Test Prep Test Prep Certifications SAT2-MATHEMATICS Questions & Answers

• Question 11:

  

  In the diagram above of f(x), for how many values does f(x) = -1?

  A. 0

  B. 1

  C. 2

  D. 3

  E. 4

  Correct Answer: C

  The function f(x) is equal to-1 every time the graph off (x) crosses the line y = -1. The graph off(x)crosses y = -1 twice; therefore, there are two values for which f(x) = -1.

• Question 12:

  The equation A. –8 or 8.

  

  B. –4 or 4.

  C. –4 or –8.

  D. 4 or –8.

  E. 4 or 8.

  Correct Answer: E

  Write the equation in quadratic form and find its roots:

  

• Question 13:

  

  In the diagram above, if angle OBE measures 110 degrees, what is the measure of arc AC?

  A. 20 degrees

  B. 40 degrees

  C. 55 degrees

  D. 80 degrees

  E. cannot be determined

  Correct Answer: B

  Explanation:

  Angles OBE and DBO form a line. Since there are 180 degrees in a line, the measure of angle DBO is

  180– 110 = 70 degrees. OB and DO are radii, which makes triangle DBO isosceles, and angles ODB and

  DBO congruent. Since DBO is 70 degrees, ODB is also 70 degrees, and DOB is 180 – (70 + 70) =180–

  140 = 40 degrees. Angles DOB and AOC are vertical angles, so the measure of angle AOC is also 40

  degrees. Angle AOC is a central angle, so its intercepted arc, AC, also measures 40 degrees.

• Question 14:

  It takes six people eight hours to stuff 10,000 envelopes. How many people would be required to do the job in three hours?

  A. 4

  B. 12

  C. 16

  D. 18

  E. 24

  Correct Answer: C

  Six people working eight hours produce (6)(8) = 48 work-hours. The number of people required to produce 48 work-hours in three hours is48/3 = 16.

• Question 15:

  The line is

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  E. Option E

  Correct Answer: B

  Parallel lines have the same slope. When an equation is written in the for my = mx + b the value of m (the coefficient of x) is the slope. The line y = -2x + 8 has a slope of-2. The line 1/2y = -x +3 is equal to y = -2x +

  6. This line has the same slope as the line y = -2x + 8; therefore, these lines are parallel.

• Question 16:

  SIMULATION

  A bus holds 68 people. If there must be one adult for every four children on the bus, how many children can fit on the bus?

  A. 52

  Correct Answer: A

  There is one adult for every four children on the bus. Divide the size of the bus, 68, by

  

  There can be no more than 13 groups of one adult, four children. Therefore, there can be no more than (13 groups)(4 children in a group) = 52 children on the bus.

• Question 17:

  SIMULATION

  In Marie's fish tank, the ratio of guppies to platies is 4:5. She adds nine guppies to her fish tank and the ratio of guppies to platies becomes 5:4. How many guppies are in the fish tank now?

  A. 25

  Correct Answer: A

  If the original ratio of guppies, g, to plates, p, is 4:5, then g =4/5p If nine guppies are added, then the new number of guppies, g + 9, is equal to 5/4p: g+9 = 5/4p.Substitute the value of g in terms of p from the first equation:4/5 p+9 = 5/4p,9 = 9/20p, =p = 20. There are 20 plates in the fish tank and there are now 20(5/4) = 25 guppies in the fish tank.

  

• Question 18:

  SIMULATION

  For any whole number x>0, how many elements are in the set that contains only the numbers that are multiples AND factors of x?

  A. 1

  Correct Answer: A

  The largest factor of a positive, whole number is itself, and the smallest multiple of a positive, whole number is itself. Therefore, the set of only the factors and multiples of a positive, whole number contains one element -- the number itself.

• Question 19:

  SIMULATION

  

  In the circle above, the measure of angle AOB is 80 degrees and the length of arc AB is 28 units. What is the radius of the circle?

  A. 63

  Correct Answer: A

  The size of an intercepted arc is equal to the measure of the intercepting angle divided by 360, multiplied by the circumference of the circle (2r, where r is the radius of the circle):

  

  units.

• Question 20:

  SIMULATION

  What is the distance from the point where the line given by the equation 3y = 4x + 24 crosses the x-axis to the point where the line crosses the y-axis?

  A. 10

  Correct Answer: A

  Write the equation in slope-intercept form

  

  The line crosses the y-axis at its y-intercept, (0,8). The line crosses the x-axis when

  

  Use the distance formula to find the distance from