Algebra II (Common Core) 18 August 2016 Questions Answer Keys

**The University of the State of New York**

Regents High School Examination

Algebra II (Common Core)

Thursday, August 18, 2016 — 12:30 to 3:30 p.m., only

Student Name:____________________________________________________

School Name:_____________________________________________________

**1. Which equation has 1 – i as a solution?**

- (1) x
^{2}– 2x – 2 = 0 - (2) x
^{2}– 2x + 2 = 0 - (3) x
^{2}– 2x – 2 = 0 - (4) x
^{2}– 2x + 2 = 0

**2. Which statement(s) about statistical studies is true?**

I. A survey of all English classes in a high school would be a good sample to determine the number of hours students throughout the school spend studying.

II. A survey of all ninth graders in a high school would be a good sample to determine the number of student parking spaces needed at that high school.

III. A survey of all students in one lunch period in a high school would be a good sample to determine the number of hours adults spend on social media websites.

IV. A survey of all Calculus students in a high school would be a good sample to determine the number of students throughout the school who don’t like math.

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

**3. To the nearest tenth, the value of x that satisfies 2 ^{x} = –2x + 11 is**

- (1) 2.5
- (2) 2.6
- (3) 5.8
- (4) 5.9

**4. The lifespan of a 60-watt lightbulb produced by a company is normally distributed with a mean of 1450 hours and a standard deviation of 8.5 hours. If a 60-watt lightbulb produced by this company is selected at random, what is the probability that its lifespan will be between 1440 and 1465 hours?**

- (1) 0.3803
- (2) 0.4612
- (3) 0.8415
- (4) 0.9612

**5. Which factorization is incorrect?**

- (1) 4k
^{2}– 49 = (2k + 7)(2k – 7) - (2) a
^{3}– 8b^{3}= (a – 2b)(a^{2}+ 2ab + 4b^{2}) - (3) m
^{3}+ 3m^{2}– 4m + 12 = (m – 2)^{2}(m + 3) - (4) t
^{3}+ 5t^{2}+ 6t + t^{2}+ 5t + 6 = (t + 1)(t + 2)(t + 3)

**6. Sally’s high school is planning their spring musical. The revenue, R, generated can be determined by the function R(t) = –33t^{2} + 360t, where t represents the price of a ticket. The production cost, C, of the musical is represented by the function C(t) = 700 + 5t. What is the highest ticket price, to the nearest dollar, they can charge in order to not lose money on the event?**

- (1) t = 3
- (2) t = 5
- (3) t = 8
- (4) t = 11

**7. The set of data in the table below shows the results of a survey on the number of messages that people of different ages text on their cell phones each month.**

If a person from this survey is selected at random, what is the probability that the person texts over 50 messages per month given that the person is between the ages of 23 and 60?

- (1)
^{157}/_{229} - (2)
^{157}/_{312} - (3)
^{157}/_{384} - (4)
^{157}/_{456}

**8. A recursive formula for the sequence 18, 9, 4.5, … is**

**9. Kristin wants to increase her running endurance. According to experts, a gradual mileage increase of 10% per week can reduce the risk of injury. If Kristin runs 8 miles in week one, which expression can help her find the total number of miles she will have run over the course of her 6-week training program?**

**10. A sine function increasing through the origin can be used to model light waves. Violet light has a wavelength of 400 nanometers. Over which interval is the height of the wave decreasing, only?**

- (1) (0, 200)
- (2) (100, 300)
- (3) (200, 400)
- (4) (300, 400)

- (1) x
^{2}+ 3 - (2) x
^{2}+ 3 +^{4}/_{x + 2} - (3) 2x
^{2}+ x + 6 - (3) 2x
^{2}+ x + 6 +^{4}/_{x + 2}

**12. A candidate for political office commissioned a poll. His staff received responses from 900 likely voters and 55% of them said they would vote for the candidate. The staff then conducted a simulation of 1000 more polls of 900 voters, assuming that 55% of voters would vote for their candidate. The output of the simulation is shown in the diagram below.**

Given this output, and assuming a 95% confidence level, the margin of error for the poll is closest to

- (1) 0.01
- (2) 0.03
- (3) 0.06
- (4) 0.12

**13. An equation to represent the value of a car after t months of ownership is v = 32,000(0.81)^{t/12}. Which statement is not correct?**

- (1) The car lost approximately 19% of its value each month.
- (2) The car maintained approximately 98% of its value each month.
- (3) The value of the car when it was purchased was $32,000.
- (4) The value of the car 1 year after it was purchased was $25,920.

**14. Which equation represents an odd function?**

- (1) y = sin x
- (2) y = cos x
- (3) y = (x + 1)
^{3} - (4) y = e
^{5x}

**15. The completely factored form of 2 d^{4} + 6d^{3} – 18d^{2} – 54d is**

- (1) 2
*d*(*d*^{2}– 9)(*d*+ 3) - (2) 2
*d*(*d*^{2}+ 9)(*d*+ 3) - (3) 2
*d*(*d*+ 3)2(*d*– 3) - (4) 2
*d*(*d*– 3)2(*d*+ 3)

**16. Which diagram shows an angle rotation of 1 radian on the unit circle?**

**17. The focal length, F, of a camera’s lens is related to the distance of the object from the lens, J, and the distance to the image area in the camera, W, by the formula below.**

^{1}/_{J} + ^{1}/_{W} = ^{1}/_{F}

When this equation is solved for *J* in terms of *F* and *W*,* J* equals

- (1) F – W
- (2)
^{FW}/_{F – W} - (3)
^{FW}/_{W – F} - (4)
^{1}/_{F}–^{1}/_{W}

**18. The sequence a _{1} = 6, a_{n} = 3a_{n– 1} can also be written as**

- (1) a
_{n}= 6 • 3^{n} - (2) a
_{n}= 6 • 3^{n+1} - (3) a
_{n}= 2 • 3^{n} - (4) a
_{n}= 2 • 3^{n+1}

**19. Which equation represents the set of points equidistant from line l and point R shown on the graph below?**

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

**20. Mr. Farison gave his class the three mathematical rules shown below to either prove or disprove. Which rules can be proved for all real numbers?**

I (*m* + *p*)^{2} + *m*^{2} + 2*mp* + *p*^{2}

II (*x* + *y*)^{3} = *x*^{3} + 3*xy* + *y*^{3}

III (*a*^{2} + *b*^{2})^{2} = (*a*^{2} – *b*^{2})^{2} + (2*ab*)^{2}

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

**Algebra II (Common Core) 18 August 2016 Questions Answers Keys**

Algebra II (Common Core) Examination Question |

Scoring Key and Rating Guide |

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