Regents Practice TEST 2
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.   What is the value of  ?
      [1]  2 - 5                       [2] 2 - 6i                      [3] 8 - 5               [4] 8 - 6i
 
 


2. 
What is the solution set for the equation   | 2x - 3 | = 6   ?

     [1]  { }                             [2]  {4.5}                    [3]  {4.5, -1.5}      [4]  {-4.5, 1.5}
 


3.
 
You are asked to write a quadratic equation where the sum of the roots is -3, and the product of the roots is -9.  Which equation meets these requirements?

   [1]  x + 3x + 7 = 0      [2]  2x + 6x - 18 = 0      [3]   x - 12 x + 27 = 0     [4]  (x + 3)(x + 9) = 0
 


4. 
What is one solution for the accompanying system of equations?       y = x - 9,        y = x + 3

     [1]  (3, 0)                      [2]  (4, 7)                       [3]  (0, -3)              [4]  (7, 4)
 


5.
 
Variable T varies directly with the square of M.  If T is 8 when M is 2, find T when M is 4.

     [1]  16                            [2]  24                           [3]  32                   [4]  64
 


6.
 
The expression , when simplified, is equivalent to

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


7. 
Find  a6   for an arithmetic sequence where a1 = 3x + 1 and the common difference is 2x + 6.

  [1]  5x + 7                           [2]  8x + 12                 [3]  13x + 31           [4]  15x + 37 
    


8. 
Which interval represents the range of the function    ?

     [1]  (1, ∞)                         [2]  (-1, ∞)                   [3]  [1, ∞)                [4]  [-1, ∞)


9. 
Find the exact value of   sin 30 + cos 30 + tan 30.

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


10.
 
If   f (x) = 5x - 1  and  g (x) = 3x - 1, find  .

     [1]  6                             [2]  11                          [3]  12                        [4]  19


11. 
If θ is a positive, acute angle and    , then 

     [1]  1                            [2]                     [3]  30                        [4]  60


12.
 
The speed of sound, V, at temperature T, in degrees Kelvin, is represented by the equation   .
      Which expression is equivalent to  log V ?

     [1]  

[3]  

     [2]   [4]  


13.
  
If θ is an angle in standard position and  P(-3,4)  is a point on the terminal side of θ, what is the value of sin θ ?

     [1]  3/5                         [2]  -3/5                      [3]  4/5                         [4]  -4/5


14. 
What is the third term in the expansion of   (x + 3y)9  ?

     [1]  108x7y2                 [2]  252x7y2                   [3]   324x6y2              [4]  324x7y2


15. 
The fraction  is equal to

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


16.
 
On a standardized test, the distribution of scores is normal, the mean of the scores is 75, and the standard deviation is 5.8.  If a student scored 83, the student's score ranks

   [1]  below the 75th percentile                       [3]  between the 75th percentile and the 84th percentile 
    [2]  above the 97th percentile                       [4]  between the 84th percentile and the 97th percentile       

 


17. 
Which diagram represents a one-to-one function?

     [1]     [3] 
     [2]   [4] 


18.
 
Which graph represents the inverse of  f (x) = { (0,1), (1,4), (2,3)} ?

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


19.
 
In the equation x is equal to

     [1]                [2]  6                        [3]  6.5                       [4]  18


20. 
If ,  then f (3) equals

     [1]               [2]                    [3]  -21                       [4]   -22  


21.
 
A solution set of the equation  5 sin θ  + 3 = 3  contains all multiples of

     [1]  45                [2]  90                     [3]  135                     [4]  180


22.
 
A student was asked to express the sum using sigma notation.  The student produced four answers.  Which of the four answers is NOT correct?

    [1]  

[3]  
    [2]     [4]  


23. 
What is the solution set of the equation  | x2 - 2x | = 3x - 6  ?

     [1]  {2, + 3}                  [2]  {2}                      [3]  { + 3}                      [4]  {2, 3}


24. 
The expression  is equivalent to

     [1]                        [2]  2 cos θ                 [3]  2 cot θ                     [4]  2 tan θ


25. 
What is the value of     

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


26. 
Given   f (x) = 2x2 - 2x + 1,  find  f (x + 3).

     [1]   2x2 + 10x +13                                              [3]   2x2 + 14x + 13  
      [2]   2x2 + 10x + 25                                             [4]   2x2 + 14x + 25


27. 
Find the domain of the function   .

     [1]   (-∞, ∞)                                       [3]   [3, ∞)
     [2]   (3, ∞)                                         [4]  All values less than 3, except -2.
 

 




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