jan-2016-nys-algebra-2-trig-regents-exam-pt-6-28-to-32-solutions-tips-tricks

26 The legs of a right triangle are represented by and .

The length of the hypotenuse of the right triangle is represented by

(1) (3)

(2) 2x2 4 (4)

27 What are the amplitude and the period of the graph represented by

the equation y 3cos θ __

3 ?

(1) amplitude: 3; period: π __

3

(2) amplitude: 3; period: 6π

(3) amplitude: 3; period: π __

3

(4) amplitude: 3; period: 6π

x 2 2

x2 2 2

2x2 1 4 x 2 1 2

x 1 2

Use this space for

computations.

28 Solve algebraically for x:

2x 1 1 1 4 5 8

Part II

Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. For all questions in this part, a correct numerical answer with no work shown will

receive only 1 credit. All answers should be written in pen, except for graphs and drawings,

which should be done in pencil. [16]

Algebra 2/Trigonometry – Jan. ’16 [10]

Algebra 2/Trigonometry – Jan. ’16 [11] [OVER]

29 Factor completely:

x3 3x2 2x 6

30 Solve algebraically for the exact value of x:

log816 x 1

Algebra 2/Trigonometry – Jan. ’16 [12]

31 Determine how many eleven-letter arrangements can be formed from the word

“CATTARAUGUS.”

Algebra 2/Trigonometry – Jan. ’16 [13] [OVER]

Algebra 2/Trigonometry – Jan. ’16 [14]

32 Express 130° in radian measure, to the nearest hundredth.

33 Determine the area, to the nearest integer, of SRO shown below.

S O

R

31.6

38° 17°

15

Algebra 2/Trigonometry – Jan. ’16 [15] [OVER]

Algebra 2/Trigonometry – Jan. ’16 [16]

34 Prove that the equation shown below is an identity for all values for which the functions are

defined:

csc θ • sin2 θ • cot θ cos θ

Algebra 2/Trigonometry – Jan. ’16 [17] [OVER]

35 Find the difference when 4 __

3 x3 5 __

8 x2 7 __

9 x is subtracted from 2x3 3 __

4 x2 2 __

9 .

Algebra 2/Trigonometry – Jan. ’16 [18]

Part III

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. For all questions in this part, a correct numerical answer with no work shown will

receive only 1 credit. All answers should be written in pen, except for graphs and drawings,

which should be done in pencil. [12]

36 Find the exact roots of x2 10x 8 0 by completing the square.

Algebra 2/Trigonometry – Jan. ’16 [19] [OVER]

37 The table below gives the relationship between x and y.

Use exponential regression to find an equation for y as a function of x, rounding all values to the

nearest hundredth.

Using this equation, predict the value of x if y is 426.21, rounding to the nearest tenth.

[Only an algebraic solution can receive full credit.]

x 1 2 3 4 5

y 4.2 33.5 113.1 268.1 523.6

Algebra 2/Trigonometry – Jan. ’16 [20]

38 Solve the equation cos 2x cos x algebraically for all values of x in the interval 0° ≤ x 360°.

Algebra 2/Trigonometry – Jan. ’16 [21] [OVER]

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly

indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc. A correct numerical answer with no work shown will receive only 1 credit.

The answer should be written in pen. [6]

39 Given: DC 10, AG 15, BE 6, FE 10,

m∠ABG 40, m∠GBD 90, m∠C 90,

BE

___

ED

___

, and GF

___

FB

___

Find m∠A to the nearest tenth.

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