August 2017 Algebra Two Regents

1. The function $f(x) = \dfrac{x - 3}{x^{2} + 2x - 8}$ is undefined when $x$ equals

(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) $9k^{2} - 12i - 4$
(4) $9k^{2} - 2i + 4$

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 $\sqrt{x + 14} - \sqrt{2x + 5} = 1$ is

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

5. As $x$ increases from $0$ to $\dfrac{\pi}{2}$ , 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, $\alpha$ , measuring $\dfrac{13\pi}{20}$ radians drawn in standard position, and its reference angle, $0$ ?

(1)
(2)
(3)
(4)

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 $log_{0.8}(\dfrac{V}{17000}) = t$ .

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 $A = 100(\dfrac{1}{2})^\frac{t}{73.83}$ .

Which equation approximates the amount of Iridium- $192$ present after $t$ days?

(1) $A = 100(\dfrac{73.83}{2})^{t}$
(2) $A = 100(\dfrac{1}{147.66})^{t}$
(3) $A = 100(0.990656)^{t}$
(4) $A = 100(0.116381)^{t}$

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) $0.9500$

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

13. Which expression is equivalent to $\dfrac{4x^{2} + 9x - 5}{2x - 1}$ , where $x \neq \dfrac{1}{2}$ ?

(1) $2x^{2} + x + 5$
(2) $2x^{2} + \dfrac{11}{2} + \dfrac{1}{2(2x + 1)}$
(3) $2x^{2} - x + 5$
(4) $2x^{2} - x + 4 + \dfrac{1}{2x - 1}$

14. The inverse of the function $f(x) = \dfrac{x + 1}{x - 2}$ is

(1) $f^{-1}(x) = \dfrac{x + 1}{x + 2}$
(2) $f^{-1}(x) = \dfrac{2x + 1}{x - 1}$
(3) $f^{-1}(x) = \dfrac{x + 1}{x + 2}$
(4) $f^{-1}(x) = \dfrac{x - 1}{x + 1}$

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) $(x^{2} - 4)^{2} - 5(x^{2} - 4) - 6 = (x^{2} - 7)(x^{2} - 7)(x^{2} - 6)$

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 $\approx.16$ ; margin of error $\approx.01$
(2) proportion $\approx.16$ ; margin of error $\approx.02$
(3) proportion $\approx.01$ ; margin of error $\approx.16$
(4) proportion $\approx.02$ ; margin of error $\approx.16$

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 student’s final exam grades.

18. Which sinusoid has the greatest amplitude?

(1)
(2) $y = 3 \sin (\theta - 3) + 5$
(3)
(4) $y = -5 \sin (\theta - 1) - 3$

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) $x - 7$

21. A ball is dropped from a height of $32$ feet. It bounces and rebounds $80\%$ of the height from which it was falling. What is the total downward distance, in feet, the ball traveled up to the $12th$ bounce?

(1) $29$
(2) $58$
(3) $120$
(4) $149$

22. A public opinion poll was conducted on behalf of Mayor Ortega’s reelection campaign shortly before the election. $264$ out of $550$ likely voters said they would vote for Mayor Ortega; the rest said they would vote for his opponent.

Which statement is least appropriate to make, according to the results of the poll?

(1) There is a $48\%$ chance that Mayor Ortega will win the election.
(2) The point estimate $(p)$ of voters who will vote for Mayor Ortega is $48\%$ .
(3) It is most likely that between $44\%$ and $52\%$ of voters will vote for Mayor Ortega.
(4) Due to the margin of error, an inference cannot be made regarding whether Mayor Ortega or his opponent is most likely to win the election.

23. What does $(\dfrac{-54x^{9}}{y^{4}})^\frac{2}{3}$ equal?

(1) $\dfrac{9ix^{6} \sqrt[3]{4}}{y\sqrt[3]{y^{2}}}$
(2) $\dfrac{9ix^{6} \sqrt[3]{4}}{y^{2} \sqrt[3]{y^{2}}}$
(3) $\dfrac{9x^{6} \sqrt[3]{4}}{y \sqrt[3]{y}}$
(4) $\dfrac{9x^{6} \sqrt[3]{4}}{y^{2} \sqrt[3]{y^{2}}}$

24. The Rickerts decided to set up an account for their daughter to pay for her college education. The day their daughter was born, they deposited $\$1000$ in an account that pays $1.8\%$ compounded annually. Beginning with her first birthday, they deposit an additional $\$750$ into the account on each of her birthdays. Which expression correctly represents the amount of money in the account $n$ years after their daughter was born?

(1) $a_{n} = 1000(1.018)^{n} + 750$
(2) $a_{n} = 1000(1.018)^{n} + 750n$
(3) $a_{0} = 1000$ ,
$a_{n} = a_{n - 1}(1.018) + 750$
(4) $a_{0} = 1000$ ,
$a_{n} = a_{n-1}(1.018) + 750n$