Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 71:

  SIMULATION A. 21

  

  Correct Answer: A

  Both figures contain five angles. Each figure contains three right angles and an angle labeled 105 degrees. Therefore, the corresponding angles in each figure whose measures are not given (angles B and G, respectively) must also be equal, which makes the two figures similar. The lengths of the sides of similar figures are in the same ratio. The length of side FJ is 36 units and the length of its corresponding side, AE, in figure ABCDE is 180 units. Therefore, the ratio of side FJ to side AE is 36:180 or 1:5. The lengths of sides FG and AB are in the same ratio. If the length of side FG is x, then:

  

  The length of side FG is 21 units.

• Question 72:

  SIMULATION Sales of the Greenvale and Smithtown Branches of SuperBooks

  

  The graph above shows the sales by month for the Greenvale and Smithtown branches of SuperBooks. From January through May, how much more money did the Smithtown branch gross in sales than the Greenvale branch?

  A. 4000

  Correct Answer: A

  The Greenvale sales, represented by the light bars, for the months of January through May respectively

  were $22,000, $36,000, $16,000, $12,000, and $36,000, for a total of $122,000. The Smithtown sales,

  represented by the dark bars, for the months of January through May respectively were $26,000, $32,000,

  $16,000, $30,000, and $22,000, for a total of $126,000. The Smithtown branch grossed

  $126,000 ?$122,000 = $4,000 more than the Greenvale branch.

• Question 73:

  SIMULATION There are seven students on the trivia team. Mr. Randall must choose four students to participate in the trivia challenge. How many different groups of four students can Mr. Randall form?

  A. 35

  Correct Answer: A

  The order of the four students chosen does not matter. This is a "seven-choose-four" combination problem -- be sure to divide to avoid counting duplicates:

  

  .

  There are 35 different groups of four students that Mr. Randall could form.

• Question 74:

  SIMULATION

  Robert is practicing for the long jump competition. His first four jumps measure 12.4 ft, 18.9 ft, 17.3 ft, and

  15.3 ft, respectively. If he averages 16.3 feet for his first five jumps, what is the length in feet of his fifth jump?

  A. 17.6

  Correct Answer: A

  If Robert averages16.3 feet for five jumps, then he jumps a total of (16.3)(5)= 81.5 feet. The sum of

  

  Robert's first four jumps is

  

  Therefore, the measure of his fifth jump is equal to

• Question 75:

  SIMULATION

  If point A is at (–1, 2) and point B is at (11, –7), what is length of line AB?

  A. 15

  Correct Answer: A

  Use the distance formula to find the distance

  

• Question 76:

  SIMULATION

  There are 750 students in the auditorium for an assembly. When the assembly ends, the students begin to leave. If 32% of the students have left so far, how many students are still in the auditorium?

  A. 510

  Correct Answer: A

  Explanation:

  If 32% of the students have left the auditorium, then 100 – 32 = 68% of the students are still in the auditorium; 68% of 750 = (0.68)(750) = 510 students.

• Question 77:

  SIMULATION

  If a number is chosen at random from a set that contains only the whole number factors of 24, what is the probability that the number is either a multiple of four or a multiple of six?

  A. 5/8

  Correct Answer: A

  Explanation: The set of whole number factors of 24 is {1, 2, 3, 4, 6, 8, 12, 24}. Of these numbers, four (4, 8, 12, 24) are multiples of four and three (6, 12, 24) are multiples of six. Be sure not to count 12 and 24 twice — there are five numbers out of the eight factors of 24 that are a multiple of either four or six. Therefore, the probability of selecting one of these numbers is 5/8.

• Question 78:

  The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface area of the cube is 2:3. What is the surface area of the cube?

  A. 16 square units

  B. 24 square units

  C. 64 square units

  D. 96 square units

  E. 144 square units

  Correct Answer: D

  The volume of a cube is equal to e3, where e is the length of an edge of the cube. The surface area of a cube is equal to 6e2. If the ratio of the number of cubic units in the volume to the number of square units in the surface area is 2:3, then three times the volume is equal to two times the surface area:

  

  The edge of the cube is four units and the surface area of the cube is square units.

• Question 79:

  

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: D

  

• Question 80:

  Line AC is a diagonal of square ABCD. What is the sine of angle ACB?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: C

  A square has four right (90-degree) angles. The diagonals of a square bisect its angles. Diagonal AC bisects C, forming two 45-degree angles, angle ACB and angle ACD. The sine of 45 degrees is equal to 2/2