Algebra II is one of three math tests included in the PARCC high-school-level exams; the others are Algebra I and geometry. The tests are meant to be given at the end of the year in which students take that course, in this case, probably 10th or 11th grades.

Students are starting to take the year-end tests this week, in what is the second phase of the new PARCC (Partnership for Assessment of Readiness for College and Careers) exams. The state isn’t yet requiring students to pass all three tests to graduate. Instead, it is giving them a range of options to meet graduation requirements, including minimum scores on the SAT or ACT.

NJ Spotlight this week is posting sample questions from PARCC. The following are from the Algebra II exam. One is from the section that allows the use of calculators and the other is from the section that does not. Correct answers will be posted the following day.

The full set of practice tests are available online.

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Instructions: Today, you will be taking Unit 1 of the Algebra II End-of-Year Assessment Practice Test.

Read each question carefully. Some questions will ask you to choose one correct answer, while others will ask you to choose more than one correct answer.

In the first section of this unit, you may not use a calculator.

*Question 1. Part A:*

The function f(x) = cos(x). Function g(x) results from a transformation on the function f(x) = cos(x). A portion of the graph of g(x) is shown.

What is the equation of g(x)?

A. g(x) = cos(x) − 2

B. g(x) = cos(x) + 2

C. g(x) = cos(2x) + 0

D. g(x) = 2cos(x) + 0

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In the second section, calculators are permitted.

*Question 2: A circular spinner is divided into five sectors of different colors. A student spun the arrow on the spinner 200 times and recorded that the arrow stopped on the orange sector 38 times out of the 200 spins. To test whether the spinner was fair, the student used a computer to simulate the number of times the arrow stops on orange in 200 spins of a fair spinner equally divided into five sectors of different colors. The results of 1,000 trials of the simulation are shown.*

Based on the results of the simulation, is there statistical evidence that the spinner is not fair?

A. Yes, because 38 was the most frequent outcome.

B. Yes, because about 8% of the outcomes were 38.

C. No, because the distribution is approximately normal.

D. No, because an outcome of 38 or less is not unusual.

*Answers to yesterday’s 9th grade language arts sample questions:*

Question 1

Part A: C

Part B: D

Question 2: D