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January 2015 Algebra 2 Trig NY Regents pt IV 16-20 Trigonometry New York NYS state common core

11 When factored completely, the expression x^3 -2x^2- 9x +18

1 In FGH, f 6, g 9, and m∠H 57. Which statement can be computations.

used to determine the numerical value of h?

(1) h2 62 92 2(9)(h) cos 57°

(2) h2 62 92 2(6)(9) cos 57°

(3) 62 92 h2 2(9)(h) cos 57°

(4) 92 62 h2 2(6)(h) cos 57°

2 The table of values below can be modeled by which equation?

(1) f(x) = |x+3| (3) f(y)= |y + 3|

(2) f(x) =|x|+3 (4) f(y) = |y|+ 3

3 The equation loga x y where x 0 and a 1 is equivalent to

(1) x^y =a (3) a^y =x

(2) y^a =x (4) a^x = y

4 Which expression is equivalent to the sum of the sequence computations.

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?

(1) x^2 + 10x + 25= 0

(2) x2 - 5x +4 = 0

(3) x2 -3x +1 =0

(4) x2 -2x +5 =0

(1) f is a relation and g is a function.

(2) f is a function and g is a relation.

(3) Both f and g are functions.

(4) Neither f nor g is a function.

8 The common ratio of the sequence -1/2, 3/4,-9/8, -3/2,-1/2, -2/3,-1/4

9 How many different ways can teams of four members be formed .

from a class of 20 students?

(1) 5 (3) 4,845

(2) 80 (4) 116,280

10 If sin A

3/8 what is the value of cos 2A? -9/64, 23/32,1/4,55/64,When factored completely, the expression x3 2x2 9x 18

is equivalent to

(1) (x^2 - 9)(x - 2) (3) (x - 2)^2(x - 3)(x + 3)

(2) (x 2)(x 3)(x 3) (4) (x -3)^2(x -2)

When 3 2i is multiplied by its conjugate, the result is

(1) 13 (3) 5

(2) 5 (4) 13

A circle with center O and passing through the origin is graphed . Which trigonometric expression does not simplify to 1?

(1) sin2 x(1 cot2 x) (3) cos2 x(tan2 x 1)

(2) sec2 x(1 sin2 x) (4) cot2 x(sec2 x 1)

.

How many different 11-letter arrangements are possible using the

letters in the word “ARRANGEMENT”?

(1) 2,494,800 (3) 19,958,400

(2) 4,989,600 (4) 39,916,800 What is the third term in the expansion of (2x -3)^5?

(1) 720x^3 (3) 540x^2

(2) 180x^3 (4) 1080x^2

Angle is in standard position and (4,0) is a point on the

terminal side of . What is the value of sec ?

(1) 4 (3) 0

(2) 1 (4) undefined The domain of f(x) is the set of all real numbers

(1) greater than 2 (3) except 2

(2) less than 2 (4) between 2 and 2

How many distinct triangles can be constructed if m∠A 30,

side a and side b 12?

(1) one acute triangle (3) two triangles

(2) one obtuse triangle (4) none

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

_2_π_

5 radians?

(1) 45 (3) 13

(2) 23 (4) 11

If p and q vary inversely and p is 25 when q is 6, determine q when p is equal to 30 Express in simplest form: 30 Solve e4x 12 algebraically for x, rounded to the nearest hundredth. Determine, to the nearest minute, the degree measure of an angle of _5__

11 π radians. 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. If x is a real number, express 2xi(i 4i2) in simplest a bi form. 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. 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.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. The periodic graph below can be represented by the trigonometric equation y a cos bx c

where a, b, and c are real numbers.

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