Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 41:

  If the statement "All students take the bus to school" is true, then which of the following must be true?

  A. If Courtney does not take the bus to school, then she is not a student.

  B. If Courtney takes the bus to school, then she is a student.

  C. If Courtney is not a student, then she does not take the bus.

  D. all of the above

  E. none of the above

  Correct Answer: A

  Since all students take the bus to school, anyone who does not take the bus cannot be a student. If Courtney does not take the bus to school, then she cannot be a student. However, it is not necessarily true that everyone who takes the bus to school is a student, nor is it necessarily true that everyone who is not a student does not take the bus. The statement "All students take the bus to school" does not, for instance, preclude the statement "Some teachers take the bus to school" from being true.

• Question 42:

  The area of a circle is equal to four times its circumference. What is the circumference of the circle?

  A. units

  B. 16 units

  C. 48 units

  D. 64 units

  E. cannot be determined

  Correct Answer: B

  If r is the radius of this circle, then the area of this circle, r2, is equal to four times its circumference, 2r: r2= 4(2r), r2= 8r,r2= 8r,r= 8 units. If the radius of the circle is eight units, then its circumference is equal to 2(8) = 16 units.

• Question 43:

  If m < n < 0, then all of the following are true EXCEPT

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: A

  Explanation:

  If m < n <0, then m and n are both negative numbers, and m is more negative than n. Therefore, -m will be more positive (greater) than-m, so the statement –m< -n cannot be true.

• Question 44:

  A line has a y-intercept of –6 and an x-intercept of 9. Which of the following is a point on the line?

  A. (–6,–10)

  B. (1,3)

  C. (0,9)

  D. (3,–8)

  E. (6,13)

  Correct Answer: A

  A line with a y-intercept of –6 passes through the point (0,–6) and a line with an x-intercept of 9 passes through the point (9,0). The slope of a line is equal to the change in y values between two points on the line divided by the change in the x values of those points. The slope of this line is equal to

  

  The equation of the line that has a slope of 2/3 and a y-intercept of –6 is

  

  When x = -6, y is equal to

  

  therefore, the point (-6, -10)is on the line

• Question 45:

  What two values are not in the domain of

  

  A. –3, 12

  B. 3, –12

  C. –6, 6

  D. –6, 36

  E. 9, 36

  Correct Answer: A

• Question 46:

  The diagonal of one face of a cube measures 42in. What is the volume of the cube?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: B

  Every face of a cube is a square. The diagonal of a square is equal to S2 where s is the length of a side of the square. If S2 = 42 then one side, or edge, of the cube is equal to 4 in. The volume of a cube is equal to e3,where is the length of an edge of the cube. The volume of the cube is equal to (4 in)3= 64 in 3.

• Question 47:

  A sack contains red, blue, and yellow marbles. The ratio of red marbles to blue marbles to yellow marbles is 3:4:8. If there are 24 yellow marbles in the sack, how many total marbles are in the sack?

  A. 45

  B. 48

  C. 72

  D. 96

  E. 144

  Correct Answer: A

  The number of yellow marbles, 24, is 24/8=3 times larger than the number of marbles given in the ratio. Multiply each number in the ratio by 3 to find the number of each color of marbles. There are 3(3) = 9 red marbles and 4(3) = 12 blue marbles. The total number of marbles in the sack is 24 + 9 + 12 = 45.

• Question 48:

  The point (6, –3) could be the midpoint of which of the following lines?

  A. a line with endpoints at (0,–1) and (12,–2)

  B. a line with endpoints at (2,–3) and (6,1)

  C. a line with endpoints at (6,0) and (6,–6)

  D. a line with endpoints at (–6,3) and (–6,–3)

  E. a line with endpoints at (3,3) and (12,–6)

  Correct Answer: C

  The midpoint of a line is equal to the average of the x-coordinates and the average of the y-coordinates of

  the endpoints of the line. The midpoint of the line with endpoints at and (6, -6) is

  

• Question 49:

  Eggs Found in a Hunt Over Time

  

  The scatter plot above shows how many eggs were found in a hunt over time. Which of the labeled points represents a number of eggs found that is greater than the number of minutes that has elapsed?

  A. A

  B. B

  C. C

  D. D

  E. E

  Correct Answer: E

  The point that represents a number of eggs found that is greater than the number of minutes that has elapsed is the point that has a y value that is greater than its x value. Only point E lies farther from the horizontal axis than it lies from the vertical axis. At point E, more eggs have been found than the number of minutes that has elapsed.

• Question 50:

  If

  

  A. –6.

  B. –4.

  C. 0.

  D. 24.

  E. 28.

  Correct Answer: D

  If b3- 64, then, taking the cube root of both sides, b = -4. Substitute -4 for b in the second equation: