January 2019 Algebra Two Regents

1. Suppose two sets of test scores have the same mean, but different standard deviations, $Q_{1}$ and $Q_{2}$ with $Q_{2} \textgreater Q_{1}$ . Which statement best describes the variability of these data sets?

(1) Data set one has the greater variability.
(2) Data set two has the greater variability.
(3) The variability will be the same for each data set.
(4) No conclusion can be made regarding the variability of either set.

2. If $f(x) = log_{3}x$ and $g(x)$ is the image of $f(x)$ after a translation five units to the left, which equation represents $g(x)$ ?

(1) $g(x) = log_{3} (x + 5)$
(2) $g(x)= log_{3} x + 5$
(3) $g(x)= log_{3} (x - 5$
(4) $g(x)= log_{3} x - 5$

3. When factoring to reveal the roots of the equation $x^{3} + 2x^{2} - 9x - 18 = 0$ , which equations can be used?

I. $x^{2}(x + 2) - 9(x + 2) = 0$
II. $x(x^{2} - 9) + 2(x^{2} - 9)=0$
III. $(x - 2)(x^{2} - 9) = 0$

(1) I and II, only
(2) I and III, only
(3) II and III, only
(4) I, II, and III

4. When a ball bounces, the heights of consecutive bounces form a geometric sequence. The height of the first bounce is $121$ centimeters and the height of the third bounce is $64$ centimeters. To the nearest centimeter, what is the height of the fifth bounce?

(1) $25$
(2) $34$
(3) $36$
(4) $42$

5. The solutions to the equation $5x^{2} - 2x + 13 = 9$ are

(1) $\dfrac{1}{5}\pm \dfrac{\sqrt{21}}{5}$
(2) $\dfrac{1}{5}\pm \dfrac{\sqrt{19}}{5}i$
(3) $\dfrac{1}{5} \pm {\sqrt{66}}{5}i$
(4) $\dfrac{1}{5} \pm {\sqrt{66}}{5}$

6. Julia deposits $\$2000$ into a savings account that earns $4\%$ interest per year. The exponential function that models this savings account is $y = 2000(1.04)^{t}$ , where $t$ is the time in years. Which equation correctly represents the amount of money in her savings account in terms of the monthly growth rate?

(1) $y = 166.67(1.04)^{0.12t}$
(2) $y = 2000(1.01)^{t}$
(3) $y = 2000(1.0032737)^{12t}$
(4) $y = 166.67(1.0032737)^{t}$

7. Tides are a periodic rise and fall of ocean water. On a typical day at a seaport, to predict the time of the next high tide, the most important value to have would be the

(1) time between consecutive low tides
(2) time when the tide height is $20$ feet
(3) average depth of water over a $24$ -hour period
(4) difference between the water heights at low and high tide

8. An estimate of the number of milligrams of a medication in the bloodstream $t$ hours after $400$ mg has been taken can be modeled by the function below.

$I(t) = 0.5t^{4} + 3.45t^{3} - 96.65t^{2} + 347.7t$ , where $0 \leq t \leq 6$

Over what time interval does the amount of medication in the bloodstream strictly increase?

(1) $0$ to $2$ hours
(2) $0$ to $3$ hours
(3) $2$ to $6$ hours
(4) $3$ to $6$

9. Which representation of a quadratic has imaginary roots?

(1)
(2) $2 (x + 3)^{2} = 64$
(3)
(4) $2x^{2} + 3 = 0$

10. A random sample of $100$ people that would best estimate the proportion of all registered voters in a district who support improvements to the high school football field should be drawn from registered voters in the district at a

(1) football game
(2) supermarket
(3) school fund-raiser
(4) high school band concert

11. Which expression is equivalent to $(2x - i)^{2} - (2x - i)(2x + 3i)$ where $i$ is the imaginary unit and $x$ is a real number?

(1) $-4 - 8xi$
(2) $-4 - 4xi$
(3) $2$
(4) $8x - 4i$

12. Suppose events $A$ and $B$ are independent and $P(A$ and $B)$ is $0.2$ . Which statement could be true?

(1) $P(A)=0.4, P(B)=0.3, P(A or B)=0.5$
(2) $P(A)=0.8, P(B)=0.25$
(3) $P(A|B)=0.2, P(B)=0.2$
(4) $P(A)=0.15, P(b)=0.05$

13. The function $f(x)=a \cos bx + c$ is plotted on the graph shown below.

What are the values of $a, b$ , and $c$ ?

