Algebra II (Common Core) 16 June 2017

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

The University of the State of New York
Regents High School Examination
Algebra II (Common Core)
Friday, June 16, 2017 — 1:15 to 4:15 p.m., only
Student Name:____________________________________________________
School Name:_____________________________________________________

1. The graph of the function p(x) is sketched below.

Which equation could represent p(x)?

(1) p(x) = (x² – 9)(x – 2)
(2) p(x) = x³ – 2x² + 9x + 18
(3) p(x) = (x² + 9)(x – 2)
(4) p(x) = x³ + 2x² – 9x – 18

Answer: (1) p(x) = (x² – 9)(x – 2)

2. What is the solution to 8(2^{x + 3}) = 48?

Answer: (1)

3. Cheap and Fast gas station is conducting a consumer satisfaction survey. Which method of collecting data would most likely lead to a biased sample?

(1) interviewing every 5th customer to come into the station
(2) interviewing customers chosen at random by a computer at the checkout
(3) interviewing customers who call an 800 number posted on the customers’ receipts
(4) interviewing every customer who comes into the station on a day of the week chosen at random out of a hat

Answer: (3) interviewing customers who call an 800 number posted on the customers’ receipts

4. The expression 6xi³(–4xi + 5) is equivalent to

(1) 2x – 5i
(2) 24x² – 30xi
(3) –24x² + 30x – i
(4) 26x – 24x²i – 5i

Answer: (2) 24x² – 30xi

5. If f(x) 3|x| –1 and g(x) 0.03x³ – x + 1, an approximate solution for the equation f(x) = g(x) is

(1) 1.96
(2) 11.29
(3) (–0.99, 1.96)
(4) (11.29, 32.87)

Answer: (2) 11.29

6. Given the parent function p(x) = cos x, which phrase best describes the transformation used to obtain the graph of g(x) = cos(x + a) – b, if a and b are positive constants?

(1) right a units, up b units
(2) right a units, down b units
(3) left a units, up b units
(4) left a units, down b units

Answer: (4) left a units, down b units

7. The solution to the equation 4x² + 98 = 0 is

(1) ±7
(2) ±7i
(3) ± ^7√2/₂
(4) ± ^7i√2/₂

Answer: (4) ± ^7i√2/₂

8. Which equation is represented by the graph shown below?

(1) y =¹/₂cos 2x
(2) y = cos x
(3) y =¹/₂cos x
(4) y = 2 cos ¹/₂x

Answer: (1) y =¹/₂cos 2x

9. A manufacturing company has developed a cost model, C(x) = 0.15x³ + 0.01x² + 2x + 120, where x is the number of items sold, in thousands. The sales price can be modeled by S(x) = 30 – 0.01x. Therefore, revenue is modeled by R(x) = x •S(x).

The company’s profit, P(x) = R(x) – C(x), could be modeled by

(1) 0.15x³ + 0.02x² – 28x + 120
(2) –0.15x³ – 0.02x² + 28x – 120
(3) –0.15x³ + 0.01x² – 2.01x – 120
(4) –0.15x³ + 32x + 120

Answer: (2) –0.15x³ – 0.02x² + 28x – 120

10. A game spinner is divided into 6 equally sized regions, as shown in the diagram below.

For Miles to win, the spinner must land on the number 6. After spinning the spinner 10 times, and losing all 10 times, Miles complained that the spinner is unfair. At home, his dad ran 100 simulations of spinning the spinner 10 times, assuming the probability of winning each spin is ¹/₆. The output of the simulation is shown in the diagram below.

Which explanation is appropriate for Miles and his dad to make?

(1) The spinner was likely unfair, since the number 6 failed to occur in about 20% of the simulations.
(2) The spinner was likely unfair, since the spinner should have landed on the number 6 by the sixth spin.
(3) The spinner was likely not unfair, since the number 6 failed to occur in about 20% of the simulations.
(4) The spinner was likely not unfair, since in the output the player wins once or twice in the majority of the simulations.

Answer: (3) The spinner was likely not unfair, since the number 6 failed to occur in about 20% of the simulations.

11. Which binomial is a factor of x⁴ – 4x² – 4x + 8?

(1) x – 2
(2) x + 2
(3) x – 4
(4) x + 4

Answer: (1) x – 2

12. Given that sin² θ + cos² θ = 1 and sin θ = –^√2/₅, what is a possible value of cos θ?

Answer: (2)

13. A student studying public policy created a model for the population of Detroit, where the population decreased 25% over a decade. He used the model P = 714(0.75)^d, where P is the population, in thousands, d decades after 2010. Another student, Suzanne, wants to use a model that would predict the population after y years. Suzanne’s model is best represented by

(1) P = 714(0.6500)^y
(2) P = 714(0.8500)^y
(3) P = 714(0.9716)^y
(4) P = 714(0.9750)^y

Answer: (3) P = 714(0.9716)^y

14. The probability that Gary and Jane have a child with blue eyes is 0.25, and the probability that they have a child with blond hair is 0.5. The probability that they have a child with both blue eyes and blond hair is 0.125. Given this information, the events blue eyes and blond hair are

I: dependent
II: independent
III: mutually exclusive

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

Answer: (2) II, only

15. Based on climate data that have been collected in Bar Harbor, Maine, the average monthly temperature, in degrees F, can be modeled by the equation B(x) = 23.914sin(0.508x – 2.116) + 55.300. The same governmental agency collected average monthly temperature data for Phoenix, Arizona, and found the temperatures could be modeled by the equation P(x) = 20.238sin(0.525x – 2.148) + 86.729.

Which statement cannot be concluded based on the average monthly temperature models x months after starting data collection?

(1) The average monthly temperature variation is more in Bar Harbor than in Phoenix.
(2) The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix.
(3) The maximum average monthly temperature for Bar Harbor is 79° F, to the nearest degree.
(4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.

Answer: (4) The minimum average monthly temperature for Phoenix is 20° F, to the nearest degree.

16. For x ≠ 0, which expressions are equivalent to one divided by the sixth root of x?

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

Answer: (4) I, II, and III

17. A parabola has its focus at (1,2) and its directrix is y = –2. The equation of this parabola could be

(1) y = 8(x + 1)²
(2) y = ¹/₈(x + 1)²
(3) y = 8(x – 1)²
(4) y = ¹/₈(x – 1)²

Answer: (4) y = ¹/₈(x – 1)²

18. The function p(t) = 110e^0.03922t models the population of a city, in millions, t years after 2010. As of today, consider the following two statements:

I. The current population is 110 million

II. The population increases continuously by approximately 3.9% per year.

This model supports