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

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

- (1) 9k
^{2}– 4 - (2) 9k
^{2}+ 4 - (3) 9k
^{2}– 12ki – 4 - (4) 9k
^{2}– 12ki + 4

**3. The roots of the equation x ^{2} + 2x + 5 = 0 are**

- (1) –3 and 1
- (2) –1, only
- (3) –1 + 2i and –1 –2i
- (4) –1 + 4i and –1 –4i

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

- (1) {
**–**6} - (2) {2}
- (3) {18}
- (4) {2, 22}

**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

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

- (1) x
^{2}= –8y - (2) x
^{2}= –4y - (3) x
^{2}= 8y - (4) x
^{2}= 4y

**7. Which diagram represents an angle, α, measuring ^{13π}/_{20 }radians drawn in standard position, and its reference angle, θ?**

**8. What are the zeros of P(m) = (m ^{2} – 4)(m^{2} – 1)?**

- (1) 2 and
**–**2, only - (2) 2,
**–**2, and**–**4 - (3)
**–**4, i, and**–**i - (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 log_{0.8}(^{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

**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?

**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

**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

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

- (1) (x + 2)
^{2}2(x + 2) – 8 = (x + 6)x - (2) x
^{4}+ 4x^{2}+ 9x^{2}y^{2}– 36y^{2}= (x + 3y)^{2}(x –2)^{2} - (3) x
^{3}+ 3x^{2}– 4xy^{2}– 12y^{2}= (x – 2y) (x + 3)^{2} - (4) (x
^{2}– 4)^{2}– 5(x^{2}– 4) – 6 = (x^{2}– 7)(x^{2}– 6)

**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

**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.

**18. Which sinusoid has the greatest amplitude?**

**19. Consider the system shown below.**

2x – y = 4

(x + 3)^{2} + y^{2} = 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

**20. Which binomial is not a factor of the expression x ^{3} – 11x^{2} + 16x + 84?**

- (1) x + 2
- (2) x + 4
- (3) x
**–**6 - (4) x
**–**7

**Algebra II (Common Core) 16 August 2017 Questions Answers Keys**

Algebra II (Common Core) Examination Question |

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