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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 August 2015.

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

Scroll down the page for the step by step solutions.

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

1 What are the zeros of the polynomial function graphed below?

2 A study compared the number of years of education a person received and that person’s average yearly salary. It was determined that the relationship between these two quantities was linear and the correlation coefficient was 0.91. Which conclusion can be made based on the findings of this study?

3 What is the value of 4^{1/2} + x^{0} +x^{-1/4} when x = 16?

5 The exact value of csc 120°

6 Which statement about the equation 3x^{0} + 9x - 12 = 0 is true?

7 A scholarship committee rewards the school’s top math students. The amount of money each winner receives is inversely proportional to the number of scholarship recipients. If there are three winners, they each receive $400. If there are eight winners, how much money will each winner receive?

8 What is the value of tan(Arc cos 15/17)?

9 The table below displays the number of siblings of each of the 20 students in a class.

What is the population standard deviation, to the nearest hundredth, for this group?

10 An arithmetic sequence has a first term of 10 and a sixth term of 40. What is the 20th term of this sequence?

11 Yusef deposits $50 into a savings account that pays 3.25% interest computations. compounded quarterly. The amount, A, in his account can be determined by the formula A = P(1 + r/n)^{nt}, where P is the initial amount invested, r is the interest rate, n is the number of times per year the money is compounded, and t is the number of years for which the money is invested. What will his investment be worth in 12 years if he makes no other deposits or withdrawals?

12 How many distinct ways can the eleven letters in the word “TALLAHASSEE” be arranged?

13 A customer will select three different toppings for a supreme pizza. If there are nine different toppings to choose from, how many different supreme pizzas can be made?

14 Which values of x in the interval 0° ≤ x < 360° satisfy the equation 2 sin^{2}x + sin x - 1 = 0?

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

15 Expressed as a function of a positive acute angle, sin 230° is

16 Which equation represents a circle with its center at (2,-3) and that passes through the point (6,2)?

17 What is the domain of the function g(x) = 3^{2} - 1?

19 What is the period of the graph of the equation y = 1/3 sin 2x?

20 The first four terms of the sequence defined by a_{1} = 1/2 and a_{n+1} = 1 + a_{n} are

21 The scores on a standardized exam have a mean of 82 and a standard deviation of 3.6. Assuming a normal distribution, a student’s score of 91 would rank

22 If cos θ = 3/4, then what is cos 2θ?

23 If m = {(1,1), (1,1), (2,4), (2,4), (3,9), (3,9)}, which statement is true?

25 The ninth term of the expansion of (3x + 2y)^{15} is

26 Six people met at a dinner party, and each person shook hands once with everyone there. Which expression represents the total number of handshakes?

27 Which value of k will make x^{2} - 1/4 x + k a perfect square trinomial?

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

28 Determine, to the nearest minute, the number of degrees in an angle whose measure is 2.5 radians

29 Solve for x: 1/16 = 2^{3x-1}

30 If f(x) = x^{2} - x and g(x) = x + 1, determine f(g(x)) in simplest form.

31 The probability of winning a game is 2/3. Determine the probability, expressed as a fraction, of winning exactly four games if seven games are played.

32 In a circle, an arc length of 6.6 is intercepted by a central angle of 2/3 radians. Determine the length of the radius.

33 Show that (sec^{2}x - 1)/sec^{2}x is equivalent to sin^{2}x.

34 Solve algebraically for the exact values of x: 5x/2 = 1/x + x/4

36 In a triangle, two sides that measure 8 centimeters and 11 centimeters form an angle that measures 82°. To the nearest tenth of a degree, determine the measure of the smallest angle in the triangle.

37 Solve the equation 2x^{3} - x^{2} - 8x + 4 = 0 algebraically for all values of x.

38 Solve algebraically for x: |3x - 5| - x < 17

39 Solve algebraically, to the nearest hundredth, for all values of x: log_{2} (x^{2} - 7x + 12) - log^{2}(2x - 10) = 3

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