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More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the RegentsExam conducted by NYSED. The following are the worked solutionsfor the Algebra 2(Common Core) Regents High School ExaminationJune 2016.

### Algebra 2 Common Core Regents New York State Exam - June 2016, Questions 1 - 39

The following are questions from the past paper Regents High School Algebra 2, June 2016 Exam (pdf).

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Algebra 2 - June 2016 Regents - Questions and solutions 1 - 12

1 When b > 0 and d is a positive integer, the expression (3b)^{2/d} isequivalent to

2 Julie averaged 85 on the first three tests of the semester in hermathematics class. If she scores 93 on each of the remaining tests,her average will be 90. Which equation could be used to determinehow many tests, T, are left in the semester?

3 Given i is the imaginary unit, (2 - yi)^{2} in simplest form is

4 Which graph has the following characteristics?

5 The solution set for the equation √(56-x) is

6 The zeros for f(x) = x^{2} - 4x^{2} - 9x^{2} + 36x are

7 Anne has a coin. She does not know if it is a fair coin. She flippedthe coin 100 times and obtained 73 heads and 27 tails. She rana computer simulation of 200 samples of 100 fair coin flips. Theoutput of the proportion of heads is shown below

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

8 If g(c) = 1 - c^{2} and m(c) = c + 1, then which statement is not true?

9 The heights of women in the United States are normally distributed computations.with a mean of 64 inches and a standard deviation of 2.75 inches.The percent of women whose heights are between 64 and 69.5 inches,to the nearest whole percent, is

10 The formula below can be used to model which scenario?

11 Sean’s team has a baseball game tomorrow. He pitches 50% ofthe games. There is a 40% chance of rain during the game tomorrow.If the probability that it rains given that Sean pitches is 40%, it canbe concluded that these two events are

12 A solution of the equation 2x^{2} + 3x + 2 = 0 is

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Algebra 2 - June 2016 Regents - Questions and solutions 13 - 24

13 The Ferris wheel at the landmark Navy Pier in Chicago takes7 minutes to make one full rotation. The height, H, in feet, abovethe ground of one of the six-person cars can be modeled byH(t) = 70 sin (2π/7(t-1.75)) + 80, where t is time, in minutes. UsingH(t) for one full rotation, this car’s minimum height, in feet, is

14 The expression (4x^{3} + 5x + 10)/(2x + 3) is equivalent to

15 Which function represents exponential decay?

16 Given f^{-1}(x) = -3/4 x + 2, which equation represents f(x)?

17 A circle centered at the origin has a radius of 10 units. The terminalside of an angle, θ, intercepts the circle in Quadrant II at point C.The y-coordinate of point C is 8. What is the value of cos θ?

18 Which statement about the graph of c(x) = log_{6}x is false?

19 The equation 4x^{2} - 24x + 4y^{2} + 72y = 76 is equivalent to

20 There was a study done on oxygen consumption of snails as a functionof pH, and the result was a degree 4 polynomial function whosegraph is shown below

21 Last year, the total revenue for Home Style, a national restaurantchain, increased 5.25% over the previous year. If this trend were tocontinue, which expression could the company’s chief financial officeruse to approximate their monthly percent increase in revenue?[Let m represent months.]

22 Which value, to the nearest tenth, is not a solution of p(x) = q(x) ifp(x) = x^{3} + 3x^{2} - 3x - 1 and q(x) = 3x + 8?

23 The population of Jamesburg for the years 2010 – 2013, respectively,was reported as follows:

24 The voltage used by most households can be modeled by a sinefunction. The maximum voltage is 120 volts, and there are 60 cyclesevery second. Which equation best represents the value of the voltageas it flows through the electric wires, where t is time in seconds?

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Algebra 2 - June 2016 Regents - Questions and solutions 25 - 39

25 Solve for x: 1/x - 1/3 = -1/(3x)

26 Describe how a controlled experiment can be created to examine the effect of ingredient X ina toothpaste.

27 Determine if x - 5 is a factor of 2x^{3} - 4x^{2} - 7x - 10. Explain your answer.

28 On the axes below, graph one cycle of a cosine function with amplitude 3, period π/2,midline y = -1, and passing through the point (0,2).

29 A suburban high school has a population of 1376 students. The number of students whoparticipate in sports is 649. The number of students who participate in music is 433. Ifthe probability that a student participates in either sports or music is 974/1376, what is the probabilitythat a student participates in both sports and music?

30 The directrix of the parabola 12(y + 3) = (x - 4)^{2} has the equation y = -6. Find the coordinatesof the focus of the parabola.

31 Algebraically prove that (x^{3} + 9)/(x^{3} + 8) = 1 + 1/(x^{3} + 8), where x ≠ -2.

Explain what this rate of change means as it relates to braking distance.

32 A house purchased 5 years ago for $100,000 was just sold for $135,000. Assuming exponentialgrowth, approximate the annual growth rate, to the nearest percent.

33 Solve the system of equations shown below algebraically

34 Alexa earns $33,000 in her first year of teaching and earns a 4% increase in each successive year.Write a geometric series formula, S_{n}, for Alexa’s total earnings over n years.Use this formula to find Alexa’s total earnings for her first 15 years of teaching, to the nearest cent

35 Fifty-five students attending the prom were randomly selected to participate in a survey aboutthe music choice at the prom. Sixty percent responded that a DJ would be preferred over a band.Members of the prom committee thought that the vote would have 50% for the DJ and 50% forthe band.A simulation was run 200 times, each of sample size 55, based on the premise that 60% ofthe students would prefer a DJ. The approximate normal simulation results are shown below.

36 Which function shown below has a greater average rate of change on the interval [-2, 4]? Justifyyour answer.

37 Drugs break down in the human body at different rates and therefore must be prescribed bydoctors carefully to prevent complications, such as overdosing. The breakdown of a drug isrepresented by the function N(t) = N_{0}(e)^{rt}, where N(t) is the amount left in the body, N0 isthe initial dosage, r is the decay rate, and t is time in hours. Patient A, A(t), is given 800 milligramsof a drug with a decay rate of 0.347. Patient B, B(t), is given 400 milligrams of another drug witha decay rate of 0.231.

Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given toeach patient.

Graph each function on the set of axes below.

To the nearest hour, t, when does the amount of the given drug remaining in patient B begin toexceed the amount of the given drug remaining in patient A?

The doctor will allow patient A to take another 800 milligram dose of the drug once only 15% ofthe original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient Awill have to wait to take another 800 milligram dose of the drug.

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