1. ALGEBRA II FINAL EXAM
REVIEW #2
Section 1—Linear Equations & Inequalities
Directions: Solve for x.
1. 5 x − 6 = 24
2. 6 ( x − 4 ) = 18
3. 3 ( x − 4 ) = 4 ( 3x + 6 )
4. 6 x + 9 < 57
5. −4 − 7 x ≤ 17
6. x = 68
7. 3 x + 6 = 15
8. x − 5 ≤ 26

2. Section 2— Important concepts to know for matching.
Directions: Determine what word best describes each example.
9. 7 x + 8 > 15
2
10. y = − x + 5
3
11. x 2 + 6 x + 5 = 0
12. −3 − 7 x = 32
5 7
14.
6 8
15. The shape of a graphed quadratic function
16. The lowest or highest point on the graph of a quadratic function
17. The vertical line that goes through the vertex of a quadratic function
18. Solve each radical to the simplest form
75 −60
108 −32
19. What does i 2 =
20. What does −4i 2 =

3. Section 3—Rational Expressions
Directions: Simplify each completely.
−7 10
21. +
x 2 x3
x+3 5
22. +
x −9 x −3
2
8 x 2 − 16 x x 2 + 6 x + 9
23. g
x2 + x − 6 8x
2x − 4
24. 2
4x − 8
4

4. Section 4—Complex Numbers
Directions: Simplify the following radical expressions, leave in simplest radical form.
25. 16 5 − 9 5 26. 4 3 g 15 27. 6 2 g 12
3
7
28. ( 3 − 2i ) ( −4 + 6i ) 29.
9−i
Directions: Solve for x
1
( x + 3) = −12
2
30. 4 x 2 − 6 = 42 31. 32. x 2 + 2 x + 10 = 0
6
33. x 2 − 8 x − 5 = 0 34. 2 x 2 − 4 x = 0

5. Section 6—Matrices
Directions: Perform the indicated operation. If it is not possible, then choose ‘Not Possible’
3 9
2 2 6 2 4   5 1 2 
. A =
2 4  , B = 0 1 5  , C = 4 0  , D = 2 1 3 
    2 7  
 
35.) B+D
36.) BC
37.) A+B
38.) CB
39.) A2
40.) A-1 (the inverse of matrix A)

6. Section 7—Intersections
Directions: solve the system of equations.
41. 3 x + 5 y = 25 42. 2 x − y = −2
x − 2 y = −10 4 x + y = 20
43. 2 x + 4 y + 3 z = 10
3 x − y + 6 z = 15
5 x + 2 y − z = 25

7. NEED TO KNOW HOW TO SOLVE - Polynomials
44.) ( −8 x 3
+ 8 x 2 − 4 x + 7 ) − ( 3 x 4 + 2 x3 − 5 x 2 − 3) 45.) ( 3 x − 4 ) ( x − 6 x − 3)
2
46.) Use Synthetic Substitution to solve f(x) 47.) Divide: x 3 − 10 x − 2 by: x − 3
f ( x ) = 3 x 5 − x 4 − 5 x + 10 when x = −2
48.) Factor: x 3 + 2 x 2 − 11x − 12 ; f ( −4 )
49.) Find the remainder of 3 x 3 − 4 x 2 + 7 x − 2 ÷ x − 3 ?
50.) Find the three algebraic factors of: x 3 + 4 x 2 − 3 x − 18

8. NEED TO KNOW HOW TO SOLVE:
51.) Solve the Matrix (using the inverse of a square matrix):
2 x + 3 y = −8
x + 2 y = −3
52.) Solve the Matrix (using the inverse of a square matrix):
3x + 2 y = 6
x+ y =2
53.) Solve the Matrix using Cramer’s Rule
3x + 5 y = 1
−2 x + 3 y = 12
54.) Solve the Matrix using Cramer’s Rule
4 x + 2 y = 16
−3 x + y = − 7

9. 55.) Betty decided to start her own business, she will take any exam for you. The fee for this service is
$4.00 per question. However, if your test has more than 30 questions on it, Betty will reduce the cost
per question by $.03, for every question on the test. For example: If your test had 35 questions on
it, then she would charge you $3.85 for each of the 35 questions.
a. How much would Martha charge for each question if there were 55 questions on the test?
b. How many questions would there be on the test if she charged $3.34 per question?
c. If x represents the number of question, in excess of 30, that Martha answered, then how much did
she charge for each question?
d. What is the greatest amount of money that a client would have to pay Martha for her services?