivalent to the equation in choice A.
Choice B is incorrect and may be the result of incorrectly calculating the slope as just the change in the value of P. Choice C is incorrect and may
be the result of the same error as in choice B, in addition to incorrectly using t to represent the year, instead of the number of years after 2000.
Choice D is incorrect and may be the result of incorrectly using t to represent the year instead of the number of years after 2000.
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