MATH 1090 Algebra and Trigonometry
Final Examination - Questions

1. Perform the indicated operation and simplify:
   
   1.  
   2.  
   3.  

2. Factor:
   
   1.  
   2.  

3. Solve the given equation or inequality.
   
   1.  
   2.  
   3.   | 4x - 3 |   >   9
   4.   x (2x + 3)   <   2

4. Find an equation of the line passing through the point (2, 3) and perpendicular to the line 2x + 3y + 1 = 0 .

5. Sketch the graph of each of the following equations.
   Label all intercepts and also label the vertex, if appropriate.
   
   1.   y   =   | 2x - 3 | - 4
   2.   y   =   -x² + 8x - 12

6. For the functions     and   ,
   find     and the domain of   .

7. If   ,   find   f ^-1 (x)   and sketch the graphs of   f   and   f ^-1   on the same set of axes.

8. 1. Use the remainder theorem to find the remainder when   f (x)   =   x⁷ + 3x⁶ - 5x³ - 5x² + 7   is divided by   .
   2. Find   c   so that   x + 2   is a factor of   g (x)   =   cx⁵ + 2x³ - 8cx - 32 .

9. For the polynomial   P(x)   =   9x⁴ - 6x³ + 37x² - 24x + 4:
   1. List all possible rational zeroes.
   2. Factor   P(x)   completely into linear factors.

10. Solve for   x:
    1. 
    2. 

11. Find all values of   q   in the interval   [0, 2p)   that satisfy the equation   sin 2q   +   sin q   =   0 .

12. Given that     and that   , find the exact value of:
    1.   sin q
    2.   tan (q + 2p)
    3.  
    4.   cos 2q
    5.  

The solutions to this final examination will appear elsewhere on this web site.

[Index of Questions]

[Problem Set & Quiz Solutions]