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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 Regents Exam conducted by NYSED. The following are the worked solutions for the Algebra 2/Trigonometry (Common Core) Regents High School Examination January 2017.

### Algebra 2/Trigonometry Common Core Regents New York State Exam - January 2017, Questions 1 - 39

The following are questions from the past paper

Regents High School Algebra 2/Trigonometry, January 2017 Exam (pdf).

Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - January 2017 Regents - Questions and solutions 1 - 14

1. What is 510° expressed in radian measure?

2. Four surveys are described below. Which survey methodology would lead to the least biased conclusion?

(1) One hundred randomly chosen heart surgeons were polled by telephone about how to get children to eat healthier foods.

(2) A country and western radio station asked one hundred of its listeners to call a telephone number and answer a question about rap music.

(3) From calls made to one hundred randomly generated telephone numbers, people replied to a question about television shows they watch.

(4) The first one hundred people who left the World of Baseball Bookstore replied to a question about the importance of baseball to society

3. When factored completely, x^{4} - 13x^{2} + 36 is equivalent to

4. Which ordered pair is a solution to the system below?

x^{2} - 4y^{2} = 16

y = x - 4

5. Three freshmen, five sophomores, and four juniors are on the school’s chess team. The coach must select three students to attend the citywide tournament. Which expression could be used to determine how many different groups of three students can be made from this team?

6. A survey of high school girls found that the mean number of text messages sent per day by the girls was 62, with a standard deviation of 12. If a normal distribution is assumed, which interval represents the number of texts sent by 68.2% of the girls?

7. The expression 9^{3/2} ˙ 27^{1/2}
is equivalent to

8. The ratio Arc cos1/2 / Arc tan 1 is equal to

9. Which summation will not produce 2 + 4 + 6 + 8 + 10 + 12?

10. The expression 1/3√6(3m √2 - k √3) is equivalent to

11. If log_{3}(x + 1) - log_{3}x = 2, then x equals

12. Which relation is not a function?

13. What is the area of parallelogram ABCD if AB = 4, AD = 5√3, and m∠A = 60?

14. The maximum point on the graph of the equation y = f(x) is (2,3). What is the maximum point on the graph of the equation y = f(x - 4)?

Algebra 2/Trigonometry - January 2017 Regents - Questions and solutions 15 - 27

15. The formula of the nth term of the sequence 3, -6, 12, -24, 48. . . is

16. The expression 3/(a-1) + 3/(1-a) is equivalent to

17. The product of (2√2 + 5i) and (2√2 - 5i) is

18. Which quadratic equation has roots with a sum of 7/6 and a product of -1/2?

19. The range of the function f(x) = 3|x - 4| - 5 is

20. The graph of the equation y = m^{x} passes through the point

21. If sin θ = 1/2 , and θ terminates in Quadrant II, what is the value of cscθ ˙ cotθ?

22. A circle has a radius of 12 units. For this circle, which expression incorrectly states the length of the arc intercepted by the given central angle?

23. How many different four-letter arrangements can be made from the letters in the word “CHAIRS,” if the same letter may be used only once?

24. The sets below represent test scores for two students in Mrs. Silvio’s trigonometry class.

Michelle: {71, 68, 84, 88}

Valerie: {78, 82, 76, 80}

Which statement correctly describes the relationship between the two students’ test scores?

25. A support wire 20 meters long runs from the top of a utility pole to a point on the ground 17 meters from the base of the pole. What is the measure, to the nearest minute, of the angle formed by the pole and the wire?

26. If f(x) = 3x - 2 and f^{-1}(x) = (x+2)/3, then f ⚬ f^{-1}(x) equals

27. The graph of f(x) is shown below. Which graph represents f^{-1}(x)?

Algebra 2/Trigonometry - January 2017 Regents - Questions and solutions 28 - 39

28. The number of bacteria that grow in a petri dish is approximated by the function G(t) = 500e^{0.216t},
where t is time, in minutes. Use this model to approximate, to the nearest integer, the number of
bacteria present after one half-hour.

29. Determine the exact value of (27/64)^{-2/3} as a fraction in simplest form.

30. State the conjugate of 7 - √-48 expressed in simplest a + bi form.

31. Express 12x^{-5}y^{5}/24x^{-3}y^{-2} in simplest form, using only positive exponents.

32. In a theater with 30 rows, the number of seats in a row increases by two with each successive row. The front row has 15 seats. Find the total seating capacity of the theater.

33. Given f(x) = x^{2} and g(x) = x - 3, express g(f(x + 2)) as a polynomial in simplest form.

34. Sketch an angle of 250° in standard position and then express cos 250° as a cosine function of a positive acute angle.

