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Interactive video lesson plan for: Jan 2016 NYS Algebra 2/ Trig Regents Exam pt 6 #28 to 32 solutions Tips Tricks

Activity overview:

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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