(1) $a=2, b=6, c=3$
(2) $a=2, b=3, c=1$
(3) $a=4, b=6, c=5$
(4) $a=4, b=\dfrac{\pi}{3}, c=3$

14. Which equation represents the equation of the parabola with focus $(-3, 3)$ and directrix $y = 7$ ?

(1) $y = \dfrac{1}{8}(x + 3)^{2} - 5$
(2) $y = \dfrac{1}{8}(x - 3)^{2} + 5$
(3) $y = -\dfrac{1}{8}(x + 3)^{2} + 5$
(4) $y = -\dfrac{1}{8}(x - 3)^{2} + 5$

15. What is the solution set of the equation $\dfrac{2}{3x + 1} = \dfrac{1}{x} - \dfrac{6x}{3x + 1}$ ?

(1) ${-\dfrac{1}{3}, \dfrac{1}{2}}$
(2) ${-\dfrac{1}{3}}$
(3) ${\dfrac{1}{2}}$
(4) ${\dfrac{1}{3}, -2}$

16. Savannah just got contact lenses. Her doctor said she can wear them $2$ hours the first day, and can then increase the length of time by $30$ minutes each day. If this pattern continues, which formula would not be appropriate to determine the length of time, in either minutes or hours, she could wear her contact lenses on the nth day?

(1) $a_{1} = 120$ ,
$a_{n} = a_{n} - 1 + 30$
(2) $a_{n} = 90 + 30n$
(3) $a_{1} = 2$ ,
$a_{n}=2.5 + 0.5n$
(4) $a_{n}=2.5 + 0.5n$

17. If $f(x)=a^{x}$ where $a \textgreater 1$ , then the inverse of the function is

(1) $f^{-1}(x) = log_{x}a$
(2) $f^{-1}(x) = alogx$
(3) $f^{-1}(x) = log_{a}x$
(4) $f^{-1}(x) = xloga$

18. Kelly-Ann has $\$20,000$ to invest. She puts half of the money into an account that grows at an annual rate of $0.9\%$ compounded monthly. At the same time, she puts the other half of the money into an account that grows continuously at an annual rate of $0.8\%$ . Which function represents the value of Kelly-Ann’s investments after $t$ years?

(1) $f(t) = 10,000(1.9)^{t} + 10,000e^{0.8t}$
(2) $f(t) = 10,000(1.009)^{t} + 10,000e^{0.008t}$
(3) $f(t) = 10,000(1.075)^{12t} + 10,000e^{0.8t}$
(4) $f(t) = 10,000(1.00075)^{12t} + 10,000e^{0.008t}$

19. Which graph represents a polynomial function that contains $x^{2} + 2x + 1$ as a factor?

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

20. Sodium iodide- $131$ , used to treat certain medical conditions, has a half-life of $1.8$ hours. The data table below shows the amount of sodium iodide- $131$ , rounded to the nearest thousandth, as the dose fades over time.

What approximate amount of sodium iodide- $131$ will remain in the body after $18$ hours?

(1) $0.001$
(2) $0.136$
(3) $0.271$
(4) $0.543$

21. Which expression(s) are equivalent to $\dfrac{x^{2} - 4x}{2x}$ , where $x \neq 0$ ?

I. $\dfrac{x}{2} - 2$
II. $\dfrac{x - 4}{2}$
III. $\dfrac{x - 1}{2} - \dfrac{3}{2}$

(1) II, only
(2) I and II
(3) II and III
(4) I, II, and III

22. Consider $f(x) = 4x^{2} + 6x - 3$ , and $p(x)$ defined by the graph below.

The difference between the values of the maximum of $p$ and minimum of $f$ is

(1) $0.25$
(2) $1.25$
(3) $3.25$
(4) $10.25$

23. The scores on a mathematics college-entry exam are normally distributed with a mean of $68$ and standard deviation $7.2$ . Students scoring higher than one standard deviation above the mean will not be enrolled in the mathematics tutoring program. How many of the $750$ incoming students can be expected to be enrolled in the tutoring program?

(1) $631$
(2) $512$
(3) $238$
(4) $119$

24. How many solutions exist for $\dfrac{1}{1 - x^{2}} = - |3x - 2| + 5$ ?

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