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/Trigonometry (Common Core) Regents High School Examination
January 2016.

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

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

Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - January 2016 Regents - Part 1: Questions 1 - 14

1. A survey is to be conducted in a small upstate village to determine computations. whether or not local residents should fund construction of a skateboard park by raising taxes. Which segment of the population would provide the most unbiased responses?

2. Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position?

4. Which relation does not represent a function?

5 In the diagram below, the spinner is divided into eight equal regions. Which expression represents the probability of the spinner landing on B exactly three times in five spins? 7 The amount of money in an account can be determined by the formula A = Pe^{rt}, where P is the initial investment, r is the annual
interest rate, and t is the number of years the money was invested.
What is the value of a $5000 investment after 18 years, if it was
invested at 4% interest compounded continuously?

8 What is x/(x-1) - 1/(2-2x) expressed as a single fraction?

9 What is the total number of points of intersection of the graphs of the equations 2x^{2} - y^{2} = 8 and y = x + 2?

10 Given the sequence: x, (x + y), (x + 2y), ...

Which expression can be used to determine the common difference of this sequence?

11 In a circle with a diameter of 24 cm, a central angle of 4π/3 radians intercepts an arc. The length of the arc, in centimeters, is

12 Which graph is the solution to the inequality 4|2x + 6| - 5 < 27?

13 What is the sum of the roots of the equation -3x^{2} + 6x - 2 = 0?

14 The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. What is the expected number of students who had scores greater than 60?

Algebra 2/Trigonometry - January 2016 Regents - Part 1: Questions 15 - 27

15. If T = 10x^{2}/y , then log T is equivalent to

16. Which statement regarding correlation is not true?

(1) The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line.

(2) A correlation coefficient measures the strength of the linear relationship between two variables.

(3) A negative correlation coefficient indicates that there is a weak relationship between two variables.

(4) A relation for which most of the data fall close to a line is considered strong.

18 The roots of the equation 4(x^{2} - 1) = -3x are

19 If f(x) = 2x^{2} - 3x + 4, then f(x + 3) is equal

20 The expression x(3i^{2})^{3} + 2xi^{12} is equivalent to

21 If the terminal side of angle θ passes through the point (-3,-4), what is the value of sec θ

22 When the inverse of tan θ is sketched, its domain is

23 What is the third term of the recursive sequence below?

24 What is the equation of a circle with its center at (0,-2) and passing through the point (3,-5)?

25 If angles A and B are complementary, then sec B equals

26 The legs of a right triangle are represented by x + √2 and x - √2. The length of the hypotenuse of the right triangle is represented by

27 What are the amplitude and the period of the graph represented by the equation y = -3cos θ/3?

Algebra 2/Trigonometry - January 2016 Regents - Questions 28 - 39

28 Solve algebraically for x: √(2x + 1) + 4 = 8

29 Factor completely: x^{2} + 3x^{2} + 2x + 6

30 Solve algebraically for the exact value of x: log_{8}16 = x + 1

31 Determine how many eleven-letter arrangements can be formed from the word “CATTARAUGUS.”

32 Express -130° in radian measure, to the nearest hundredth.

33 Determine the area, to the nearest integer, of triangle SRO shown below.

34 Prove that the equation shown below is an identity for all values for which the functions are defined:

csc θ ˙ sin^{2}θ ˙ cot θ = cos θ

35 Find the difference when 4/3x^{3} - 5/8x^{2} + 7/9x is subtracted from 2x^{3} + 3/4x^{2} - 2/9.

36 Find the exact roots of x^{2} + 10x - 8 = 0 by completing the square.

37 The table below gives the relationship between x and y.

Use exponential regression to find an equation for y as a function of x, rounding all values to the nearest hundredth.

Using this equation, predict the value of x if y is 426.21, rounding to the nearest tenth. [Only an algebraic solution can receive full credit.]

38 Solve the equation cos 2x = cos x algebraically for all values of x in the interval 0° ≤ x < 360°.

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

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Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - January 2016 Regents - Part 1: Questions 1 - 14

1. A survey is to be conducted in a small upstate village to determine computations. whether or not local residents should fund construction of a skateboard park by raising taxes. Which segment of the population would provide the most unbiased responses?

2. Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position?

4. Which relation does not represent a function?

5 In the diagram below, the spinner is divided into eight equal regions. Which expression represents the probability of the spinner landing on B exactly three times in five spins? 7 The amount of money in an account can be determined by the formula A = Pe

8 What is x/(x-1) - 1/(2-2x) expressed as a single fraction?

9 What is the total number of points of intersection of the graphs of the equations 2x

10 Given the sequence: x, (x + y), (x + 2y), ...

Which expression can be used to determine the common difference of this sequence?

11 In a circle with a diameter of 24 cm, a central angle of 4π/3 radians intercepts an arc. The length of the arc, in centimeters, is

12 Which graph is the solution to the inequality 4|2x + 6| - 5 < 27?

13 What is the sum of the roots of the equation -3x

14 The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. What is the expected number of students who had scores greater than 60?

15. If T = 10x

16. Which statement regarding correlation is not true?

(1) The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line.

(2) A correlation coefficient measures the strength of the linear relationship between two variables.

(3) A negative correlation coefficient indicates that there is a weak relationship between two variables.

(4) A relation for which most of the data fall close to a line is considered strong.

18 The roots of the equation 4(x

19 If f(x) = 2x

20 The expression x(3i

21 If the terminal side of angle θ passes through the point (-3,-4), what is the value of sec θ

22 When the inverse of tan θ is sketched, its domain is

23 What is the third term of the recursive sequence below?

24 What is the equation of a circle with its center at (0,-2) and passing through the point (3,-5)?

25 If angles A and B are complementary, then sec B equals

26 The legs of a right triangle are represented by x + √2 and x - √2. The length of the hypotenuse of the right triangle is represented by

27 What are the amplitude and the period of the graph represented by the equation y = -3cos θ/3?

Algebra 2/Trigonometry - January 2016 Regents - Questions 28 - 39

28 Solve algebraically for x: √(2x + 1) + 4 = 8

29 Factor completely: x

30 Solve algebraically for the exact value of x: log

31 Determine how many eleven-letter arrangements can be formed from the word “CATTARAUGUS.”

32 Express -130° in radian measure, to the nearest hundredth.

33 Determine the area, to the nearest integer, of triangle SRO shown below.

34 Prove that the equation shown below is an identity for all values for which the functions are defined:

csc θ ˙ sin

35 Find the difference when 4/3x

36 Find the exact roots of x

37 The table below gives the relationship between x and y.

Use exponential regression to find an equation for y as a function of x, rounding all values to the nearest hundredth.

Using this equation, predict the value of x if y is 426.21, rounding to the nearest tenth. [Only an algebraic solution can receive full credit.]

38 Solve the equation cos 2x = cos x algebraically for all values of x in the interval 0° ≤ x < 360°.

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