The expression is equivalent to
(1) 3 __
2 (3)
_3_x_y_
2
(2) ___ 3x __y_
2xy (4) ___ 3x __y_
2
1 3
2
x y
Problem 4 Which relation does not represent a function?
January 2016 algebra 2 trig new york regents 4 Which relation does not represent a function?
problem 5
NYS Regents 2016 January algebra 2 Solutions in the diagram below the spinner is divided In the diagram below, the spinner is divided into eight equal regions.
Which expression represents the probability of the spinner landing
on B exactly three times in five spins?
(1) 8C3(1 __
5 )3(4 __
5 )5
(3) 5C3(1 __
8 )2(7 __
8 )3
(2) 8C3(1 __
5 )5(4 __
5 )3
(4) 5C3(1 __
8 )3(7 __
8 )2
Problem 6
NYS Regents 2016 January algebra 2 Solutions 6 The expression is equivalent to
Problem 7
NYS Regents 2016 January algebra 2 Solutions
7 The amount of money in an account can be determined by the
formula A Pert, where P is the initial investment, r is the annual
interest rate, and t is the number of years the money was invested.
What is the value of a $5000 investment after 18 years, if it was
invested at 4% interest compounded continuously?
(1) $9367.30 (3) $10,129.08
(2) $9869.39 (4) $10,272.17
Problem 8
NYS Regents 2016 January algebra 2 Solutions 8 What is expressed as a single fraction?
(1) (3)
(2) (4) 2 1
2 1
x
x
2
( 2 )
2 1
2 1
x
x
1
( 2 )
2 1
2 2
x
x
2
2
x
x
1
2
1
1
x
x2 2 x
2
1
1
2 2
3 3 3 2
2
b c
a
3 6 5
3
b c
a
3 9 6
18
b c
a
3
2
3
2
bc
a
3 27 6 3 2 a2 b c
Use this space for
computations.
Algebra
Problem 9
NYS Regents 2016 January algebra 2 Solutions
What is the total number of points of intersection of the graphs of computations.
the equations 2x2 y2 8 and y x 2?
(1) 1 (3) 3
(2) 2 (4) 0
Problem 10
NYS Regents 2016 January algebra 2 Solutions
9 What is the total number of points of intersection of the graphs of computations.
the equations 2x2 y2 8 and y x 2?
(1) 1 (3) 3
(2) 2 (4) 0
Problem 1
NYS Regents 2016 January algebra 2 Solutions A survey in a small upstate village to determine whether or not local residents should fund construction of a skateboard park by raising taxes
Title 10
NYS Regents 2016 January algebra 2 Solutions
10 Given the sequence: x, (x y), (x 2y),…
Which expression can be used to determine the common difference
of this sequence?
(1) x (x y) (3)
(2) (x 2y) (x y)
Title 11
NYS Regents 2016 January algebra 2 Solutions
11 In a circle with a diameter of 24 cm, a central angle of _4_π_
3 radians
intercepts an arc. The length of the arc, in centimeters, is
(1) 8π (3) 16π
(2) 9π (4) 32π
Title 12
NYS Regents 2016 January algebra 2 Solutions 12 Which graph is the solution to the inequality 4|2x 6| 5 27?
–9 –7 –5 –3 –1 1 3 5
–9 –7 –5 –3 –1 1 3 5
–9 –7 –5 –3 –1 1 3 5
(1)
(2)
(3)
(4)
–9 –7 –5 –3 –1 1 3 5
( )
( )
x y
x y
1
1
2
x
(x1y)
Algebra
Title 13
NYS Regents 2016 January algebra 2 Solutions 13 What is the sum of the roots of the equation 3x2 6x 2 0? computations.
(1) 2 __
3 (3) 2 __
3
(2) 2 (4) 2
Title 14
NYS Regents 2016 January algebra 2 Solutions
14 The scores of 1000 students on a standardized test were normally
distributed with a mean of 50 and a standard deviation of 5. What is
the expected number of students who had scores greater than 60?
