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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 RegentsExam conducted by NYSED. The following are the worked solutionsfor the Algebra 2/Trigonometry (Common Core) Regents High School ExaminationAugust 2016.

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

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

Scroll down the page for the step by step solutions.

Algebra 2/Trigonometry - August 2016 Regents - Questions and solutions 1 - 14

1. If the roots of the quadratic equation ax^{2} + bx + c = 0 are real, irrational, and unequal, then the value of the discriminant is

2. Factored completely, the expression 16 tanθ - tan^{3}θ is equivalent to

3. High school officials wanted to assess the need for a new diving board.They created a survey and distributed it to a large, diverse crowd atthe State Swim Meet held at their school. Which characteristic ofthe survey is most likely to create a bias?

4. Which expression is equivalent to cos P cos 50 - sin P sin 50?

5. What is the product of the roots of the quadratic equation 2x^{2} - x = 4?6. In which method of data collection does the researcher intentionallyintervene to arrange for a comparison of results?

7. Which equation could be represented by the graph below?

8. The first four terms of the sequence with a_{1} = 40 and a_{n} = 3/4 a_{n-1} are

9. Which diagram represents an angle of 7/4 pi; radians in standard position?

10. For all values for which the function is defined, the expression √(a/bc)is equivalent to

11. The expression (x^{1/2}y^{-2/3})^{-6}is equivalent to

13. Which expression has a value of √3/3?

14. The solution set of -|2x - 9| = -11 is

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Algebra 2/Trigonometry - August 2016 Regents - Questions and solutions 15 - 27

15. Which relation is not a function?

16. The expression (1 - sin^{2}x)/cos^{2}x is equivalent to

17. Which relation is one-to-one?

18. If log a = x and log b = y, then log (ab^{2}) equals

19. For a member of a certain species of bird, the probability of survivingto adulthood is 4/7. In a nest of five eggs, what is the probability, tothe nearest hundredth, that at least four eggs will survive to adulthood?

20. In triangle XYZ, m∠X = 71, x = 6, and z = 2. How many distinct trianglescan be created with these parameters?

21. Which expression could be used to determine the value of y inthe equation log_{x} 8 = y?

22. An electron travels along a circular path with a radius of 4.6 miles.What is the number of miles the electron traveled during an intervalwhen the central angle formed by the electron’s path was 220°?

23. Which statement about the function f(x) = (x-3)/(x+2) is true?

24. Which value of a correlation coefficient represents the strongestrelationship between the two variables in a given linear regressionmodel?

25. The fourth term of the expansion of (2x - 3)^{5} is

26. What are the center and radius of the circle whose equation isx^{2} + y^{2} + 4x = 5?

27. The product of ^{3}√(4m^{2}) and ^{3}√(10m) expressed in simplest radical form is

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Algebra 2/Trigonometry - August 2016 Regents - Questions and solutions 28 - 39

28. Jamal has forgotten his password for the school computers. He knows that it must be 4 characterslong (only lowercase letters or digits). He also knows that his password begins with one of26 letters and ends with a digit. Determine how many different 4-character passwords arepossible for Jamal if no letter or digit may be repeated.

29. Emma’s parents deposited $5000 into a bank account during her freshman year. The account pays5% interest compounded continuously using the formula A = Pe^{rt}, where A is the total amountaccrued, P is the principal, r is the annual interest rate, and t is time, in years.Determine, to the nearest dollar, the amount in the account 4 years later.

30. Find the common difference in the arithmetic sequence, a_{n}, in which a_{1} = 16 and a_{9} = 36.

31. Solve the equation below algebraically for all values of θ in the interval 0 ≤ θ < 360°.

3 cos θ - 1 = cos θ

32. Bacteria are being grown in a Petri dish in a biology lab. The number of bacteria in the cultureafter a given number of hours is shown in the table below. Assuming this exponential trend continues, is it reasonable to expect at least 3500 bacteria at hour 7?Justify your answer

33. Express in simplest form:

(a/b - b/a) ÷ (b/a - a/b)

34. Determine the exact value of csc P if P is an angle in standard position and its terminal side passesthrough the point (5,-8).

35. Determine the number of degrees in 8π/9 radians.

36. Solve for x:

8^{x+3} = 32^{x2-1}

37. Determine algebraically the solution to 4x^{2} - 5x ≥ 6(5 - 4x).

38. The table below shows the number of hurricanes in the North Atlantic Ocean from 1990 to 2002. Determine the interquartile range for this set of data.Determine the population variance for this set of data, to the nearest tenth.

39. The Bermuda Triangle on a map is a section of the Atlantic Ocean bordered by line segmentsstretching from Miami to Bermuda to Puerto Rico and back to Miami. The distance from Miamito Bermuda is 1042 miles; the distance from Bermuda to Puerto Rico is 2057 miles; and the distancefrom Puerto Rico to Miami is 1127 miles. Find the area contained within the Bermuda Triangle,to the nearest square mile.

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