Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 81:

  If the height of a cylinder is doubled and the radius of the cylinder is halved, the volume of the cylinder

  A. remains the same.

  B. becomes twice as large.

  C. becomes half as large.

  D. becomes four times larger.

  E. becomes four times smaller.

  Correct Answer: C

  The volume of a cylinder is equal to r2h, where r is the radius of the cylinder and h is

  

  the height. The volume of a cylinder with a radius of 1 and a height of 1 is . If the height is doubled and the radius is halved, then the volume becomes

  The volume of the cylinder has become half as large.

• Question 82:

  The average of five consecutive odd integers is –21. What is the least of these integers?

  A. –17

  B. –19

  C. –21

  D. –23

  E. –25

  Correct Answer: E

  Explanation:

  If the average of five consecutive odd integers is –21, then the third integer must be –21. The two larger

  integers are –19 and –17 and the two lesser integers are –23 and –25. –25 is the least of the five integers.

  Remember, the more a number is negative, the less is its value.

• Question 83:

  If graphed, which of the following pairs of equations would be parallel to each other?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  Parallel lines have the same slope. The lines y= 6x+6 and y= 6x-6 both have a slope of 6, so they are parallel to each other.

• Question 84:

  

  If , then when a = 8, b could be equal to

  A. -2

  B. 4

  C. 6

  D. 7

  E. 8

  Correct Answer: C

  

  Substitute 8 for

  Rewrite 1 as 8/8 and add it to 4b/8 then cross multiply:

  

• Question 85:

  Which of the following expressions is undefined when x = -2?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  

  An expression is undefined when a denominator of the expression is equal to zero. When

• Question 86:

  The value of d is increased 50%, then decreased 50%. Compared to its original value, the value of d is now

  A. 25% smaller

  B. 25% larger

  C. 50% smaller

  D. 50% larger

  E. the same

  Correct Answer: A

  To increased by 50%, multiply d by 1.5:d= 1.5d. To find 50% of 1.5d, multiply 1.5d by 0.5: (1.5d)(0.5) = 0.75d. Compared to its original value, d is now 75% of what it was. The value of d is now 25% smaller.

• Question 87:

  

  In the diagram above, the length of a side of square ABCD is four units. What is the area of the shaded region?

  A. 4

  B. 4 – π

  C. 4 – 4π

  D. 16π

  E. 16 – 4π

  Correct Answer: B

  Explanation:

  The area of a square is equal to S2, where s is the length of a side of the square. The area of ABCD is 42=

  16 square units. The area of a circle is equal to πr2, where r is the radius of the circle.

  The diameter of the circle is four units. The radius of the circle is 4/2 = 2 square units. The area of the

  circle is equal to π(2)2= 4π. The shaded area is equal to one-fourth of the difference between the area of

  the square and the area of the circle:1/4(16 – 4π)= 4 – π.

• Question 88:

  

  Based on the diagram above, which of the following is true?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: A

  The measure of an exterior angle of a triangle is equal to the sum of the two interior angles of the triangle to which the exterior angle is NOT supplementary. Angle i is supplementary to angle g, so the sum of the interior angles e and f is equal to the measure of angle

  

• Question 89:

  Which of the following is an irrational number?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: E

  An irrational number is a number that cannot be expressed as a repeating or terminating decimal.

  

  Cannot be expressed as a repeating or terminating decimal, therefore, is an irrational number.

• Question 90:

  The area of an isosceles right triangle is 18 cm2.What is the length of the hypotenuse of the triangle?

  A. 6 cm

  B. 62cm

  C. 18 2 cm

  D. 18 3 cm

  E. 36 2 cm

  Correct Answer: B

  The area of a triangle is equal to where b is the base of the triangle and h is the height of the triangle. The

  

  base and height of an isosceles right triangle are equal in length. Therefore,