High School Math based on the topics required for the Regents
Exam conducted by NYSED. The following are the worked solutions
for the Algebra 2(Common Core) Regents High School Examination
June 2016.

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### 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).

Scroll down the page for the step by step solutions.

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} is
equivalent to

2 Julie averaged 85 on the first three tests of the semester in her mathematics class. If she scores 93 on each of the remaining tests, her average will be 90. Which equation could be used to determine how 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 flipped the coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips. The output of the proportion of heads is shown below

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?

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% of the 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 can be concluded that these two events are

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

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

13 The Ferris wheel at the landmark Navy Pier in Chicago takes 7 minutes to make one full rotation. The height, H, in feet, above the ground of one of the six-person cars can be modeled by H(t) = 70 sin (2π/7(t-1.75)) + 80, where t is time, in minutes. Using H(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 terminal side 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 function of pH, and the result was a degree 4 polynomial function whose graph is shown below

21 Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% over the previous year. If this trend were to continue, which expression could the company’s chief financial officer use 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) if p(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 sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds?

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 in a 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 who participate in sports is 649. The number of students who participate in music is 433. If the probability that a student participates in either sports or music is 974/1376, what is the probability that 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 coordinates
of 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 exponential growth, 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 about the 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% for the band. A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the 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]? Justify your answer.

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

Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given to each 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 to exceed 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% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient A will have to wait to take another 800 milligram dose of the drug.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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More Lessons for the Regents High School Exam

More Lessons for Algebra

Scroll down the page for the step by step solutions.

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

1 When b > 0 and d is a positive integer, the expression (3b)

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

3 Given i is the imaginary unit, (2 - yi)

4 Which graph has the following characteristics?

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

6 The zeros for f(x) = x

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

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?

8 If g(c) = 1 - c

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% of the 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 can be concluded that these two events are

12 A solution of the equation 2x

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

14 The expression (4x

15 Which function represents exponential decay?

16 Given f

17 A circle centered at the origin has a radius of 10 units. The terminal side 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

19 The equation 4x

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

21 Last year, the total revenue for Home Style, a national restaurant chain, increased 5.25% over the previous year. If this trend were to continue, which expression could the company’s chief financial officer use 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) if p(x) = x

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 sine function. The maximum voltage is 120 volts, and there are 60 cycles every second. Which equation best represents the value of the voltage as it flows through the electric wires, where t is time in seconds?

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 in a toothpaste.

27 Determine if x - 5 is a factor of 2x

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 who participate in sports is 649. The number of students who participate in music is 433. If the probability that a student participates in either sports or music is 974/1376, what is the probability that a student participates in both sports and music?

30 The directrix of the parabola 12(y + 3) = (x - 4)

31 Algebraically prove that (x

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 exponential growth, 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

35 Fifty-five students attending the prom were randomly selected to participate in a survey about the 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% for the band. A simulation was run 200 times, each of sample size 55, based on the premise that 60% of the 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]? Justify your answer.

37 Drugs break down in the human body at different rates and therefore must be prescribed by doctors carefully to prevent complications, such as overdosing. The breakdown of a drug is represented by the function N(t) = N

Write two functions, A(t) and B(t), to represent the breakdown of the respective drug given to each 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 to exceed 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% of the original dose is left in the body. Determine, to the nearest tenth of an hour, how long patient A will have to wait to take another 800 milligram dose of the drug.

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