Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 1:

  

  In the diagram above, ABCD is a square with an area of 100 cm2 and lines BD and AC are the diagonals of ABCD. If line EF is parallel to line BC and the length of line CF = 32 cm, which of the following is equal to the shaded area?

  A. 25 cm2

  B. 39 cm2

  C. 64 cm2

  D. 78 cm2 E. 89 cm2

  Correct Answer: B

  The area of a square is equal to S2 where s is the length of one side of the square. A square with an area of 100cm2 has sides that are each equal to 100 = 10 cm. The diagonal of a square is equal to2 times the length of a side of the square. Therefore, the lengths of diagonals AC and BD are 102 cm. Diagonals of a square bisect each other at right angles, so the lengths of segments OB and OC are each 52 cm. Since lines BC and EF are parallel and lines OC and OB are congruent, lines BE and CF are also congruent. The length of line OF is equal to the length of line OC plus the length of line CF:52 + 32 = 82 cm. In the same way, OE = OB + BE =52 + 32 = 82 cm. 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. EOF is a right triangle, and its area is equal to

  

  The size of the shaded area is equal to the area of EOF minus one-fourth of the area of ABCD:

  

• Question 2:

  If set M contains only the positive factors of 8 and set N contains only the positive factors of 16, then the union of sets M and N

  A. contains exactly the same elements that are in set N.

  B. contains only the elements that are in both sets M and N.

  C. contains nine elements.

  D. contains four elements.

  E. contains only even elements.

  Correct Answer: A

  Set M contains the positive factors of 8: 1, 2, 4, and 8. Set N contains the positive factors of 16: 1, 2, 4, 8, and 16. The union of these sets is equal to all of the elements that are in either set. Since every element in set M is in set N, the union of N and M is the same as set N: {1, 2, 4, 8, 16}.

• Question 3:

  

  In the diagram above, what is the area of the rectangle?

  A. 6ab square units

  B. 8ab square units

  C. 9b2 square units

  D. 12ab square units

  E. 16b square units

  Correct Answer: B

  The y-axis divides the rectangle in half. Half of the width of the rectangle is a units to the left of the y-axis and the other half is a units to the right of the y-axis. Therefore, the width of the rectangle is 2a units. The length of the rectangle stretches from 3b units above the x-axis to b units below the x-axis. Therefore, the length of the rectangle is 4b units. The area of a rectangle is equal to low, where l is the length of the rectangle and w is the width of the rectangle. The area of this rectangle is equal to (2a)(4b) = 8ab square units.

• Question 4:

  A bank contains one penny, two quarters, four nickels, and three dimes. What is the probability of selecting a coin that is worth more than five cents but less than 30 cents?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: C

  

  There are ten coins in the bank (1 penny + 2 quarters + 4 nickels + 3 dimes). The two quarters and three dimes are each worth more than five cents but less than 30 cents, so the probability of selecting one of these coins is

• Question 5:

  The product of A. Option A

  

  

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  A fraction with a negative exponent can be rewritten as a fraction with a positive exponent by switching the numerator with the denominator.

  

• Question 6:

  Gil drives five times farther in 40 minutes than Warrick drives in 30 minutes. If Gil drives 45 miles per hour, how fast does Warrick drive?

  A. 6 mph

  B. 9 mph

  C. 12 mph

  D. 15 mph

  E. 30 mph

  Correct Answer: C

  If d is the distance Warrick drives and s is the speed Warrick drives, then 30s = d. Gil drives five times farther, 5d, in 40 minutes, traveling 45 miles per hour: 5d = (40)(45). Substitute the value of d in terms of s into the second equation and solve for s, Warrick's speed: 5(30s) = (40)(45), 150s = 1,800, s = 12. Warrick drives 12 mph.

• Question 7:

  If q is decreased by p percent, then the value of q is now

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: D

• Question 8:

  

  In the diagram above, ABC and DEC are right triangles, the length of side BC is 15 units, and the measure of angle A is 60 degrees. If angle A is congruent to angle EDC, what is the length of side DC?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: B

  Explanation: Since triangle DEC is a right triangle, triangle AED is also a right triangle, with a right angle at AED. There are 180 degrees in a triangle, so the measure of angle ADE is 180 – (60 + 90) = 30 degrees. Angle A and angle EDC are congruent, so angle EDC is also 60 degrees. Since there are 180 degrees in a line, angle BDC must be 90 degrees, making triangle BDC a right triangle. Triangle ABC is a right triangle with angle A measuring 60 degrees, which means that angle B must be 30 degrees, and BDC must be a 30-60- 90 right triangle. The leg opposite the 30-degree angle in a 30-60-90 right triangle is half the length of the

  hypotenuse. Therefore, the length of DC is 15/2 units.

• Question 9:

  If A. Option A

  

  

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: D

  Cross multiply:

  

• Question 10:

  The volume of a cylinder is 486 cubic units. If the height of the cylinder is six units, what is the total area of the bases of the cylinder?

  A. 9 square units

  B. 18 square units

  C. 27 square units

  D. 81 square units

  E. 162 square units

  Correct Answer: E

  The volume of a cylinder is equal to h, where r is the radius of the cylinder and h is the height of the cylinder. If the height of a cylinder with a volume of 486 cubic units is six units, then the radius is equal to:

  

  A cylinder has two circular bases. The area of a circle is equal to r2, so the total area of the bases of the cylinder is equal to 2r2, or 2(9)2 = 2(81) = 162 square units.