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 2014.

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Algebra 2/ Trigonometry - January 2014 Regents - Q #1 - 5

- What is the common difference in the sequence 2a + 1, 4a + 4, 6a + 7, 8a + 10, …?
- Which expression is equivalent to (3x
^{2})^{-1}? - If g(x) = 1/ 2 x + 8 and h(x) = 1/ 2 x - 2, what is the value of g(h(-8))?
- The expression 1/(7 - √11) is equivalent to
- The expression (a + b/c)/ (d - b/c) is equivalent to

Algebra 2/ Trigonometry - January 2014 Regents - Q #6 - 10

- A school cafeteria has five different lunch periods. The cafeteria staff wants to find out which items on the menu are most popular, so they give every student in the first lunch period a list of questions to answer in order to collect data to represent the school. Which type of study does this represent?
- Which relation is both one-to-one and onto?
- Max solves a quadratic equation by completing the square. He shows a correct step:

(x + 2)^{2}= -9

What are the solutions to his equation? - Which expression represents the total number of different 11-letter arrangements that can be made using the letters in the word “MATHEMATICS”?
- If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in 5 years? (Use the formula A = P(1 + r/n)
^{nt}where A is the amount accrued, P is the principal, r is the interest rate, n is the number of times per year the money is compounded, and t is the length of time, in years.)

Algebra 2/ Trigonometry - January 2014 Regents - Q #11 - 15

- The roots of the equation 2x
^{2}+ 4 = 9x are - If d varies inversely as t, and d = 20 when t = 2, what is the value computations.

of t when d = -5? - If sin A = -7/25 and ∠A terminates in Quadrant IV, tan A equals
- Which expression is equivalent to
- What are the coordinates of the center of a circle whose equation is x
^{2}+ y^{2}- 16x + 6y + 53 = 0?

Algebra 2/ Trigonometry - January 2014 Regents - Q #16 - 20

- What are the domain and range?
17 A math club has 30 boys and 20 girls. Which expression represents the total number of different 5-member teams, consisting of 3 boys and 2 girls, that can be formed?
18 What is the product of the roots of x
^{2}- 4x + k = 0 if one of the roots is 7? 19 In triangle DEF, d = 5, e = 8, and m∠D = 32. How many distinct triangles can be drawn given these measurements 20 Liz has applied to a college that requires students to score in the top 6.7% on the mathematics portion of an aptitude test. The scores on the test are approximately normally distributed with a mean score of 576 and a standard deviation of 104. What is the minimum score Liz must earn to meet this requirement?

Algebra 2/ Trigonometry - January 2014 Regents - Q #21 - 27

- The expression is equivalent to
- Which sketch shows the inverse of y = a
^{x}, where a > 1? - The expression is equivalent to
- Which graph represents the solution set of (x + 16)/(x -2) ≤ 7?
- Which equation represents a graph that has a period of 4π?
- The expression x
^{2}(x + 2) - (x + 2) is equivalent to - Approximately how many degrees does five radians equal?

Algebra 2/ Trigonometry - January 2014 Regents - Q #28 - 30

- Show that sec θ sin θ cot θ = 1 is an identity
- Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50°.
- The following is a list of the individual points scored by all twelve members of the Webster High School basketball team at a recent game:

2 2 3 4 6 7 9 10 10 11 12 14

Find the interquartile range for this set of data.

Algebra 2/ Trigonometry - January 2014 Regents - Q #31 - 33

- Determine algebraically the x-coordinate of all points where the graphs of xy = 10 and y = x + 3 intersect.
- Solve |-4x + 5| < 13 algebraically for x.
- Express 4xi + 5yi
^{8}+ 6xi^{3}+ 2yi^{4}in simplest a + bi form.

Algebra 2/ Trigonometry - January 2014 Regents - Q #34 - 36

- In an arithmetic sequence, a
_{4}= 19 and a_{7}= 31. Determine a formula for a_{n}, the n^{th}term of this sequence. - Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of 83°50′.
- Solve algebraically for all exact values of x in the interval 0 ≤ x ≤ 2π: 2sin
^{2}x + 5 sin x = 3

Algebra 2/ Trigonometry - January 2014 Regents - Q #37 - 39

- Because Sam’s backyard gets very little sunlight, the probability that a geranium planted there will flower is 0.28. Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower.
- Two sides of a parallelogram measure 27 cm and 32 cm. The included angle measures 48°. Find the length of the longer diagonal of the parallelogram, to the nearest centimeter
- Solve algebraically for all values of x:

log(x +3)(2x + 3) log(x +3)(x + 5) = 2

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