Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 31:

  Wendy tutors math students after school every day for five days. Each day, she tutors twice as many students as she tutored the previous day. If she tutors t students the first day, what is the average (arithmetic mean) number of students she tutors each day over the course of the week?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  If Wendy tutors t students the first day, then she tutors 2t students the second day, 4t students the third day, 8t students the fourth day, and 16t students the fifth day. The average number of students tutored each day over the course of the week is equal to the sum of the tutored students divided by the number of days:

  

• Question 32:

  What is the tenth term of the sequence: 5, 15, 45, 135 . . . ?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: D

  The first term in the sequence is equal to 5x30, the second term is equal to 5x31, and so on. Each term in the pattern is equal to 5x3n-1 , where n is the position of the term in the pattern. The tenth term in the pattern is equal to 5x3(10-1), or 5x39.

• Question 33:

  If y = -x3 + 3x -3, what is the value of y when x= -3?

  A. –35

  B. –21

  C. 15

  D. 18

  E. 33

  Correct Answer: C

  Substitute –3 for x and solve for y:

  

• Question 34:

  In a restaurant, the ratio of four-person booths to two-person booths is 3:5. If 154 people can be seated in the restaurant, how many two-person booths are in the restaurant?

  A. 14

  B. 21

  C. 35

  D. 57

  E. 70

  Correct Answer: C

  Let 3x equal the number of four-person booths and let 5x equal the number of two-person booths. Each four-person booth holds four people and each two-person booth holds two people. Therefore,

  

  There are (7)(3) = 21 four-person booths and (7)(5) = 35 two person booths.

• Question 35:

  

  In the diagram above, triangle ABC is a right triangle and the diameter of circle O is 2/3 the length of AB. Which of the following is equal to the shaded area?

  A. 20π square units

  B. 24 – 4π square units

  C. 24 – 16π square units

  D. 48 – 4π square units

  E. 48 – 16π square units

  Correct Answer: B

  Since ABC is a right triangle, the sum of the squares of its legs is equal to the square of the hypotenuse: (AB)2+82=102, (AB)2+ 64 = 100, (AB)2= 36, AB= 6 units. The diameter of circle O is 2/3 of AB, or 2/3(6) = 4 units. The area of a triangle is equal to 1/2bh where b is the base of the triangle and h is the height of the triangle.

  

  The area of ABC square units.

  The area of a circle is equal to r2, where r is the radius of the circle. The radius of a circle is equal to half the diameter of the circle, so the radius of O is 1/2(4) = 2 units. The area of circle O = (2)2= 4. The shaded area is equal to the area of the triangle minus the area of the circle: 24 ?4 square units.

• Question 36:

  If A. Option A

  

  

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: A

  

  To go from you would multiply the exponent of g(2/5) by (-1/2). Therefore, to go from 16 (the value of g (2/5)to the value of g(-1/5)multiply the exponent of 16 by (-1/5) The exponent of 16 is one, so the value of g (- 1/5) = 16 to the(-1/2) power, which is 1/4.

• Question 37:

  Simon plays a video game four times. His game scores are 18 points, 27 points, 12 points, and 15 points. How many points must Simon score in his fifth game in order for the mean, median, and mode of the give games to equal each other?

  A. 12 points

  B. 15 points

  C. 18 points

  D. 21 points

  E. 27 points

  Correct Answer: C

  For the median and mode to equal each other, the fifth score must be the same as one of the first four, and, it must fall in the middle position when the five scores are ordered. Therefore, Simon must have scored either 15 or 18 points in his fifth game. If he scored 15 points, then his mean score would have been greater than 15: 17.4. Simon scored 18 points in his fifth game, making the mean, median, and mode for the five games equal to 18.

• Question 38:

  If the lengths of the edges of a cube are decreased by 20%, the surface area of the cube will decrease by A. 20%.

  B. 36%.

  C. 40%.

  D. 51%.

  E. 120%.

  Correct Answer: B

  The surface area of a cube is equal to 6e2, where e is the length of an edge of a cube. The surface area of a cube with an edge equal to one unit is 6 cubic units. If the lengths of the edges are decreased by 20%, then the surface area

  

  becomes cubic units, a decrease of

  

• Question 39:

  

  In the diagram above, if line AB is parallel to line CD, and line EF is perpendicular to lines AB and CD, all of the following are true EXCEPT

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  Since AB and CD are parallel lines cut by a transversal, angle f is equal to the sum of angles c and b. However, angle f and angle g are not equal -- they are supplementary. Therefore, the sum of angles c and b is also supplementary -- and not equal -- tog.

• Question 40:

  

  In the diagram above, line AB is parallel to line CD, both lines are tangents to circle O and the diameter of circle O is equal in measure to the length of line OH. If the diameter of circle O is 24 in, what is the measure of angle BGH?

  A. 30 degrees

  B. 45 degrees

  C. 60 degrees

  D. 75 degrees

  E. cannot be determined

  Correct Answer: A

  Lines OF and OE are radii of circle O and since a tangent and a radius form a right angle, triangles OFH and OGE are right triangles. If the length of the diameter of the circle is 24 in, then the length of the radius is 12 in. The sine of angle OHF is equal to 12/24, or1/2. The measure of an angle with a sine of 1/2 is 30 degrees. Therefore, angle OHF measures 30 degrees. Since angles BGH and OHF are alternating angles,

  they are equal in measure. Therefore, angle BGH also measures 30 degrees.