Multiple Choice Practice
 Equations & Inequalities
Algebra 2 Trigonometry Level
 Algebra 2Trig Index | Regents Exam Prep Center

Also available in Hardcopy (.pdf):
Equations and Inequalities
 

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 a calculator when working on these problems.

1.   The solution of  |2x - 3| < 5  is
       [1]      [2]  (-1, 4)                [3]               [4] 
 

 

2.  What is the solution set of the equation ?

     [1] { }                    [2] {4, 6}                [3]  {-6}                  [4]   {4}
 

 

3.  In the equation  x2 - 7x + 2 = 0, the sum of the roots exceeds the product of the roots by

     [1] 9                       [2] 5                      [3]  -9                      [4]  -5
 

 

4.  The roots of the equation  3x2 - 4x + 2 = 0 are

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

 

5.  The roots of the equation 2x2 + 3x + 2 = 0 are

     [1]  real, rational, and equal        
     [2]  real, rational, and unequal
     [3]  real, irrational, and unequal
     [4]  imaginary
 

 

 

6.  When solved by the method of completing the square, the solutions to the equation -8x = 4x2 -1 are 

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

 

 

7.  What are the solution(s) to the system of equations   y = x2 - 9  and   y - 3 = x?

    [1] (-3, 0) and (4, 7)       [2]  (-3, 0)               [3]  (4, 7)           [4]  no solutions
 

 

8.  

     [1]                        [2]                      [3]  5               [4]  25
 

 

9.  The growth of bacteria in a dish is modeled by the function .  For which value of t is  f (t) = 32 ?

     [1]  8                            [2]   2                    [3]  15                [4]  16
 

 

10.  What is the value of  b  in the equation ?

     [1]  3/7                       [2]  7/9                   [3]  9/7                [4]  10/7
 

 

11.  Which expression is equivalent to ?

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

 

12.  The volume of a soap bubble is represented by the equation , where A represents the surface of the bubble.  Which expression is also equivalent to V ?

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

 

 

13.  What is the sum of  5 - 3i  and the conjugate of 3 + 2i ?
  
     [1]  2 + 5i                      [2]  2 - 5i             [3]  8 - i                 [4]  8 - 5i 

 


 

14.   Which equation is equivalent to  ?
       [1]   (t - 3)(t + 2) = 0                          [3]  (2t + 1)(3t - 1) = 0
       [2]   (t - 2)(t + 3) = 0                          [4]  (2t - 1)(3t + 1) = 0

 

 

15.  If  then x is equal to

     [1]  1                            [2]  2                         [3]   5                  [4]  4
 

 

16.  What is the solution set of the inequality  x2 + 3x - 10 > 8  ? 

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

 

17.  The flight paths of two Thunderbird jets are plotted on a Cartesian coordinate plane, and the equations of the jets' flight paths are represented by  y = 2x + 3  and  y = 0.5x.  The best approximation of the intersection of the flight paths is
     [1]  (-1.50, 2.82)              [2]  (0,1)                    [3]  (-1.72, 3.3)       [4]  (-2, -1)
 

 

18.   In the diagram, figure b is the reflection of  y = 2x  in the line  y = x.  Which is an expression for the equation of figure b?
     [1] 

     [2]  

     [3] 

     [4] 
 

19.  A certain radioactive material decays according to the law , where A0 is the initial amount present and A is the amount present in t years.  What is the half-life of this material?  Round the answer to two decimal places.
     [1] 66.01 years             [2]  95.24 years          [3]  33.01 years     
     [4]  impossible to determine without knowing the value of A0
 

 

20.  When solved using the quadratic formula, the solutions to the equation 3x2 - 4x - 6 = 0, rounded to the nearest hundredth, are
     [1]  2.46, -3.79           [3]   3.79, -2.46    
     [2]  2.23, -0.90          [4]   0.90, -2.23
 

Algebra 2 Trig Index | Regents Exam Prep Center