Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 141:

  

  In the diagram above, line OA is congruent to line OB. What is the measure of arc CD?

  A. 27.5 degrees

  B. 55 degrees

  C. 70 degrees

  D. 110 degrees

  E. 125 degrees

  Correct Answer: C

  Explanation:

  Triangle AOB is isosceles because line OA is congruent to line OB. Angles A and B are both 55 degrees, which means that angle O = 180 – (55 + 55) = 70 degrees. Angle O is a central angle and arc CD is its intercepted arc. A central angle and its intercepted arc are equal in measure, so the measure of arc CD is 70 degrees.

• Question 142:

  Given the following figure with one tangent and one secant drawn to the circle, what is the measure of angle ADB?

  

  A. 50 degrees

  B. 85 degrees

  C. 60 degrees

  D. 110 degrees

  E. 25 degrees

  Correct Answer: E

  The measure of an angle in the exterior of a circle formed by a tangent and a secant is equal to half the difference of the intercepted arcs. The two intercepted arcs are AB which is 60°, and AB which is 110°. Find half of the difference of the two arcs;

  

  (50) = 25°.

• Question 143:

  If the surface area of a cube is 384 cm2, what is the volume of the cube?

  A. 64 cm3

  B. 256 cm3

  C. 512 cm3

  D. 1,152 cm3

  E. 4,096 cm3

  Correct Answer: C

  The surface area of a cube is equal to 6e2, where e is the length of one edge of the cube; 6e2= 384 cm,e2= 64, e = 8 cm. The volume of a cube is equal to e3; (8 cm)3= 512 cm3.

• Question 144:

  

  In the diagram above, what is the sum of the measures of the angles x, y, and z?

  A. 180 degrees

  B. 360 degrees

  C. 540 degrees

  D. 720 degrees

  E. cannot be determined

  Correct Answer: B

  There are 180 degrees in a line: (x + (supplement of angle x)) + (y + (supplement of angle y)) + (z + (supplement of angle z)) = 540. The supplement of angle x, the supplement of angle y, and the supplement of angle z are the interior angles of a triangle. There are 180 degrees in a triangle, so those supplements sum to 180. Therefore, x + y + z + 180 = 540, and x + y + z = 360.

• Question 145:

  Greg has nine paintings. The Hickory Museum has enough space to display three of them. From how many different sets of three paintings does Greg have to choose?

  A. 27

  B. 56

  C. 84

  D. 168

  E. 504

  Correct Answer: C

  Be careful not to count the same set of three paintings more than once -- order is not important. A ninechoose-three combination is equal to

  

• Question 146:

  It takes eight people 12 hours to clean an office. How long would it take six people to clean the office?

  A. 9 hours

  B. 15 hours

  C. 16 hours

  D. 18 hours

  E. 24 hours

  Correct Answer: C

  There is an inverse relationship between the number of people and the time needed to clean the office. Multiply the number of people by the hours needed to clean the office: (8)(12) = 96. Divide the total number of hours by the new number of people, = 16. It takes six people 16 hours to clean the office.

  

• Question 147:

  The point (2, 1) is the midpoint of a line with endpoints at (?,3) and

  A. (–3,4)

  B. (–7,2)

  C. (7,1)

  D. (9,–1)

  E. (–10, 3)

  Correct Answer: D

  The midpoint of a line is equal to the average x-coordinates and the average y-coordinates of the line's endpoints:

  

  The other endpoint of this line is at (9,–1).

• Question 148:

  Lindsay grows only roses and tulips in her garden. The ratio of roses to tulips in her garden is 5:6. If there are 242 total flowers in her garden, how many of them are tulips?

  A. 22

  B. 40

  C. 110

  D. 121

  E. 132

  Correct Answer: E

  The number of roses, 5x, plus the number of tulips, 6x, is equal to 242 total flowers: 5x + 6x = 242, 11x = 242, x = 22. There are 5(22) = 110 roses and 6(22) = 132 tulips in Lindsay's garden.

• Question 149:

  The statement "Raphael runs every Sunday" is always true. Which of the following statements is also true?

  A. If Raphael does not run, then it is not Sunday.

  B. If Raphael runs, then it is Sunday.

  C. If it is not Sunday, then Raphael does not run.

  D. If it is Sunday, then Raphael does not run.

  E. If it is Sunday, it is impossible to determine if Raphael runs.

  Correct Answer: A

  The statement "Raphael runs every Sunday" is equivalent to "If it is Sunday, Raphael runs." The contrapositive of a true statement is also true. The contrapositive of "If it is Sunday, Raphael runs" is "If Raphael does not run, it is not Sunday."

• Question 150:

  

  In the diagram above, lines EF and GH are parallel, and line AB is perpendicular to lines EF and GH. What is the length of line AB?

  A. 5

  B. 52

  C. 53

  D. 102

  E. 103

  Correct Answer: C

  

  Line AB is perpendicular to line BC, which makes triangle ABC a right triangle. Angles DAF and DCH are alternating angles -- angles made by a pair of parallel lines cut by a transversal. Angle DAF angle DCH, therefore, angle DCH = 120 degrees. Angles DCH and ACB form a line. There are 180 degrees in a line, so the measure of angle ACB = 180 ?120 = 60 degrees. Triangle ABC is a 30-60-90 right triangle, which means that the length of the hypotenuse, AC, is equal to twice the length of the leg opposite the 30-degree angle, BC. Therefore, the length of BC is 10/2, or 5. The length of the leg opposite the 60-degree angle, AB, is 3 times the length of the other leg, BC. Therefore, the length of AB is.