Name __________________________ Date _________ Mod ________
Analysis Final Exam Review
1. Solve the following system of equations using the elimination method.
2 5
 5
x y
3 10

 18
x y
2. Solve the following system of equations using the substitution method.
10x + 3y = -16
9x – 7y = 5
3. Determine whether the equations in the system are independent, dependent, or inconsistent.
15x -12y = 8
10x + 8y = 13
4. Solve the following system of equations using Cramer’s Rule.
2x + 3y = 2
4x – 9y = -1
5. Using the following equations, evaluate the equation.
f(x) = 3x + 11
g(x) = x2 + x + 1
Find g(f(-5)).
6. Solve the following system of equations.
3x + 2y – z = 10
x + 4y + 2z = 3
2x + 3y – 5z = 23
7. Find the determinant of the following matrix using both the expansion by minors method .
3x + 2y – z = 10
x + 4y + 2z = 3
2x + 3y – 5z = 23
8. Solve the following system of equations using the elimination method.
5y-2x = 0
3y+x = -1
9. Solve the following system of equations using the matrix multiplication method.
10x + 3y = -16
9x – 7y = 5
10. Use matrices A,B, and C to find each sum, difference, or product.
 2
A
- 4
3

9
a. A+B
 8
B
- 5
b. B-A
1 3

-6 
 12 
C

-7 
c. AB
d. BC
e. CA
11. Solve the following system of equations two ways: using Cramer’s Rule and using
the multiplicative inverse
2x + 3y = 2
4x – 9y = -1
12. Find the determinant of the following matrix using expansion by minors.
3x + 2y – z
x + 4y + 2z
2x + 3y – 5z
13. Solve the following system of equations using the elimination method.
3x + 2y – z = 10
x + 4y + 2z = 3
2x + 3y – 5z = 23
Name three other pairs of polar coordinates for each point.
14.
5 

 2 ,


4
15.


3 ,  

6
Identify each polar equation.
16.
r = 10 sin 2
______________________________
17.
r = 2 + 4sin 
______________________________
18.
r = 3
______________________________
19.
r = 3 + 3cos 
______________________________
Find the rectangular coordinates of each point with the given polar coordinates.
20.
5 

3 , - 

4


2 2 , 

4
21.
Simplify.
22.
i23
25.
( 3 + 5i )( 3 – 2i )
23. ( 2-5i ) + ( -2 + 4i )
26.
24.
( -4 + i ) - ( 4 – 2i )
6  2i
2i
Express each complex number in polar form.
27.
-4 + 4i
28.
-5
29.
6-6i 3
Find each product or quotient. Then write the result in rectangular form.
30.
3
3 




4  cos
+ i sin
+ i sin 
  3  cos


2
2
4
4
31.
2
2 

2 3  cos
+ i sin
 

3
3
32.
(1 – i )8
33.
3
Find:
Find:
 8i



3  cos
+ i sin 

4
4
Evaluate.
34.
3
216
35.
5 7
36.
2 2
3
8
37.
3
 73 
4 
 
3
Express using rational exponents.
x 5y 6
38.
144 x 6 y10
39.
40.
1024 a 3
Express using radicals.
41.
64
1
3
1
2
3
2
5
2
42.
2 a b
44.
x 7 x 5x 7 x 5
Simplify.
 x  2  3   x 3  2
43.
Use a calculator to evaluate each expression to the nearest ten thousandth.
44. e 2.3
45. e4.6
46. e 2
47. 3 e 3
Given the original principal; the annual interest rate, and the amount of time for each investment,
and the type of compounded interest, find the amount at the end of the investment.
48.
P = $1250,
r = 8.5%,
t = 3 years,
quarterly
49.
P = $2575,
r = 6.25%,
t = 5 years, 3 months, continuously
Use a calculator to find the common logarithm of each number to the nearest ten thousandth.
50.
726.5
51.
.6351
52. .0026
53.
Use a calculator to find the antilogarithm of each number to the nearest hundredth.
16,256
54.
.6259
55.
2.7356
56.
-0.0251
Evaluate each expression by using logarithms. Check your work with a calculator.
57.
261 x 32 x .32
60.
3
58.
181.72 x 7.01
4.62
61.
(2.69)(420)
2.43 x (8.9)4
59.
16.21 
4
4.29
Write each equation in logarithmic form.
62.
25 = 32
1
216
63.
6-3 =
65.
log4 16 = 2
Write each equation in exponential form.
64.
log3 27 = 3
Evaluate each expression.
66.
log 7 73
67.
log .0001
Solve each equation.
68.
log x 64 = 3
69.
log 4 0.25 = x
70.
71. Find the 45th term in the sequence -17, -11, -5...
72. Find the sum of the first 13 terms in the series: -5 + 1 + 7 +........
73. Find the ninth term of the geometric sequence
74. Find the sum of the first eight terms of the series:
3 ,  3, 3 3 
3 9 27
,
,

4 20 100
log 4 ( 2x – 1 ) =x