Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 131:

  The number p is greater than 0, a multiple of 6, and a factor of 180. How many possibilities are there for the value of p?

  A. 7

  B. 8

  C. 9

  D. 10

  E. 11

  Correct Answer: B

  The positive factors of 180 (the positive numbers that divide evenly into 180) are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. Of these numbers, 8 (6, 12, 18, 30, 36, 60, 90, and 180) are multiples of 6.

• Question 132:

  

  In the diagram above, angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of triangle BED = 5 + 10, what is area of triangle ABC?

  A. 5a2+ 10

  B. 25a2+ 50

  C. 25a2+ 100

  D. 125a2+ 250

  E. cannot be determined

  Correct Answer: D

  

  Triangles ABC and BED have two pairs of congruent angles. Therefore, the third pair of angles must be congruent, which makes these triangles similar. If the area of the smaller triangle, BED, is equal to , then the area of the larger triangle, ABC, is equal to

  

  

  or 25 .

  The area of triangle ABC is 25 times larger than the area of triangle BED. Multiply the area of triangle BED

  by 25: 25(5a2+ 10) = 125a2+ 250.

• Question 133:

  

  The equation is undefined when

  A. –9.

  B. –2.

  C. –6.

  D. 0.

  E. 9.

  Correct Answer: A

  An equation is undefined when the value of a denominator in the equation is equal to zero. Set x 2?7x +18 equal to zero and factor the quadratic to find its roots:

  

• Question 134:

  How does the area of a rectangle change if both the base and the height of the original rectangle are tripled?

  A. The area is tripled.

  B. The area is six times larger.

  C. The area is nine times larger.

  D. The area remains the same.

  E. The area cannot be determined.

  Correct Answer: C

  Since both dimensions are tripled, there are two additional factors of 3. Therefore, the new area is 3*3 = 9 times as large as the original. For example, use a rectangle with a base of 5 and height of 6. The area is 5*6 = 30 square units. If you multiply the each side length by 3, the new dimensions are 15 and 18. The new area is 15*18, which is 270 square units. By comparing the new area with the original area, 270 square units is nine times larger than 30 square units; 30*9 = 270.

• Question 135:

  What is the tenth term of the pattern below?

  

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  

  Each term in the pattern is equal to the fraction 2/3 raised to an exponent that is equal to the position of the term in the sequence. The first term in the sequence is equal to ,

  

  the second term is equal to ,

  

  and so on. Therefore, the tenth term in the sequence will be equal to

• Question 136:

  The volume of a glass of water placed in the sun decreases by 20%. If there are 240 mL of water in the glass now, what was the original volume of water in the glass?

  A. 192ml

  B. 260ml

  C. 288ml

  D. 300ml

  E. 360ml

  Correct Answer: D

  The original volume of water, x, minus 20% of x, 0.20x, is equal to the current volume of water, 240ml:

  

• Question 137:

  What is the next number in the series below? 3 16 6 12 12 8

  A. 4

  B. 15

  C. 20

  D. 24

  E. 32

  Correct Answer: D

  This series actually has two alternating sets of numbers. The first number is doubled, giving the third number. The second number has 4 subtracted from it, giving it the fourth number. Therefore, the blank space will be 12 doubled, or 24.

• Question 138:

  

  The expression is equivalent to A. Option A

  

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  

  Simplify the numerator

  

  Simplify the denominator:

  

  Divide the numerator and denominator by 2:

• Question 139:

  

  Balloons are sold according to the chart above. If a customer buys one balloon at a time, the cost is $1.00 per balloon. If a customer buys ten balloons at a time, the cost is $0.90 per balloon. If Carlos wants to buy 2,000 balloons, how much money does he save by buying 1,000 balloons at a time rather than ten balloons at a time?

  A. $200

  B. $300

  C. $500

  D. $600

  E. $800

  Correct Answer: D

  Explanation:

  If Carlos buys ten balloons, he will pay (10)($0.90) = $9. In order to total 2,000 balloons, Carlos will have to make this purchase 2,000/10 = 200 times. It will cost him a total of (200)($9) = $1,800. If Carlos buys 1,000 balloons, he will pay (1,000)($0.60) = $600. In order to total 2,000 balloons, Carlos will have to make this purchase 2,000/1,000 = 2 times. It will cost him a total of (2)($600) = $1,200. It will save Carlos $1,800 – $1,200 = $600 to buy the balloons 1,000 at a time.

• Question 140:

  If ab/c = d, and a and c are doubled, what happens to the value of d?

  A. The value of d remains the same.

  B. The value of d is doubled.

  C. The value of d is four times greater.

  D. The value of d is halved.

  E. The value of d is four times smaller.

  Correct Answer: A