Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 121:

  SIMULATION

  Stephanie buys almonds at the grocery store for $1.00 per pound. If she buys 4 pounds of almonds and pays a 5% tax on her purchase, what is Stephanie's total bill?

  A. 4.20

  Correct Answer: A

  If one pound of almonds costs $1.00, then 4 pounds of almonds costs 4($1.00) = $4.00. If Stephanie pays a 5% tax, then she pays ($4.00)(0.05) = $0.20 in tax. Her total bill is $4.00 + $0.20 = $4.20.

• Question 122:

  SIMULATION

  

  If 2a2 + b = 10 and ?what is the positive value of a?

  A. 3

  Correct Answer: A

  Solve 2a2+b= 10 for b: b=10-2a2. Substitute (10-2a2) for b in the second equation and solve for a:

  

  The positive value of a is 3

• Question 123:

  SIMULATION

  The length of a rectangular prism is four times the height of the prism and one-third the width of the prism. If the volume of the prism is 384 in 3, what is the width of the prism?

  A. 24

  Correct Answer: A

  If the height of the prism is h, then the length of the prism is four times that, 4h. The length is one-third of the width, so the width is three times the length: 12h. The volume of the prism is equal to its length multiplied by its width multiplied by its height:

  

  The height of the prism is 2 in, the length of the prism is (2 in)(4) = 8 in, and the width of the prism is (8 in)

  (3) = 24 in.

• Question 124:

  SIMULATION If

  

  A. 27

  Correct Answer: A

  

  Substitute 3 for = 9.

  

  To solve for z, raise both sides of the equation to the power

  

• Question 125:

  SIMULATION

  If the distance from point (–2,m) to point (4,–1) is 10 units, what is the positive value of m?

  A. 7

  Correct Answer: A

  First, use the distance formula to form an equation that can be solved for m:

  

• Question 126:

  SIMULATION

  Find the measure of angle Z.

  

  A. 90

  Correct Answer: A

  Explanation:

  Triangle DBC and triangle DEF are isosceles right triangles, which means the measures of ∟ BDC and ∟EDF both equal 45°; 180 – (m∟BDC + m∟EDF) = m∟Z; 180 – 90 = m∟Z; m∟Z = 90°.

• Question 127:

  SIMULATION

  If 6x + 9y – 15 = –6, what is the value of –2x – 3y + 5?

  A. 2

  Correct Answer: A

  The first expression, 6x + 9y – 15, is –3 times the second expression, –2x – 3y + 5 (multiply each term in the second expression by –3 and you’d get the first expression). Therefore, the value of the first expression, –6, is –3 times the value of the second expression. So, you can find the value of the second expression by dividing the value of the first expression by–3: The value of is just-1/3 times the value of since itself is-1/3times 6x + 9y - 15.

  

• Question 128:

  SIMULATION

  

  In the diagram above, lines K and L are parallel, and lines M and N are parallel. If b = 8, then a =?

  A. 11

  Correct Answer: A

  The labeled angle formed by lines M and K and the supplement of the labeled angle formed by lines L and

  N are alternating angles. Therefore, they are congruent. The angle labeled (10a + 5) and its supplement,

  which is equal to (8b + 1), total 180 degrees: (10a + 5) + (8b + 1) = 180. If b = 8, then:

  (10a + 5) + (8(8) + 1) = 18010a + 70 = 18010a = 110a = 11

• Question 129:

  SIMULATION

  The length of a room is three more than twice the width of the room. The perimeter of the room is 66 feet.

  What is the length of the room?

  A. 23

  Correct Answer: A

  If x is the width of the room, then 3 + 2x is the length of the room. The perimeter is equal to x + x + (3 + 2x)

  + (3 + 2x) = 66; 6x + 6 = 66; 6x = 60; x = 10. The length of the room is equal to 2x + 3, 2(10) + 3 = 23 feet.

• Question 130:

  If g > 0 and h < 0, which of the following is always positive?

  A. gh

  B. g + h

  C. g – h

  D. |h| – |g|

  E. h2

  Correct Answer: C

  A positive number minus a negative number will not only always be a positive number, but will also be a positive number greater than the first operand. gh will always be negative when one multiplicand is positive and the other is negative. g + h will be positive when the absolute value of g is greater than the absolute value of h, but g + h will be negative when the absolute value of g is less than the absolute value of h. |h| ?| g| will be positive when |h| is greater than g, but |h| ?|g| will be negative when |h| is less than g. hg will be positive when g is an even, whole number, but negative when g is an odd, whole number.