Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 51:

  Which of the following is the equation of a parabola whose vertex is at (5,–4)?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: A

  Explanation:

  The equation of a parabola with its turning point five units to the right of the y-axis is written as y = (x - 5)2.

  The equation of a parabola with its turning point four units below the x-axis is written as y = x2- 4.

  Therefore, the equation of a parabola with its vertex at (5, 4) is y= (x - 5)2 – 4.

• Question 52:

  There are seven vocalists, four guitarists, four drummers, and two bassists in Glen Oak's music program, while there are five vocalists, eight guitarists, two drummers, and three bassists in Belmont's music program. If a band comprises one vocalist, one guitarist, one drummer, and one bassist, how many more bands can be formed in Belmont?

  A. 4

  B. 10

  C. 16

  D. 18

  E. 26

  Correct Answer: C

  Explanation: Multiply the numbers of vocalists, guitarists, drummers, and b assists in each town to find the number of bands that can be formed in each town. There are (7)(4)(4)(2) = 224 bands that can be formed in Glen Oak. There are (5)(8)(2)(3) = 240 bands that can be formed in Belmont; 240 – 224 = 16 more bands that can be formed in Belmont.

• Question 53:

  If 40% of j is equal to 50% of k, then j is

  A. 10% larger than k.

  B. 15% larger than k.

  C. 20% larger than k.

  D. 25% larger than k.

  E. 80% larger than k.

  Correct Answer: D

  40% of j= 0.4j, 50% of k = 0.5k. If 0.4j= 0.5k, = 1.25kis equal to 125% of k, which means that j is 25% larger thank.

• Question 54:

  Which of the following could be equal to x/4x?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  Divide the numerator and denominator of x/4x by x, leaving 1/4 Divide the numerator and denominator of 5/20 by 5. This fraction is also equal to 1/4.

• Question 55:

  

  In the diagram above, side OB side OC. Which of the following is the measure of minor arc BC?

  A. 27.5 degrees B. 45 degrees

  C. 55 degrees

  D. 70 degrees

  E. 110 degrees

  Correct Answer: D

  

  Line OB line OC, which means the angles opposite line OB and OC (angles C and B) are congruent. Since angle B = 55 degrees, then angle C = 55 degrees. There are 180 degrees in a triangle, so the measure of angle O is equal to 180 ?(55 + 55) = 180 ?110 = 70 degrees. Angle O is a central angle. The measure of its intercepted arc, minor arc BC, is equal to the measure of angle O, 70 degrees.

• Question 56:

  Four copy machines make 240 total copies in three minutes. How long will it take five copy machines to make the same number of copies?

  A. 2 minutes

  B. 2 minutes, 15 seconds

  C. 2 minutes, 24 seconds

  D. 2 minutes, 45 seconds

  E. 3 minutes, 36 seconds

  Correct Answer: C

  If four copy machines make 240 copies in three minutes, then five copy machines will make 240 copies in x minutes:

  

  Five copy machines will make 240 copies in 2.4 minutes. Since there are 60 seconds in a minute, 0.4 of a minute is equal to (0.4)(60) = 24 seconds. The copies will be made in 2 minutes, 24 seconds.

• Question 57:

  Which of the following statements is always true if p is a rational number?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: A

  No matter whether p is positive or negative, or whether p is a fraction, whole number, or mixed number, the absolute value of three times any number will always be positive and greater than the absolute value of that number.

• Question 58:

  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: A

  The denominator of each term in the pattern is equal to 2 raised to the power given in the numerator. The numerator decreases by 1 from one term to the next. Since 10 is the numerator of the first term, 10 ?9, or 1, will be the numerator of the tenth term. 21= 2 so the tenth term will be1/2.

• Question 59:

  Monica sells pretzels in the cafeteria every school day for a week. She sells 14 pretzels on Monday, 12 pretzels on Tuesday, 16 pretzels on Wednesday, and 12 pretzels on Thursday. Then, she calculates the mean, median, and mode of her sales. If she sells 13 pretzels on Friday, then

  A. the mode will increase.

  B. the mean will stay the same.

  C. the median will stay the same.

  D. the median will decrease.

  E. the mean will increase.

  Correct Answer: C

  For the first four days of the week, Monica sells 12 pretzels, 12 pretzels, 14 pretzels, and 16 pretzels. The median value is the average of the second and third values:

  

  If Monica sells 13 pretzels on Friday, the median will still be 13. She will have sold 12 pretzels, 12 pretzels, 13 pretzels, 14 pretzels, and 16 pretzels. The median stays the same.

• Question 60:

  

  In the diagram above, lines NO and PQ are parallel to each other and perpendicular to lines JK and LM. Line JK is parallel to line LM. If angle CBD is 70 degrees, what is the measure of angle ZBK?

  A. 10 degrees

  B. 20 degrees

  C. 70 degrees

  D. 90 degrees

  E. 110 degrees

  Correct Answer: B

  Explanation:

  Angle CBD and angle PBZ are alternating angles — their measures are equal. Angle PBZ= 70 degrees. Angle PBZ+ angle ZBK form angle PBK. Line PQ is perpendicular to line JK; therefore, angle PBK is a right angle (90 degrees). Angle ZBK= angle PBK– angle PBZ= 90 – 70 = 20 degrees.