Multiple-Choice Exercise From the New York State Education Department. Regents High School Examination. Internet. Available from http://www.nysedregents.org; accessed January 22, 2012.; All rights reserved. No commercial, for-profit use of this material is allowed. E-mail comments and questions to Tami Maloney.

Choose the correct answer for each question.

Which graph does not represent a function?

The roots of the equation x^{2} − 10x + 25 = 0 are

imaginary

real and irrational

real, rational, and equal

real, rational, and unequal

Which values of x are solutions of the equation x^{3} + x^{2} − 2x = 0?

0, 1, 2

0, 1, −2

0, −1, 2

0, −1, −2

45

135

225

240

What is the fifteenth term of the sequence 5, −10, 20, −40, 80, . . . ?

−163,840

−81,920

81,920

327,680

If darts thrown at this board are equally likely to land anywhere on the board, what is the probability that a dart that hits the board will land in either sector 1 or sector 3?

6x^{3} − 30x

6x^{2} − 30

36x^{2} − 5

x^{2} + 6x − 5

Which arithmetic sequence has a common difference of 4?

{0, 4n, 8n, 12n, . . .}

{n, 4n, 16n, 64n, . . .}

{n + 1, n + 5, n + 9, n + 13, . . .}

{n + 4, n + 16, n + 64, n + 256, . . .}

The conjugate of 7 − 5i is

−7 − 5i

−7 + 5i

7 − 5i

7 + 5i

How many distinct triangles can be formed if m∠A = 35, a = 10, and b = 13?

1

2

3

0

The solution set of the inequality x^{2} − 3x > 10 is

If x^{2} + 2 = 6x is solved by completing the square, an intermediate step would be

(x + 3)^{2} = 7

(x − 3)^{2} = 7

(x − 3)^{2} = 11

(x − 6)^{2} = 34

Three marbles are to be drawn at random, without replacement, from a bag containing 15 red marbles, 10 blue marbles, and 5 white marbles. Which expression can be used to calculate the probability of drawing 2 red marbles and 1 white marble from the bag?

On January 1, a share of a certain stock cost $180. Each month thereafter, the cost of a share of this stock decreased by one-third. If x represents the time, in months, and y represents the cost of the stock, in dollars, which graph best represents the cost of a share over the following 5 months?

In the diagram below of right triangle JTM, JT = 12, JM = 6, and m∠JMT = 90.

What is the value of cot J ?

For which equation does the sum of the roots equal −3 and the product of the roots equal 2?

x^{2} + 2x − 3 = 0

x^{2} − 3x + 2 = 0

2 x^{2} + 6x + 4 = 0

2 x^{2} − 6x + 4 = 0

Which equation is sketched in the diagram below?

y = csc x

y = sec x

y = cot x

y = tan x

A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5?

448

504

2,240

2,520

Which equation represents the circle shown in the graph below that passes through the point (0,−1)?

(x − 3)^{2} + (y + 4)^{2} = 16

(x − 3)^{2} + (y + 4)^{2} = 18

(x + 3)^{2} + (y − 4)^{2} = 16

(x + 3)^{2} + (y − 4)^{2} = 18

Which task is not a component of an observational study?

The researcher decides who will make up the sample.

The researcher analyzes the data received from the sample.

The researcher gathers data from the sample, using surveys or taking measurements.

The researcher divides the sample into two groups, with one group acting as a control group.