(1) 1.7 (3) 46
(2) 23 (4) 304
Problem 15
NYS Regents 2016 January algebra 2 Solutions
15 If T 10x2 ____
y , then log T is equivalent to
(1) (1 2log x) log y (3) (1 2log x) log y
(2) log(1 2x) log y (4) 2(1 log x) log y
Problem 16
NYS Regents 2016 January algebra 2 Solutions
16 Which statement regarding correlation is not true?
(1) The closer the absolute value of the correlation coefficient is to
one, the closer the data conform to a line.
(2) A correlation coefficient measures the strength of the linear
relationship between two variables.
(3) A negative correlation coefficient indicates that there is a weak
relationship between two variables.
(4) A relation for which most of the data fall close to a line is
considered strong.
Title 17
NYS Regents 2016 January algebra 2 Solutions
18 The roots of the equation 4(x2 1) 3x are
(1) imaginary (3) real, rational, unequal
(2) real, rational, equal (4) real, irrational, unequal
Title 18
NYS Regents 2016 January algebra 2 Solutions18 The roots of the equation 4(x2 1) 3x are
(1) imaginary (3) real, rational, unequal
(2) real, rational, equal (4) real, irrational, unequal
Title 19
NYS Regents 2016 January algebra 2 Solutions
19 If f(x) 2x2 3x 4, then f(x 3) is equal to
(1) 2x2 3x 7 (3) 2x2 9x 13
(2) 2x2 3x 13 (4) 2x2 9x 25
Problem 20
NYS Regents 2016 January algebra 2 Solutions
The expression x(3i2)3 2xi12 is equivalent to
(1) 2x 27xi (3) 25x
(2) 7x (4) 29x
problem 21
NYS Regents 2016 January algebra 2 Solutions
21 If the terminal side of angle θ passes through the point (3,4),
what is the value of sec θ?
(1) 5 __
3 (3) 5 __
4
(2) 5 __
3 (4) 5 __
Title 22
NYS Regents 2016 January algebra 2 Solutions
Title 23
NYS Regents 2016 January algebra 2 Solutions
23 What is the third term of the recursive sequence below?
a1 6
an 1 __
2 an 1 n
(1) 1_1_
2 (3) 1 __
2
(2) 5 __
2 (4) 4
Title 24
NYS Regents 2016 January algebra 2 Solutions
24 What is the equation of a circle with its center at (0,2) and passing
through the point (3,5)?
(1) x2 (y 2)2 9 (3) x2 (y 2)2 18
(2) (x 2)2 y2 9 (4) (x 2)2 y2 18
Title 25
NYS Regents 2016 January algebra 2 Solutions 25 If angles A and B are complementary, then sec B equals
(1) csc(90° B) (3) cos(B 90°)
(2) csc(B 90°) (4) cos(90° B)
Title 26
NYS Regents 2016 January algebra 2 Solutions
26 The legs of a right triangle are represented by and .
The length of the hypotenuse of the right triangle is represented by
Title 27
NYS Regents 2016 January algebra 2 Solutions
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
Title 28
NYS Regents 2016 January algebra 2 Solutions 28 Solve algebraically for x:
2x 1 1 1 4 5 8
NYS Regents 2016 January algebra 2 Solutions 30 Solve algebraically for the exact value of x:
log816 x 1
Title 31
NYS Regents 2016 January algebra 2 Solutions Determine how many eleven-letter arrangements can be formed from the word
“CATTARAUGUS.”
problem 32
NYS Regents 2016 January algebra 2 Solutions 32 Express 130° in radian measure, to the nearest hundredth.
Problem 33
NYS Regents 2016 January algebra 2 Solutions 33 Determine the area, to the nearest integer, of SRO shown below.
Title 34
NYS Regents 2016 January algebra 2 Solutions 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
Title 35
NYS Regents 2016 January algebra 2 Solutions 35 Find the difference when 4 __
3 x3 5 __
8 x2 7 __
9 x is subtracted from 2x3 3 __
4 x2 2 __
9 .
Title 36
NYS Regents 2016 January algebra 2 Solutions 36 Find the exact roots of x2 10x 8 0 by completing the square.
Title 37
NYS Regents 2016 January algebra 2 Solutions 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.]
Title 38
NYS Regents 2016 January algebra 2 Solutions 38 Solve the equation cos 2x cos x algebraically for all values of x in the interval 0° ≤ x 360°.
Title 39
NYS Regents 2016 January algebra 2 Solutions
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.
Find BC to the nearest tenth.
G
B