Regents Practice TEST 3
Interactive Version - Multiple Choice

Algebra 2 and Trigonometry
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Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.

1.   Rationalize the denominator and simplify:  
      [1]                   [2]                   [3]   11                    [4]  
 


2. 
The expression     is equivalent to

     [1]                             [2]                         [3]                   [4] 
 


3.
 
The roots of the equation  x2 - 7x + 3 = 0   are

     [1]                      [2]               [3]            [4]   
 


4. 
Find, to the nearest tenth, the standard deviation of this distribution:
 

Score 1 2 3 4 5
Frequency 14 15 14 17 10

 

     [1]  1.3                              [2]  1.4                       [3]  2.8                    [4]  2.9
 


5.
 
A circle has a radius of 3.5 cm.  In centimeters, what is the length of an arc intercepted by a central angle of 4 radians?

     [1]  14 cm                      [2]   12 cm               [3]  8 cm               [4]  1.1 cm
 


6.
 
Which of the following is NOT equivalent to 6C5?

     [1]                 [2]                     [3]                [4]  6C1
 


7. 
Expressed in interval notation, the solution set of       is

  [1]  [-8, 8]                           [2]   (-8, 8)                  [3]    [-32, 8]                [4]   (-32, 8)
    


8. 
The expression is equivalent to

     [1]                    [2]                 [3]              [4] 


9. 
What are the values of θ in the interval 0 θ < 360 that satisfy the equation     ?

     [1]   30, 150                             [3]   60, 120, 240, 300
     [2]   60, 120                            [4]   30, 150, 210, 330


10.
 
A fair coin is tossed 5 times.  What is the probability that the coin will land tails up exactly 3 times?

     [1]                          [2]                         [3]                      [4] 


11. 
A bag of cookies contains 6 oatmeal cookies, 5 pecan cookies, and 1 peanut butter cookie.  Alisha selects 2 cookies at random.  What is the probability that she selected 2 oatmeal cookies?

     [1]  5/22                          [2]  5/11                    [3]  6/11                          [4]  1/6
 

 

 12.  Which equation represents the equation of a circle that is tangent to the x-axis with a center located at (4, -6)?

     [1]   (x + 4)2 + (y - 6)2 = 36

 

     [2]   (x - 4)2 + (y + 6)2 = 36
     [3]   (x + 4)2 + (y - 6)2 = 6
     [4]   (x - 4)2 + (y + 6)2 = 6


13.
 
In ABC, AB = 12 meters and AC = 20 meters.  If the area of the triangle is 77 square meters, find the measure of angle A to the nearest degree.

     [1]  64                          [2]  50                          [3]   40                         [4]   39


14. 
The expression  sin 5x cos 2x - cos 5x sin 2x   is equivalent to

     [1]  cos 7x
     [2]  cos 3x
     [3]  sin 7x
     [4]  sin 3x


15. 
What is the domain of the function ?

     [1]  x = 1 and x = -3/2                                       [3]  All real numbers, except 1 and -3/2 
     [2]  x = -1 and x = 3/2                                       [4]  All real numbers, except -1 and 3/2


16.
 
Factored completely, the expression       is equivalent to

   [1]  2x(4x - 2)(x − 1)     [2]  -2x(4x +1)(x + 2)     [3] 2x(4x + 2)(x + 1)     [4]  2x(4x - 1)(x 2) 


17. 
The equation     is true for all rational values of x, such that x does NOT equal

     [1]   -5                         [2]   3                              [3]  -5 or 3                     [4]  -5, 3, or 1   


18.
 
The expression  ln [(x + 5)(2x - 1)2] is equivalent to

     [1]    2 [ ln (x + 5) + ln (2x - 1) ]                                    [3]    2 ln (x + 5) + 2 ln (x - 1)
     [2]    ln (x + 5) + 2 ln (2x - 1)                                       [4]    ln (x + 5) 2 ln (2x - 1)


19.
 
Find the exact value of  sin 30 + cos 30 + tan 30.

     [1]                    [2]                 [3]             [4] 


20. 
In the equation    the value of x rounded to the nearest thousandth is

     [1]  0.834             [2]  -0.834                [3]  0.631                  [4]  -0.631  


21.
  
In terms of transformations, which description describes how the graph of  g(x) = (x + 2)2   was produced from the graph of   f (x) = x2

     [1]  Function f was translated (shifted) horizontally two units to the left.
    
[2]  Function f was translated (shifted) horizontally two units to the right.
    
[3]  Function f was translated (shifted) vertically two units up.
     [4]  Function f was translated (shifted) vertically two units down.


22.
 
The period of the graph shown below is

    [1]  π

    [2]  π/2

   
[3]  

    [4]  3π/2       



23. 
If a function is defined by the equation f (x) = 2x - 5, which graph represents the inverse of this function?

     [1]                                                                             [3]
                  
     [2]                                                                              [4] 
                 


24. 
What is the 12th term in the sequence     ?

     [1]  -e144                       [2]  e144                        [3]  -144                         [4]   144


25. 
Which notation represents the series   -3 + 6 - 12 + 24 - 48 + ...  for 35 terms?

     [1]     
    
[2]                       
  [3]      
  [4]   


26. 
Which function is the inverse function of  y = ln?

     [1]  y = ex                          [2]   y = e-x                [3]  y = ln x-1                 [4]  y = log x   

 



27. 
Which of the following is ALWAYS true?

     [1]                                             [3] 
     [2]                                              [4] 
 

 


 



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