Download PRACTICE Final Exam MAT121 NAME: Directions: Approved c

PRACTICE Final Exam MAT121
NAME:______________________________
Directions: Approved calculators may be used on this final exam BUT you must show correct work leading to your
answer!
25 problems worth 10 points each (parts as indicated!)
1. Factor completely.
B) (4) 18x2  33x  9
A) (3) x2  4x 12
C) (3) 12x3 19x2  5x
2. Factor completely.
B) (5) 2x3  16
A) (5) x4 16
3. Solve by factoring.
B) (5) 2x  x  3  5x  x  4  8
A) (5) 2x2 10x 12  0
4. A) (5) Write the domain of
x2
using interval notation. ___________________________
x  3x  4
2
B) (5) Reduce to lowest terms (show work!)
2x2  x  6
x2  x  2
5. (10) Divide (be sure to leave your answer in simplest form). Show work.
2 x 2  5 x  12 2 x 2  3x  9

3x 2  8 x  16 3x 2  13x  12
6. (10) Add and simplify as much as possible, Show work.
2
5

y 2  3 y  4 y 2  16
7. (10) Solve the rational equation. Show work.
x
2
2


x  1 x  3 x2  2x  3
8. (10) Find the equation of the line that passes through the points  2, 3 and  5,1 Write your final answer in the
form y  mx  b .
9. (10) Find the x and y-intercepts for 3x  2 y  6 and then graph!
X-intercept = _________
Y-intercept = ____________
10. (10) The distance a ball rolls down an incline plane varies directly as the square of the time it takes to roll.
During the first second it rolls 8 feet. How far will the ball roll during the first three seconds?
11. Simplify each of the following expressions. Write the answers with positive exponents only.
A) (5)
 3 x 2 y 5
2 x 4 y 1
B) (5)
16 x 2 y
24 x 4 y 1
12. Simplify (be sure to show your work!). Hint: Convert to radicals and simplify.
A) (5) 27
3
4
 625 
B) (5) 

 256 

3
4
13. Simplify the expression using the properties of rational exponents. Write the final answer using positive
exponents, simplify if appropriate. Do NOT convert to radicals!
A) (5) x

1
2
5 1


B) (5)  3x 2 y 3 


7
 x3
6
14. Simplify. Assume all variables represent positive real numbers.
A) (5)
4
9 x2 y5  4 9 x2 y3
B) (5)
3
16x 2 y 9 z 4
15. (10) Rationalize the denominator and simplify if possible.
3 2
5 2
16. (10) Solve the equation. Be sure to check your answers. If a solution is extraneous, say so in your answer.
x 1  3  x
17. Simplify the following, write your answer as a complex number in standard form.
A) (5)
3  2i  4  5i 
B) (5)
2  3i
5  2i
18. (10) Solve the following by completing the square.
x2  6x  11  0
19. (10) Solve the following by using the quadratic formula. Be sure to show ALL of your steps (just like I did
in class) AND be sure to simplify your answers!
 x  3 x  4  8
20. f  x     x  1  4
2
A. (2) Vertex = _________________
B. (2) Equation for the axis of symmetry ___________
C. (2) Maximum or Minimum Value (circle which it is AND give the value) ___________
D. (4) Draw the graph
21. (10) Solve the following equation.
x4  2x2  24  0
22. f  x   3x  2
A) (5)
Find
B) (5) Find
g
g
g  x   2x2  4x
f  2
f  x 
2
1
23. (10) f  x    x 
3
5
find
f 1  x 
24. (10) Expand into sums and differences of logarithms. Show all steps and be sure to simplify if possible.
log a
a 4 x3
y2
25. (10) Solve the following logarithmic equation. If a solution is extraneous, say so in your answer.
log4  x  6  log4  x   2