Free Online Math Questions Calculator Permitted Exam 2

Question 1

Which of the following must be true?

Accepted Answer

Answer

Choice C is correct. Given that triangle A B C is similar to increment E D C, students can determine that the corresponding angle BAC is congruent to angle CED. The converse of the alternate interior angle theorem tells us that stack A B with bar on top parallel to stack D E with bar on top. (Students can also use the fact that angle A B C and angle C D E are congruent to make a similar argument.)

Choice A is not the correct answer. This answer may result from multiple misconceptions. The student may have visually identified the segments as perpendicular and used the wrong notation to express this statement.

Choice B is not the correct answer. This answer may result from visual inspection of the diagram. The line segments appear to be perpendicular, but need not be, given the information provided.

Choice D is not the correct answer. This answer may result from misunderstanding either the notation or the vocabulary of parallel and perpendicular lines. The student has incorrectly identified or notated parallel lines as perpendicular.

Question 2

The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?

Accepted Answer

300 randomly selected undergraduate psychology-degree program students

Answer

The question asks for a function modeling the number of gallons of gas remaining, but the provided options describe sampling populations for a statistics problem, making them irrelevant. To solve the actual math problem, first calculate the car's fuel consumption rate: 50 miles/hour divided by 21 miles/gallon equals 50/21 gallons per hour. Then, the function f(t) for remaining gas would be the initial amount minus the consumed amount: f(t) = 17 - (50/21)t.

Question 3

The toll rates for crossing a bridge are $6.50 for a car and $10 for a truck. During a two-hour period, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was $1,338. Solving which of the following systems of equations yields the number of cars, x, and the number of trucks, y, that crossed the bridge during the two hours?

Accepted Answer

4

Answer

Choice C is correct. If x is the number of cars that crossed the bridge during the two hours and y is the number of trucks that crossed the bridge during the two hours, then x space plus space y represents the total number of cars and trucks that crossed the bridge during the two hours, and 6.5 x space plus space 10 y represents the total amount collected in the two hours. Therefore, the correct system of equations is x space plus thin space y space equals space 187 and 6.5 x space plus space 10 y space equals space 1 comma 338.

Choice A is not the correct answer. The student may have mismatched the symbolic expressions for total cars and trucks and total tolls collected with the two numerical values given. The expression x space plus space y represents the total number of cars and trucks that crossed the bridge, which is 187.

Choice B is not the correct answer. The student may have attempted to use the information that the counts of cars, trucks, and tolls were taken over a period of two hours, but this information is not needed in setting up the correct system of equations. The expression 6.5 x space plus space 10 y represents the total amount of tolls collected, which is $1,338, not fraction numerator text $ end text 1 comma 338 over denominator 2 end fraction.

Choice D is not the correct answer. The student may have attempted to use the information that the counts of cars, trucks, and tolls were taken over a period of two hours, but this information is not needed in setting up the correct system of equations. The expression 6.5 x space plus space 10 y represents the total amount of tolls collected, which is $1,338 not text $ end text 1 comma 338 cross times 2.

Question 4

When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

Accepted Answer

The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone

Answer

Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives fraction numerator 20.9 minus 18.7 over denominator 14 minus 9 end fraction space equals space fraction numerator 2.2 over denominator 5 end fraction comma or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation 18.7 space equals space 0.44 left parenthesis 9 right parenthesis space plus space b gives b space equals space 14.74. Therefore, the model that can be used to relate the pressure and the depth is p space equals space 0.44 d space plus space 14.74.

Choice A is not the correct answer. The rate is calculated correctly, but the student may have incorrectly used the ordered pair left parenthesis 18.7 comma space 9 right parenthesis rather than left parenthesis 9 comma space 18.7 right parenthesis to calculate the pressure at a depth of 0 feet.

Choice C is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and not dividing by 5. The student then uses the coordinate pair d space equals space 9 and p equals 18.7 in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Choice D is not the correct answer. The rate here is incorrectly calculated by subtracting 20.9 and 18.7 and not dividing by 5. The student then uses the coordinate pair d space equals space 14 and p space equals space 20.9 in conjunction with the incorrect slope of 2.2 to write the equation of the linear model.

Question 5

The scatterplot above shows counts of Florida manatees, a type of sea mammal, from 1991 to 2011. Based on the line of best fit to the data shown, which of the following values is closest to the average yearly increase in the number of manatees?

Accepted Answer

170 centimeters

Answer

Choice C is correct. The slope of the line of best fit is the value of the average increase in manatees per year. Using approximate values found along the line of best fit (1,200 manatees in 1991 and 4,200 manatees in 2011), the approximate slope can be calculated as fraction numerator 3 comma 000 over denominator 20 end fraction space equals space 150.

Choice A is not the correct answer. This value may result from disregarding the actual scale when approximating the slope and interpreting the scale as if each square represents one unit.

Choice B is not the correct answer. This value may result from disregarding the actual scale when approximating the slope, and interpreting the scale as if each square along the x-axis represents one year and each tick mark along the y-axis represents 100 manatees.

Choice D is not the correct answer. This value may result from disregarding the actual scale along the x-axis when approximating the slope and interpreting each square along the x-axis as one year.

Math Practice Test

Math Practice Test

Free Online Math Questions Calculator Permitted Exam 2