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Name: _________________
Period: ____
Pre-Calculus
Algebra Review Part I
1. For what value of k are the points  4, 6  ,  2, 10  , and  2k , k  collinear?
2. Write the equation of a line with x-intercept 6, and is parallel to the line through  7, 2  and  4,9 
3. A triangle has vertices at  0,18 ,  2, 2  and  5,8  . Find the area of the triangle.
4. What is the equation of the line that contains  5,6  and is perpendicular to the line through  6, 2 
and  0,11 ?
Find all real-valued solutions to the following radical equations:
5. 3  a  a  1
6.
m3  m 4
7.
3 27  2 v  300
8.
c  c  16  2
9.
2x  5  x  1  x  2
Find all solutions to the following equations:
10. r 4  7r 2  12  0
11. 4a4  7a2  15
12. 4a 4  4a3  a 2  a  0
13. m4  6m3  9m2  0
14. 20  c  6  c
4
15. m2  2  5
m
1 1
16. 2   2
t
t
Find all real-valued solutions to the following rational equations:
2m  1 m  1
17.

3m  1 m  1
3
1
2
18.
 
x 6 2 x 5
2
 c 
 c 
19. 49  2
  6  35  2

c 2
c 2
3
4
20.
2
y 8
y2
2 x  11 x  1
5
21.


x 8
2
x 8
2x  3
x3
3
22. 2


x  5x  6 x  2 x  3
Name: _________________
Period: ____
Pre-Calculus
Algebra Review Part II
Solve the following systems of equations:
2 x  3 y  13
23. 
 y  4x  6
 1
 x  5y  0
24.  2
6 x  4 y  14
 x  2 y  5z  4

25.  2 x  y  2 z  4
6 x  3 y  4 z  6

 a  2b  c  3

26.  2a  3b  2c  1
3a  b  3c  14

Find all real solutions to the following exponential and logarithmic equations:
y
1
27.    32 y 1
4
28. 63 x1  10
29. 2x 1  31 x
30. e2 x 6  e x 4
31. 32 x  11 3x   18  0
32. e16 x  8
33. log2 x3  6

34. 6  log x2  4

3
35. 2  log 4  2 x   log 4  x  2 
36. ln  x  5  ln 3x  ln  x  1
37. log x  log  x  3  1
Find the center and radius of each of the following circles:
38. x2  y 2  10x  12 y  45  0
5
39. x2  y 2  3x  2 y 
4
1
1
2


c c  4 c 1
41. Solve the equation: x3  8
40. Solve the equation:
42. (a) Write an equation of a circle with center  5, 3 and is tangent to the y-axis.
(b) A line is tangent to the circle in part (a) at the point  2,1 . Find the equation of this line.