35. Solve the inequality x^{2} - 3x - 4 > 0 algebraically for x.

36. The table below shows the minimum hourly wage, in U.S. dollars, for selected years since 1955. Write the linear regression equation for this set of data, rounding all values to three decimal places. State the strength and direction indicated by the correlation coefficient

37. Solve the system of equations algebraically for x and y:

38. A rocket is shot vertically into the air. Its height, h, at any time, t, in seconds, can be modeled by the equation h = -16t^{2} + 184t. Determine algebraically, the number of seconds it will take
the rocket to reach a height of 529 feet.

39. Forces of 22 pounds and 43 pounds act on an object at an angle of 52°. Determine, to the nearest pound, the magnitude of the resultant force. Find, to the nearest degree, the angle between the smaller force and the resultant force.

More Lessons for the Regents High School Exam

More Lessons for Algebra

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 2017.

Regents High School Algebra 2/Trigonometry, January 2017 Exam (pdf).

Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - January 2017 Regents - Questions and solutions 1 - 14

1. What is 510° expressed in radian measure?

2. Four surveys are described below. Which survey methodology would lead to the least biased conclusion?

(1) One hundred randomly chosen heart surgeons were polled by telephone about how to get children to eat healthier foods.

(2) A country and western radio station asked one hundred of its listeners to call a telephone number and answer a question about rap music.

(3) From calls made to one hundred randomly generated telephone numbers, people replied to a question about television shows they watch.

(4) The first one hundred people who left the World of Baseball Bookstore replied to a question about the importance of baseball to society

3. When factored completely, x

4. Which ordered pair is a solution to the system below?

x

y = x - 4

5. Three freshmen, five sophomores, and four juniors are on the school’s chess team. The coach must select three students to attend the citywide tournament. Which expression could be used to determine how many different groups of three students can be made from this team?

6. A survey of high school girls found that the mean number of text messages sent per day by the girls was 62, with a standard deviation of 12. If a normal distribution is assumed, which interval represents the number of texts sent by 68.2% of the girls?

7. The expression 9

8. The ratio Arc cos1/2 / Arc tan 1 is equal to

9. Which summation will not produce 2 + 4 + 6 + 8 + 10 + 12?

10. The expression 1/3√6(3m √2 - k √3) is equivalent to

11. If log

12. Which relation is not a function?

13. What is the area of parallelogram ABCD if AB = 4, AD = 5√3, and m∠A = 60?

14. The maximum point on the graph of the equation y = f(x) is (2,3). What is the maximum point on the graph of the equation y = f(x - 4)?

15. The formula of the nth term of the sequence 3, -6, 12, -24, 48. . . is

16. The expression 3/(a-1) + 3/(1-a) is equivalent to

17. The product of (2√2 + 5i) and (2√2 - 5i) is

18. Which quadratic equation has roots with a sum of 7/6 and a product of -1/2?

19. The range of the function f(x) = 3|x - 4| - 5 is

20. The graph of the equation y = m

21. If sin θ = 1/2 , and θ terminates in Quadrant II, what is the value of cscθ ˙ cotθ?

22. A circle has a radius of 12 units. For this circle, which expression incorrectly states the length of the arc intercepted by the given central angle?

23. How many different four-letter arrangements can be made from the letters in the word “CHAIRS,” if the same letter may be used only once?

24. The sets below represent test scores for two students in Mrs. Silvio’s trigonometry class.

Michelle: {71, 68, 84, 88}

Valerie: {78, 82, 76, 80}

Which statement correctly describes the relationship between the two students’ test scores?

25. A support wire 20 meters long runs from the top of a utility pole to a point on the ground 17 meters from the base of the pole. What is the measure, to the nearest minute, of the angle formed by the pole and the wire?

26. If f(x) = 3x - 2 and f

27. The graph of f(x) is shown below. Which graph represents f

Algebra 2/Trigonometry - January 2017 Regents - Questions and solutions 28 - 39

28. The number of bacteria that grow in a petri dish is approximated by the function G(t) = 500e

29. Determine the exact value of (27/64)

30. State the conjugate of 7 - √-48 expressed in simplest a + bi form.

31. Express 12x

32. In a theater with 30 rows, the number of seats in a row increases by two with each successive row. The front row has 15 seats. Find the total seating capacity of the theater.

33. Given f(x) = x

34. Sketch an angle of 250° in standard position and then express cos 250° as a cosine function of a positive acute angle.

35. Solve the inequality x

36. The table below shows the minimum hourly wage, in U.S. dollars, for selected years since 1955. Write the linear regression equation for this set of data, rounding all values to three decimal places. State the strength and direction indicated by the correlation coefficient

37. Solve the system of equations algebraically for x and y:

38. A rocket is shot vertically into the air. Its height, h, at any time, t, in seconds, can be modeled by the equation h = -16t

39. Forces of 22 pounds and 43 pounds act on an object at an angle of 52°. Determine, to the nearest pound, the magnitude of the resultant force. Find, to the nearest degree, the angle between the smaller force and the resultant force.

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