# Algebra II (Common Core) 16 August 2017

Algebra II (Common Core) 16 August 2017 Questions Answer Keys

The University of the State of New York
Regents High School Examination
Algebra II (Common Core)
Wednesday, August 16, 2017 — 12:30 to 3:30 p.m., only
Student Name:____________________________________________________
School Name:_____________________________________________________ • (1) 2 or –4
• (2) 4 or –2
• (3) 3, only
• (4) 2, only
Answer: (1) 2 or –4

2. Which expression is equivalent to (3k – 2i)2 , where i is the imaginary unit?

• (1) 9k2 – 4
• (2) 9k2 + 4
• (3) 9k2 – 12ki – 4
• (4) 9k2 – 12ki + 4
Answer: (3) 9k2 – 12ki – 4

3. The roots of the equation x2 + 2x + 5 = 0 are

• (1) –3 and 1
• (2) –1, only
• (3) –1 + 2i  and –1 –2i
• (4) –1 + 4i and –1 –4i
Answer: (3) –1 + 2i  and –1 –2i

4. The solution set for the equation √x + 14 – √2x + 5 = 1 is

• (1) {6}
• (2) {2}
• (3) {18}
• (4) {2, 22}
Answer: (2) {2}

5. As x increases from 0 to π/2, , the graph of the equation y = 2 tan x will

• (1) increase from 0 to 2
• (2) decrease from 0 to –2
• (3) increase without limit
• (4) decrease without limit
Answer: (3) increase without limit

6. Which equation represents a parabola with the focus at (0, –1) and the directrix y = 1?

• (1) x2 = –8y
• (2) x2 = –4y
• (3) x2 = 8y
• (4) x2 = 4y
Answer: (2) x2 = –4y

7. Which diagram represents an angle, α, measuring 13π/20 radians drawn in standard position, and its reference angle, θ? Answer: (4)

8. What are the zeros of P(m) = (m2 – 4)(m2 – 1)?

• (1) 2 and 2, only
• (2) 2, 2, and 4
• (3) 4, i, and i
• (4) 2, 2, i, and i
Answer: (4) 2, –2, i, and –i

9. The value of a new car depreciates over time. Greg purchased a new car in June 2011. The value, V, of his car after t years can be modeled by the equation log0.8(V/1700) = t.

What is the average decreasing rate of change per year of the value of the car from June 2012 to June 2014, to the nearest ten dollars per year?

• (1) 1960
• (2) 2180
• (3) 2450
• (4) 2770
Answer: (3) 2450

10. Iridium-192 is an isotope of iridium and has a half-life of 73.83 days. If a laboratory experiment begins with 100 grams of Iridium-192, the number of grams, A, of Iridium-192 present after t days would be A = 100 (½)t/73.83

Which equation approximates the amount of Iridium-192 present after t days? Answer: (3) A = 100(0.990656)t

11. The distribution of the diameters of ball bearings made under a given manufacturing process is normally distributed with a mean of 4 cm and a standard deviation of 0.2 cm. What proportion of the ball bearings will have a diameter less than 3.7 cm?

• (1) 0.0668
• (2) 0.4332
• (3) 0.8664
• (4) 0.9500
Answer: (1) 0.0668

12. A polynomial equation of degree three, p(x), is used to model the volume of a rectangular box. The graph of p(x) has x intercepts at –2, 10, and 14. Which statements regarding p(x) could be true?

A. The equation of p(x) = (x – 2)(x + 10)(x + 14).

B. The equation of p(x) = –(x + 2)(x – 10)(x – 14).

C. The maximum volume occurs when x = 10.

D. The maximum volume of the box is approximately 56.

• (1) A and C
• (2) A and D
• (3) B and C
• (4) B and D
Answer: (4) B and D Answer: (1) Answer: (2)

15. Which expression has been rewritten correctly to form a true statement?

• (1) (x + 2)2 2(x + 2) – 8 = (x + 6)x
• (2) x4 + 4x2 + 9x2y2 – 36y2 = (x + 3y)2 (x –2)2
• (3) x3 + 3x2 – 4xy2 – 12y2 = (x – 2y) (x + 3)2
• (4) (x2 – 4)2 – 5(x2 – 4) – 6 = (x2 – 7)(x2 – 6)
Answer: (1) (x + 2)2 2(x + 2) – 8 = (x + 6)x

16. A study conducted in 2004 in New York City found that 212 out of 1334 participants had hypertension. Kim ran a simulation of 100 studies based on these data. The output of the simulation is shown in the diagram below. At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to

• (1) proportion ≈ .16; margin of error ≈ .01
• (2) proportion ≈ .16; margin of error ≈ .02
• (3) proportion ≈ .01; margin of error ≈ .16
• (4) proportion ≈ .02; margin of error ≈ .16
Answer: (2) proportion ≈ .16; margin of error ≈ .02

17. Which scenario is best described as an observational study?

• (1) For a class project, students in Health class ask every tenth student entering the school if they eat breakfast in the morning.
• (2) A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.
• (3) A researcher wants to learn whether or not there is a link between children’s daily amount of physical activity and their overall energy level. During lunch at the local high school, she distributed a short questionnaire to students in the cafeteria.
• (4) Sixty seniors taking a course in Advanced Algebra Concepts are randomly divided into two classes. One class uses a graphing calculator all the time, and the other class never uses graphing calculators. A guidance counselor wants to determine whether there is a link between graphing calculator use and students’ final exam grades.
Answer: (2) A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.

18. Which sinusoid has the greatest amplitude? Answer: (4) y = –5 sin (θ – 1) – 3

19. Consider the system shown below.

2x – y = 4

(x + 3)2 + y2 = 8

The two solutions of the system can be described as

• (1) both imaginary
• (2) both irrational
• (3) both rational
• (4) one rational and one irrational
Answer: (1) both imaginary

20. Which binomial is not a factor of the expression x3 – 11x2 + 16x + 84?

• (1) x + 2
• (2) x + 4
• (3) x – 6
• (4) x – 7
Answer: (2) x + 4

Algebra II (Common Core) 16 August 2017 Questions Answers Keys Algebra II (Common Core) Examination Question Scoring Key and Rating Guide

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