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 Regents High School Examination
January 2013.

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### January 2013 Algebra 2/ Trigonometry Regents Exam

Algebra 2/ Trigonometry - January 2013 Regents - Q #1 - 5

1. What is the equation of the graph shown below?

2. Which ordered pair is a solution of the system of equations shown

below?

x + y = 5

(x + 3)^{2} + (y - 3)^{2} = 53

3. The relationship between t, a student's test scores, and d, the student's success in college, is modeled by the equation d = 0.48t +75.2. Based on this linear regression model, the correlation coefficient could be

4. What is the common ratio of the geometric sequence shown below?

5. Given the relation {(8,2), (3,6), (7,5), (k,4)}, which value of k will result in the relation not being a function? Algebra 2/ Trigonometry - January 2013 Regents - Q #6 - 10

6. Which expression is equivalent to (9x^{2}y^{6})^{-1/2}?

7. In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution, what is the range of the number of bottled waters that approximately 68.2% of the students drink?

8. What is the fourth term in the binomial expansion (x -2)^{8}?

9. Which value of k satisfies the equation 8^{3k+4} = 4^{2k-1}?

10. There are eight people in a tennis club. Which expression can be used to find the number of different ways they can place first, second, and third in a tournament? Algebra 2/ Trigonometry - January 2013 Regents - Q #11 - 15

11. If sin A = 1/3 , what is the value of cos 2A?

12. In the interval, tan x is undefined when x equals

13. Given f(x) what are its domain and range?

14. When x^{2} + 3x - 4 is subtracted from x^{3} +
3x^{2} - 2x, the difference is

15. In the diagram below, the length of which line segment is equal the exact value of sin θ?

Algebra 2/ Trigonometry - January 2013 Regents - Q #16 - 20

16. The area of triangle ABC is 42. If AB 8 and m∠B 61, the length of BC is approximately

17. When factored completely, the expression 3x^{3}
- 5x^{2} - 48x + 80 is equivalent to

18. The value of sin (180 + x) is equivalent to

19. The sum of radicals

20. Which equation is represented by the graph below? Algebra 2/ Trigonometry - January 2013 Regents - Q #21 - 25

21. The quantities p and q vary inversely. If p = 20 when q = -2, and p = x when q = -2x + 2, then x equals

22. Find the solution set of the equation that involves secant

23. The discriminant of a quadratic equation is 24. The roots are

24. How many different six-letter arrangements can be made using the letters of the word "TATTOO"?

25. Expressed in simplest form, 3y/(2y - 6) + 9/(6 - 2y) is equivalent to ... Algebra 2/ Trigonometry - January 2013 Regents - Q #26 - 30

26. If log 2 = a and log 3 = b, the expression log 9/20 is equivalent to

27. The expression (x + i)^{2} - (x - i)^{2} is
equivalent to

28. Determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23, 32, and 41.

29. Determine the sum and the product of the roots of 3x^{2}
= 11x - 6.

30. If sec (a + 15) = csc (2a), find the smallest positive value of a, in degrees. Algebra 2/ Trigonometry - January 2013 Regents - Q #31 - 35

31. The heights, in inches, of 10 high school varsity basketball players are 78, 79, 79, 72, 75, 71, 74, 74, 83, and 71. Find the interquartile range of this data set.

32. Solve the equation 6x^{2} - 2x - 3 = 0 and express the
answer in simplest radical form.

33. The number of bacteria present in a Petri dish can be modeled by the function N 50e^{3t}, where N is the number of
bacteria present in the Petri dish after t hours. Using this model,
determine, to the nearest hundredth, the number of hours it will
take for N to reach 30,700.

34. Determine the solution of the inequality

35. Convert 3 radians to degrees and express the answer to the nearest minute. More Questions, Worked Solutions and Revision Resources for the Math Regents Examination

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 Geometry

1. What is the equation of the graph shown below?

2. Which ordered pair is a solution of the system of equations shown

below?

x + y = 5

(x + 3)

3. The relationship between t, a student's test scores, and d, the student's success in college, is modeled by the equation d = 0.48t +75.2. Based on this linear regression model, the correlation coefficient could be

4. What is the common ratio of the geometric sequence shown below?

5. Given the relation {(8,2), (3,6), (7,5), (k,4)}, which value of k will result in the relation not being a function? Algebra 2/ Trigonometry - January 2013 Regents - Q #6 - 10

6. Which expression is equivalent to (9x

7. In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution, what is the range of the number of bottled waters that approximately 68.2% of the students drink?

8. What is the fourth term in the binomial expansion (x -2)

9. Which value of k satisfies the equation 8

10. There are eight people in a tennis club. Which expression can be used to find the number of different ways they can place first, second, and third in a tournament? Algebra 2/ Trigonometry - January 2013 Regents - Q #11 - 15

11. If sin A = 1/3 , what is the value of cos 2A?

12. In the interval, tan x is undefined when x equals

13. Given f(x) what are its domain and range?

14. When x

15. In the diagram below, the length of which line segment is equal the exact value of sin θ?

16. The area of triangle ABC is 42. If AB 8 and m∠B 61, the length of BC is approximately

17. When factored completely, the expression 3x

18. The value of sin (180 + x) is equivalent to

19. The sum of radicals

20. Which equation is represented by the graph below? Algebra 2/ Trigonometry - January 2013 Regents - Q #21 - 25

21. The quantities p and q vary inversely. If p = 20 when q = -2, and p = x when q = -2x + 2, then x equals

22. Find the solution set of the equation that involves secant

23. The discriminant of a quadratic equation is 24. The roots are

24. How many different six-letter arrangements can be made using the letters of the word "TATTOO"?

25. Expressed in simplest form, 3y/(2y - 6) + 9/(6 - 2y) is equivalent to ... Algebra 2/ Trigonometry - January 2013 Regents - Q #26 - 30

26. If log 2 = a and log 3 = b, the expression log 9/20 is equivalent to

27. The expression (x + i)

28. Determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23, 32, and 41.

29. Determine the sum and the product of the roots of 3x

30. If sec (a + 15) = csc (2a), find the smallest positive value of a, in degrees. Algebra 2/ Trigonometry - January 2013 Regents - Q #31 - 35

31. The heights, in inches, of 10 high school varsity basketball players are 78, 79, 79, 72, 75, 71, 74, 74, 83, and 71. Find the interquartile range of this data set.

32. Solve the equation 6x

33. The number of bacteria present in a Petri dish can be modeled by the function N 50e

34. Determine the solution of the inequality

35. Convert 3 radians to degrees and express the answer to the nearest minute. More Questions, Worked Solutions and Revision Resources for the Math Regents Examination

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