Algebra II R Semester 1 Final Exam Review
2012
Name ______________________________
1. Multiply: (2 x2  5)(3x 2  7 x)
2. Evaluate: a  2, b  -3 and c  4
a(b  c)

c ( a  b)
3. Solve for x:
4. Solve the equations for “a ”
1
1
K  ap
H  at
2
3
3  8(5x  2)  2 x  (7 x  4)
5.
The Perimeter of a rectangle is 12. The
length is 2 more than the width. Find
both dimensions.
7. Solve for x:
6.
3x  5  9 x  8
8. Factor:
x 3 5  9
20 x5 y 6 z 7  15x 2 y 4 z 3  35x7 y 2 z 2
9.
10.
a. State the slope of the line containing
the points (4, 3) and (-9,6) . _______
b. What is the slope of a line parallel to
this line?
_______
c. What is the slope of a line
perpendicular to this line?
Solve the inequality, and graph the
solution on a number line
_______
Factor:
a. 9 x2  12 x  4 _______________
b. 16 x2  8x  1 _______________
2
11. Describe these lines as parallel, intersecting,
or same. hint: check the slopes
3
y  x 1
4
a.
3
y  x5
4
4
y  x2
3
b.
4
y  x2
14. 3
c.
x y 4
2x  2 y  8
Graph: 2 x  3 y  6
m = _______
b = _______
_______________
_______________
_______________
13. Write the equation of a line in slope-intercept
form. hint: for problem b use point-slope
y  y1  m  x  x1 
a. m  6 b  4
12.
14. Write an equation of a line in Standard
form. hint: for problem b use point-slope
a. m  4 b  6 __________________
___________________
b. m  5 pt.  2,1 ___________________
m  3 pt. 1, 5 ________________
b.
15.
f ( x)  2 x 2  3 x  6
16.
Which of the following are functions?
f (1)  _______
a.
(4,5),(4, 2),(5, 2)
f (3)  ______
b.
(5, 4),(6, 4),(3,1)
17. Factor
a. x3  125 ______________________
b. 8 y 3  1 ______________________
18.
Solve the system:
2x  3y  7
5 x  2 y  30
________
________
3
19.
20. Factor:
a. 2 x 2  32 ___________________
Solve the system
y  2 x  1 4 x  3 y  23
b. xy 2  49 x ___________________
21.
22.
A collection of dimes and quarters has $1.55.
There is a total of 8 coins. Write and solve a
system of equations to find the number of
each.
State the equation of each line.
(5, 4)
(6,3)
_________________ _______________
24. Name all of the subsets of the real
numbers to which each is a member.
Use: R I Q Z W N
2
____________________
23. Graph and shade the system
y  2
2
y  x2
5
25.
2.5
____________________
5
____________________
26.
Factor:
x2  2 x  3  ________________
Simplify:
5x2  12 x  4  ______________
(4 x  3 y)(4 x  3 y)  _____________________
(3x  2)(4 x  5)  _______________________
4
27.
(2 x3  3x2  2)  (6 x2  4 x  5)
(2 x3  3x2  2)  (6 x2  4 x  5)
29
28.
Solve the system:
x yz 2
( ____, ____, ____ )
2 x  y  z  1
x
 2z  5
30. Graph. y  x  2  3
Simplify:
2 x(4 x 2  3)  ___________
3x 2 (5 x  1)  _______________
32. Multiply:
31. Multiply:
.
(6 x  1)  _________________
2
(2 x  1)( x2  6 x  3)  _____________________
(4 x  7)2  _________________
33. Simplify:
4 x 2 y 4  2 xy 3
3xy 6
st
34. Divide: 1 by long
5 xy 2  10 x 2 y 6
15 x3 y 4
3x  2 6 x 2  10 x  4
2nd by synthetic
8 x3  6 x 2  x  3
x 1
5
35. Solve and graph the Solution Set.
36. Solve and graph the solution set.
4x  3  9 or 4 x  3  11
37.
3x  4  17
38.
Solve by any method
4 x  10 y  3
2x  y  5
x
39.
( x  3)5
(2 x  b)4
y
40.
Factor each expression.
12 x2  71x  6
x4  13x2  36
4 x3  100 x
x3  125
27 x3  64 y3
2 x2  7 x  15
Factor by grouping
cx  cy  dx  dy
_______________
ax2  bx2  4a  4b
_______________
6
i17  _____
41.
42. (3  2i )(5  7i )
i 27  _____
i 36  _____
(4  2i )(4  2i )
43.
3
4i
44. x2  8  3
3
6  2i
46. Graph y  2 x 2  4 x  7
45.
3  7i
5  4i
Which direction does the graph open? ______
Find the vertex V (___, ___)
Write the equation for the axis of symmetry.
Find the y-int.
47.
9 x2  7  4
 ___, ___ 
7
48. Identify the solutions to the following quadratic
equation by using the given graph.
49. Write a quadratic equation in standard
form with solutions, x  3 and x  4 .
Use integers for a, b and c.
x2  4 x  3  0
50. Write a quadratic equation in standard
2
and x  5 .
form with solutions, x 
3
Use integers for a, b and c.
___  x  ___
and
___  x  ___
51. Solve by factoring
x2  8x  0
2 x2  5x  3  0
x2  10 x  25
5x2  20 x
x2  72  x
x 2  81
8
Use synthetic substitution to find the given value
for each function.
Given a polynomial, determine if the binomial
is a factor.
52. 2 x3  6 x2  x  15 for f (3)
54. x3  6 x2  x  30, x  3
53. 3x4  2 x3  x2  2 for f (2)
55. x3  6 x 2  11x  6, x  2
Solve each system.
56.
6x – y +2 z = 8
2x + 3y – z = -9
4x +2y +5z + 1
57.
5x - 6y + 2z = 21
2x + 3y - 3z = -9
-3x + 9y – 4z = -24