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SAT Practice Test 2015.
Two samples of water of equal mass are heated to 60 degrees Celsius (°C). One sample is poured into an insulated container, and the other sample is poured into a non-insulated container. The samples are then left for 70 minutes to cool in a room having a temperature of 25°C. The graph above shows the temperature of each sample at 10-minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change?
A) In every 10-minute interval, the magnitude of the rate of change of temperature of the insulated sample is greater than that of the non-insulated sample.
B) In every 10-minute interval, the magnitude of the rate of change of temperature of the non-insulated sample is greater than that of the insulated sample.
C) In the intervals from 0 to 10 minutes and from 10 to 20 minutes, the rates of change of temperature of the insulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude.
D) In the intervals from 0 to 10 minutes and from 10 to 20 minutes, the rates of change of temperature of the non-insulated sample are of greater magnitude, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the rates of change of temperature of the insulated sample are of greater magnitude.
Answer:
The rate of change of temperature corresponds to the slope of the graph.
In the intervals from 0 to 10 minutes and from 10 to 20 minutes, the slope of the curve of the non-insulated sample is greater than that of the insulated sample, whereas in the intervals from 40 to 50 minutes and from 50 to 60 minutes, the slope of the curve of the insulated sample is greater than that of the non-insulated sample.
Answer: D
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SAT Practice Test 2015.
According to the line of best fit in the scatterplot above, which of the following best approximates the year in which the number of miles traveled by air passengers in Country X was estimated to be 550 billion?
A) 1997
B) 2000
C) 2003
D) 2008
Answer:
The horizontal line that corresponds to 550 billion miles intersects the line of best fit at a point between 2000 and 2005, closer to 2005. Therefore, the choice that best approximates the year in which the number of miles traveled was estimated to be 550 billion is 2003.
Answer: C
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SAT Test 2015.
The graph above displays the total cost C, in dollars, of renting a boat for h hours.
What does the C-intercept represent in the graph?
A) The initial cost of renting the boat
B) The total number of boats rented
C) The total number of hours the boat is rented
D) The increase in cost to rent the boat for each additional hour
Answer:
The total cost C of renting a boat is the sum of the initial cost to rent the boat plus the product of the cost per hour and the number of hours, h, that the boat is rented. The C-intercept represents the point where h=0, that is, the initial cost of renting the boat.
Answer: A
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SAT Test 2015. The following question refers to the graph in the previous question.
Which of the following represents the relationship between h and C?
A) C=5h
B) C=(3/4)h+5
C) C=3h+5
D) h=3C
Answer:
This is the graph of a 1st degree equation: C=ah+5, where 5 is the initial cost, as seen in the previous question.
The graph shows that a 5-hour rent costs 20 dollars. Substituting this in the equation:
$C=ah+5$
$20=a5+5$
$20-5=a5$
$15=a5$
$a=3$
And the equation is $C=3h+5$
Answer: C
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SAT Test 2015.
The number of rooftops with solar panel installations in 5 cities (A, B, C, D and E) is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?
A) Number of installations (in tens)
B) Number of installations (in hundreds)
C) Number of installations (in thousands)
D) Number of installations (in tens of thousands)
Answer:
City A has 9(x) installations;
City B has 5(x) installations;
City C has 6(x) installations;
City D has 4(x) installations;
City E has 3.5(x) installations.
The sum of these five cities is: (9+5+6+4+3.5)(x) installations, that is, 27.5(x) installations.
This total should equal to the given 27,500 installations:
27.5(x)=27,500
x=1,000
Answer: C
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