Name _____________________________
Final Exam Review
Date _____________
1.
Simplify:
8  2  2  3(2  1)  3  23  15
2.
Evaluate for x= -6 :
x 2  3x  2
3.
Simplify:
9  6  3  2x
4.
Solve:
2x  6  8
5.
The slope of the line through the points with coordinates (-1,4) and (-5,-4) is:
6.
The slope of the line with equation 3x – 5y = -30 is:
7.
Find the equation of the line through (-1,4) and (-5, -4):
8.
Find the equation of the line that passes through (-3, 4) and is perpendicular to x=8
9.
Solve the following system:
10.
Find f(g(3)), if g(x) = 3x + 11 and f(x) = x2 + x + 1 :
11.
Simplify:
12.
Simplify:
13.
Simplify:
14.
Simplify and express in scientific notation:
15.
Express in scientific notation:
16.
Suppose:
log 3 x  4
17.
Suppose:
log 3 27  x
4x   2x
3 2
3
y1
4x  3y  2
2x  9y  1

3
 8 a 5b6    24a4b 3 

 


 

3 729
 9  10 5  7  10 4 






.0000563
Find x:
Find x:
18.
Suppose:
x  5 log 2 4
19.
Multiply:
(3x + 2) (x - 1) (x - 3)
20.
Factor completely:
4x 2  16 y 2
21.
Multiply / Simplify:
x 2  49
7

49
7x
22.
Divide/Simplify:
23.
Subtract / Simplify:
24.
Solve:
25.
Simplify:
2  3  5  27  7  48
26.
Simplify:
i 57
27.
Simplify:
7 3
28.
Simplify:
x 36
29.
Simplify:
i + i2 + i3+ i4 + i5
30.
Solve:
x2 – 6x + 4 = 0
31.
Simplify:
3i
2i
32.
Given the equations 3x – 4y = 8 and 4x + 3y = 9. Which of the following is true about
the graphs of these equations?
Find x:
x 2  7 x  12
x 2  16

x2  x  6
x2  x  2
x 2  5x  4 x 2  5x  6

x4
x2
x2  5  x  5
12
 75
3
a. They are inconsistent
b. They are dependent
c. They are independent
33.
2 6
34.
Write the equation, in Standard Form, of the line passing through the points
(1,-2) and (5,3).
35.
log (xy)2
Find the product.
36. (x + 2y) (x + y)
37. (2x – 5)(2x + 5)
40. (2x + 3) (x – 1)
39. ((x + y) +2) ((x + y) – 2)
41. Square 3x + 2
Factor.
42. 4x2 + 6x + 8
43. x2 – 3x – 10
44. x3 + 8
45. 4 x2 – 9y2
Factor completely. (Use the Factor Theorem where necessary)
46. x3 + 5 x2 + 4x
47. x4 – 16
48.
x 4 - x3 - 8
Solve.
49. (x + 3)2 - (x + 2)2 = 3(x-6)
50. x2 – 6x = 0
51. (x+1)(x-3) = x-5
52. What are the solutions of (3x + 1) = (x+2) – 5 ?
53. What is the product of (5 + (x+y)) (5 – (x+y) ? Simplify your answer completely.
54. What is the product of ( x – 3y) and (x – 3y) ?
55. How is 14 x3 + 21 x2 + 35x written in completely factored form?
Solve.
56.
rt = 2t – 5
for t.
57. What is the remainder when x3 + x2 + 5 is divided by x - 1 ?