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.

A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation?

census

survey

observation

controlled experiment

An auditorium has 21 rows of seats. The first row has 18 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium?

540

567

760

798

Expressed as a function of a positive acute angle, cos (−305°) is equal to

−cos 55°

cos 55°

−sin 55°

sin 55°

The value of x in the equation 4^{2x + 5} = 8^{3x} is

1

2

5

−10

What is the value of x in the equation log_{5}x = 4?

1.16

20

625

1,024

Which equation is represented by the graph below?

y = 5^{x}

y = 0.5^{x}

y = 5^{−x}

y = 0.5^{−x}

In △ABC, a = 15, b = 14, and c = 13, as shown in the diagram below. What is the m∠C, to the nearest degree?

53

59

67

127

What is the range of f(x) = (x + 4)^{2} + 7?

Ms. Bell’s mathematics class consists of 4 sophomores, 10 juniors, and 5 seniors. How many different ways can Ms. Bell create a four-member committee of juniors if each junior has an equal chance of being selected?

210

3,876

5,040

93,024

Which graph represents a relation that is not a function?

The value of tan 126°43′ to the nearest ten-thousandth is

−1.3407

−1.3408

−1.3548

−1.3549

Akeem invests $25,000 in an account that pays 4.75% annual interest compounded continuously. Using the formula A = Pe^{rt}, where A = the amount in the account after t years, P = principal invested, and r = the annual interest rate, how many years, to the nearest tenth, will it take for Akeem’s investment to triple?

10.0

14.6

23.1

24.0

−38

−12

26

62

Which graph shows y = cos^{−1}x?

{−3, 4}

{−4, 3}

{3}

{−4}

Brian correctly used a method of completing the square to solve the equation x^{2} + 7x − 11 = 0. Brian’s first step was to rewrite the equation as x^{2} + 7x = 11. He then added a number to both sides of the equation. Which number did he add?

The number of minutes students took to complete a quiz is summarized in the table below.

If the mean number of minutes was 17, which equation could be used to calculate the value of x?

What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock?

What is the coefficient of the fourth term in the expansion of (a − 4b)^{9}?

−5,376

−336

336

5,376

Samantha constructs the scatter plot below from a set of data.

Based on her scatter plot, which regression model would be most appropriate?