Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 21:

  SIMULATION

  Matt weighs 3/5 of Paul's weight. If Matt were to gain 4.8 pounds, he would weigh 2/3of Paul's weight. What is Matt's weight in pounds?

  A. 43.2

  Correct Answer: A

  Matt's weight, m, is equal to 3/5 of Paul's weight, p:

  

  If 4.8 is added to m, the sum is equal to

  

  Substitute the value of min terms of p into the second equation:

  

  

  pounds.

  Paul weighs 72 pounds, and Matt weighs

• Question 22:

  SIMULATION

  If –6b + 2a – 25 = 5 and a/b + 6 = 4, what is the value of (b/a)2?

  A. 1/4

  Correct Answer: A

  Solve-6b + 2a – 25 = 25 for a in terms of b: -6b + 2a – 25 = 5, -3b + a = 15, a = 15+3b. Substitute a in terms of b into the second equation:

  

  Substitute b into the first equation to find the value of a: -6b + 2a – 25 = 5, -6(-3) 2a – 25 = 5, 18+2a = 30, 2a = 12, a = 6. Finally, ,

  

• Question 23:

  SIMULATION

  

  The function

  –8 when j = -3 j = -3, what is the value of k?

  A. 6

  Correct Answer: A

  j@k = -8 when j = -3 then:

  

• Question 24:

  SIMULATION Ages of Spring Island Concert Attendees

  

  The diagram above shows the breakdown by age of the 1,560 people who attended the Spring Island Concert last weekend. How many people between the ages of 18 and 34 attended the concert?

  A. 1,014

  Correct Answer: A

  Explanation:

  Of the concert attendees, 41% were between the ages of 18–24 and 24% were between the ages of 25–

  34. Therefore, 41 + 24 = 65% of the attendees, or (1,560)(0.65) = 1,014 people between the ages of 18 and 34 attended the concert.

• Question 25:

  SIMULATION

  

  What is the value of when x = 2 and y = 5?

  A. 4

  Correct Answer: A

  Substitute 2 for x and 5 for

  

  the 5th root of 32 is 2, 2 raised to the 2nd power is 4.

• Question 26:

  

  In the diagram above, ABDE is a square and BCD is an equilateral triangle. If cm, what is the perimeter of ABCDE?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: C

  Since BCD is an equilateral triangle, angles CBD, BDC, and BCD all measure 60 degrees. FCD and BCF are both 30-60-90 right triangles that are congruent to each other. The side opposite the 60-degree angle of triangle BCF, side FC, is equal to times the length of the side opposite the 30-degree angle, side BF. Therefore, BF is equal to = 6 cm. The hypotenuse, BC, is equal to twice the length of side BF. The length of BC is 2(6) = 12 cm. Since BC= 12 cm, CD and BD are also 12 cm. BD is one side of square ABDE; therefore, each side of ABDE is equal to 12 cm. The perimeter of ABCDE = 12 cm + 12 cm + 12 cm + 12 cm + 12 cm = 60 cm.

• Question 27:

  The area of one square face of a rectangular prism is 121 square units. If the volume of the prism is 968

  cubic units, what is the surface area of the prism?

  A. 352 square units

  B. 512 square units

  C. 528 square units

  D. 594 square units

  E. 1,452 square units

  Correct Answer: D

  The area of a square is equal to the length of a side, or edge, of the square times itself. If the area of a square face is 121 square units, then the lengths of two edges of the prism are 11 units. The volume of the prism is 968 cubic units. The volume of prism is equal to, where is the length of the prism, w is the width of the prism, and h is the height of the prism. The length and width of the prism are both 11 units. The height is equal to: 968 = (11)(11) h, 968 = 121= 8. The prism has two square faces and four rectangular faces. The area of one square face is 121 square units. The area of one rectangular face is (8)(11) = 88 square units. Therefore, the total surface area of the prism is equal to: 2(121) + 4(88) = 242 + 352 = 594 square units.

• Question 28:

  A number cube is labeled with the numbers one through six, with one number on each side of the cube. What is the probability of rolling either a number that is even or a number that is a factor of 9?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: D

  

  There are three numbers on the cube that are even (2, 4, 6), so the probability of rolling an even number is 1/2. There are two numbers on the cube that are factors of 9 (1, 3), so the probability of rolling a factor of 9 is

  No numbers are members of both sets, so to find the probability of rolling either a number that is even or a number that is a factor of 9, add the probability of each event:

  

• Question 29:

  

  In the diagram above, line AB is parallel to line CD, angle EIJ measures 140 degrees and angle CKG measures 55 degrees. What is the measure of angle IKJ?

  A. 40 degrees

  B. 55 degrees

  C. 85 degrees

  D. 95 degrees

  E. 135 degrees

  Correct Answer: C

  Explanation: Since AB and CD are parallel lines cut by transversals EF and GH respectively, angles CKG and IJK are alternating angles. Alternating angles are equal in measure, so angle IJK= 55 degrees. Angles EIJ and JIK form a line. They are supplementary and their measures sum to degrees. Angle JIK 180 - 140 = 40 degrees. Angles JIK, IJK, and IKJ comprise a triangle. There are 180 degrees in a triangle; therefore, the

  measure of angle IKJ= 180 – (55 + 40) = 85 degrees.

• Question 30:

  A pair of Jump sneakers costs $60 and a pair of Speed sneakers costs $45. For the two pairs of sneakers to be the same price

  A. the price of a pair of Jump sneakers must decrease by 15%.

  B. the price of a pair of Speed sneakers must increase by 15%.

  C. the price of a pair of Jump sneakers must decrease by 25%.

  D. the price of a pair of Speed sneakers must increase by 25%.

  E. the price of a pair of Jump sneakers must decrease by 33%.

  Correct Answer: C

  

  Jump sneakers cost $60 ?$45 = $15 more, or more than Speed sneakers. Speed sneakers cost $15 less, or less than Jump sneakers. For the two pairs of sneakers to be the same price, either the price of Speed sneakers must increase by 33 or the price of Jump sneakers must decrease by 25.