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
June 2015.

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### Algebra 2/Trigonometry Common Core Regents New York State Exam - June 2015, Questions 1 - 39

The following are questions from the past paper Regents High School Algebra 2/Trigonometry, June 2015 Exam (pdf).

Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - June 2015 Regents - Part 1: Questions 1 - 14

1. Which list of ordered pairs does not represent a one-to-one function?

2. The terminal side of an angle measuring 4π/5 radians lies in Quadrant

3. If f(x) = 2x^{2} + 1 and g(x) = 3x - 2, what is the value of f(g(-2))?

5. If x^{2} - 12x - 7 is solved by completing the square, one of the steps
in the process is

7. What is the solution of the inequality 9 - x^{2} < 0?

8. What is the area of a parallelogram that has sides measuring 8 cm and 12 cm and includes an angle of 120°?

9. The expression 5/(4 - √11) is equivalent to

10. Given y varies inversely as x, when y is multiplied by 1/2, then x is multiplied by

11. What is the total number of different nine-letter arrangements that can be formed using the letters in the word “TENNESSEE”?

12. What is the fourth term of the sequence defined by

13. What is the solution set of |x - 2| = 3x + 10?

14. By law, a wheelchair service ramp may be inclined no more than 4.76°. If the base of a ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building’s entrance?

Algebra 2/Trigonometry - June 2015 Regents - Part 1: Questions 15 - 27

15. When computations. 7/8 x^{2} - 3/4 x is subtracted from 5/8x^{2} - 1/4 x + 2, the difference is

16. Which transformation of y f(x) moves the graph 7 units to the left and 3 units down?

17. If log x = 2 log a + log b, then x equals

18. Which value is in the domain of the function graphed below, but is not in its range?

19. How many full cycles of the function y = 3 sin 2x appear in π radians?

20. A theater has 35 seats in the first row. Each row has four more seats than the row before it. Which expression represents the number of seats in the nth row?

21. What is the inverse of the function f(x) = log_{4} x?

22. The expression (1 + cos 2A)/sin 2A is equivalent to

23. A video-streaming service can choose from six half-hour shows and four one-hour shows. Which expression could be used to calculate the number of different ways the service can choose four half-hour shows and two one-hour shows?

24. The roots of 3x^{2} + x = 14 are

25. Circle O has a radius of 2 units. An angle with a measure of π/6 radians is in standard position. If the terminal side of the angle intersects the circle at point B, what are the coordinates of B?

27. A population, p(x), of wild turkeys in a certain area is represented by the function p(x) = 17(1.15)^{2x}, where x is the number of years
since 2010. How many more turkeys will be in the population for the
year 2015 than 2010?

Algebra 2/Trigonometry - June 2015 Regents - Questions 28 - 39

28. Solve algebraically for x: 54^{x} = 125^{x} - 1

29. In triangle ABC, determine the number of distinct triangles that can be formed if m∠A = 85, side a = 8, and side c = 2. Justify your answer.

30. The probability that Kay and Joseph Dowling will have a redheaded child is 1 out of 4. If the Dowlings plan to have three children, what is the exact probability that only one child will have red hair?

31. If log_{(x + 1)} 64 = 3, find the value of x.

32. Factor completely: x^{3} - 6x^{2} - 25x + 150

33. Express xi^{8} - yi^{6} in simplest form.

34. Given the equation 3x^{2} + 2x + k = 0, state the sum and product of the roots

35. Determine which set of data given below has the stronger linear relationship between x and y. Justify your choice.

36. Find the measure of the smallest angle, to the nearest degree, of a triangle whose sides measure 28, 47, and 34.

37. Solve algebraically for x: 3/x + x/(x+2) = -2/(x+2)

38. The table below shows the final examination scores for Mr. Spear’s class last year.

Find the population standard deviation based on these data, to the nearest hundredth.

Determine the number of students whose scores are within one population standard deviation of the mean.

39. In the interval 0° ≤ θ < 360°, solve the equation 5 cos θ = 2 sec θ - 3 algebraically for all values of θ, to the nearest tenth of a degree.

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Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - June 2015 Regents - Part 1: Questions 1 - 14

1. Which list of ordered pairs does not represent a one-to-one function?

2. The terminal side of an angle measuring 4π/5 radians lies in Quadrant

3. If f(x) = 2x

5. If x

7. What is the solution of the inequality 9 - x

8. What is the area of a parallelogram that has sides measuring 8 cm and 12 cm and includes an angle of 120°?

9. The expression 5/(4 - √11) is equivalent to

10. Given y varies inversely as x, when y is multiplied by 1/2, then x is multiplied by

11. What is the total number of different nine-letter arrangements that can be formed using the letters in the word “TENNESSEE”?

12. What is the fourth term of the sequence defined by

13. What is the solution set of |x - 2| = 3x + 10?

14. By law, a wheelchair service ramp may be inclined no more than 4.76°. If the base of a ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building’s entrance?

15. When computations. 7/8 x

16. Which transformation of y f(x) moves the graph 7 units to the left and 3 units down?

17. If log x = 2 log a + log b, then x equals

18. Which value is in the domain of the function graphed below, but is not in its range?

19. How many full cycles of the function y = 3 sin 2x appear in π radians?

20. A theater has 35 seats in the first row. Each row has four more seats than the row before it. Which expression represents the number of seats in the nth row?

21. What is the inverse of the function f(x) = log

22. The expression (1 + cos 2A)/sin 2A is equivalent to

23. A video-streaming service can choose from six half-hour shows and four one-hour shows. Which expression could be used to calculate the number of different ways the service can choose four half-hour shows and two one-hour shows?

24. The roots of 3x

25. Circle O has a radius of 2 units. An angle with a measure of π/6 radians is in standard position. If the terminal side of the angle intersects the circle at point B, what are the coordinates of B?

27. A population, p(x), of wild turkeys in a certain area is represented by the function p(x) = 17(1.15)

Algebra 2/Trigonometry - June 2015 Regents - Questions 28 - 39

28. Solve algebraically for x: 54

29. In triangle ABC, determine the number of distinct triangles that can be formed if m∠A = 85, side a = 8, and side c = 2. Justify your answer.

30. The probability that Kay and Joseph Dowling will have a redheaded child is 1 out of 4. If the Dowlings plan to have three children, what is the exact probability that only one child will have red hair?

31. If log

32. Factor completely: x

33. Express xi

34. Given the equation 3x

35. Determine which set of data given below has the stronger linear relationship between x and y. Justify your choice.

36. Find the measure of the smallest angle, to the nearest degree, of a triangle whose sides measure 28, 47, and 34.

37. Solve algebraically for x: 3/x + x/(x+2) = -2/(x+2)

38. The table below shows the final examination scores for Mr. Spear’s class last year.

Find the population standard deviation based on these data, to the nearest hundredth.

Determine the number of students whose scores are within one population standard deviation of the mean.

39. In the interval 0° ≤ θ < 360°, solve the equation 5 cos θ = 2 sec θ - 3 algebraically for all values of θ, to the nearest tenth of a degree.

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