Math 1010 Section 5 Finalreview
Name:
Read all directions carefully. The review will be graded on completion and will be
worth 26 homework points. You can nd the complete solutions to the review posted
on my website www.math.utah.edu/~malone.
1. Find all real and complex solutions to
4 +2 2 +3 =0
+1
+2
2. Find the Distance between the two points, and nd the midpoint on the line
segment connecting the points.
x
x
x
x
(3 1)
;
and
( 5 3)
;
3. Find the slope, y-intercept, x-intercept, and graph the following line. 5x+2y=7
4. Multiply out the following expression and simplify by combining like terms.
(3
a
5)(2
4)( + 2)
a
a
5. Use either substitution or elimination to solve the following systems
4x-3y=-5
20x+6y=10
p
p
6. Find all complex and real solutions to 5 2 2 + 1 5 2 2 + 5 = 0
7. Find all real and complex solutions to
s
5
4
x
s
2 3+9 2 =2
x
x
s
2
x
8. Use your knowledge of shifts and reections of functions to graph
( ) = ( + 4)3 1
P x
x
9. Find all solutions to the absolute value equation j2 + 1j = 7 + 6
10. Perform the Division
6 4 7 3 + 2 11
3 +1
11. Use either substitution or elimination to solve the following system
x-5y=4
3x+y=-36
x
x
x
x
x
x
12. Write down the equation for a line that passes through (6,2) and is perpendicular
to the line 4x+5y=11
13. Sketch the graph on the real number line of all solutions to 3 + 7 2 9
14. Factor the following polynomial completely. 6 7 + 150 5 6 4 150 2
15. Perform the Division
10 5 27 4 13 3 25 2 + 50 + 13
3
16. Factor the following polynomial completely 4 + 4 3 + 2 72 10 + 5 3
17. Simplify the following expression as far as you can using the laws of exponents.
p2
2
(
+
1)
p8 ( 2 + 2 + 3)+4(p23 ++31)3
18. Evaluate the function (don't need to simplify) Y(p)= 2 p + 1p at Y(4) and
p=4t+1
19. Find the equation for a line that passes through the points (7,-6) and (-1,3)
20. Find the domain of the function
p3 3
p p4
7
2
+
5
4 +1
()=
3
3 2 +3
21. Solve the following system using the method of substitution. Hint(Look at the
last two equations rst; solve them then look at the rst equation)
x-2y+z=5
y+3z=7
y+z=3
22. Find all solutions(there are 4) to the absolute value equation j +4j j3 +6j =
3 7
p 5p5 = 0
p
23. Find all real and complex solutions of + 5 3
24. Find all real and complex solutions to
2
3 +1 =1
2+4 +3
2+3 +2
25. Find all real and complex solutions to
p
p3 2
+p3 + 3 + 1 + ( 3p 2 + 1)2 = 0
3 2
+1
+1
Hint(divide 3 + 3 2 + 3 + 1 by x+1 twice)
26. Graph all solutions to the absolute value equation 3 jj2 + 5j 4j 6 on the
real number line.
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