Algebra 2/Trigonometry Common Core Regents Exam - January 2015

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 2015.

Algebra 2/Trigonometry Common Core Regents New York State Exam - January 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 - January 2015 Regents - Part 1: Questions 1 - 14

1. In triangle FGH, f = 6, g = 9, and m∠H = 57. Which statement can be used to determine the numerical value of h?
   
2. The table of values below can be modeled by which equation?
   
3. The equation log_a x = y where x > 0 and a > 1 is equivalent to
   
4. Which expression is equivalent to the sum of the sequence 6, 12, 20, 30?
   
5. An investment is earning 5% interest compounded quarterly. The equation A = P(1+r/n)^nt represents the total amount of money, A, where P is the original investment, r is the interest rate, t is the number of years, and n represents the number of times per year the money earns interest.
   Which graph could represent this investment over at least 50 years?
   
6. Which equation has real, rational, and unequal roots?
   
7. Which statement is true about the graphs of f and g shown below?
   
   
8. The common ratio of the sequence -1/2, 3/4, -9/8 is
   
9. How many different ways can teams of four members be formed from a class of 20 students?
   
10. If sin A = 3/8 , what is the value of cos 2A?
    
11. When factored completely, the expression x³ - 2x² - 9x + 18 is equivalent to
    
12. When -3 - 2i is multiplied by its conjugate, the result is
    
13. A circle with center O and passing through the origin is graphed computations. below.
    
14. Which expression is equivalent to (5^-2a³b^-4)^-1?
    

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Algebra 2/Trigonometry - January 2015 Regents - Part 1: Questions 15 - 27
15. Which trigonometric expression does not simplify to 1?
17. What is the product of the roots of 4x² - 5x = 3?
18. How many different 11-letter arrangements are possible using the letters in the word “ARRANGEMENT”?
19. What is the third term in the expansion of (2x - 3)⁵?
20. Angle θ is in standard position and (-4,0) is a point on the terminal side of θ. What is the value of sec θ?
21. The domain of f(x) = -3/√(2-x) is the set of all real numbers
22. Which equation could be used to solve 5/(x-3) - 2/x = 1?

23. How many distinct triangles can be constructed if m∠A = 30, side a = √34 and side b = 12?
24. The expression (3/2 x + 1)(3/2 x - 1) - (3/2x - 1)² is equivalent to
25. The table below shows five numbers and their frequency of occurrence.
26. A wheel has a radius of 18 inches. Which distance, to the nearest inch, does the wheel travel when it rotates through an angle of 2π/5 radians?
27. If f(x) = 4x² - x + 1, then f(a + 1) equals

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Algebra 2/Trigonometry - January 2015 Regents - Questions 28 - 39
28. If p and q vary inversely and p is 25 when q is 6, determine q when p is equal to 30
30. Solve e^4x = 12 algebraically for x, rounded to the nearest hundredth.
31. Determine, to the nearest minute, the degree measure of an angle of 5/11 π radians.
32. The probability of Ashley being the catcher in a softball game is 2/5. Calculate the exact probability that she will be the catcher in exactly five of the next six games.
33. If x is a real number, express 2xi(i - 4i²) in simplest a + bi form.
34. On a test that has a normal distribution of scores, a score of 57 falls one standard deviation below the mean, and a score of 81 is two standard deviations above the mean. Determine the mean score of this test.
35. The area of a parallelogram is 594, and the lengths of its sides are 32 and 46. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram.
36. The table below shows the amount of a decaying radioactive substance that remained for selected years after 1990.
Write an exponential regression equation for this set of data, rounding all values to the nearest thousandth.
Using this equation, determine the amount of the substance that remained in 2002, to the nearest integer.

37. Use the recursive sequence defined below to express the next three terms as fractions reduced to lowest terms.
a₁ = 2
a_n = 3(a_n-1)^-2
38. The periodic graph below can be represented by the trigonometric equation y = a cos bx + c where a, b, and c are real numbers.
State the values of a, b, and c, and write an equation for the graph.
39. A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. The building code allows for a deck to have a maximum area of 800 square feet. If the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased and not exceed the building code. [Only an algebraic solution can receive full credit.]

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