Download Math Analysis Second Quarter Review

Math Analysis First Quarter Review
Name: _________________________
Period: ___________
Identifying Properties: Identify the property and operation shown.
1. (2 + x) + (3 + y) = (3 + y) + (2 + x)
Rationalize the Denominator.
3.
3
4
2x
4
4.
5 3
Simplify Expressions:

3 5
 10a b
5. 
2 1

 20a 3 b 6
6.
3





2
81x 11 y 15
7. 2x (x2 + 3x – 4) – (3x2 + 5x – 2)
2. (a + b) + c = a + (b + c)
2
6

8. x  7 x  5
2 x  13
x 2  12 x  35
Evaluate the functions:
9. (f – g)(5) using f(x) = -6x + 4 and g(x) = 2x - 1
10. Factor f(x) = x3 + 3x2 – 4x – 12
11. (f  g)(9) using f(x) = 3 – 2x and g(x) =
12. Simplify the expression:
12( x  y) 2
9( x  y)
x
13. Simplify (5x2z6)3(5x2z6)-3
14. Simplify:
15 x 2  24 x
3x 2
15. Factor: x2 – 144
1
3
x
16. Simplify:
2x
x 1
17. Multiply: (2 – i)(3 + 2i)
18. Solve: (2 + 3i) – (-4 + 7i)
19. Solve the following by completing the square: 4x2 + x + 3 = 0
20. Write the complex number in standard form:
3  2i
2  4i
21. Write the Complex Number in Standard Form: 6 +
 25
Find the Domain:
x 8
1 x
2
x  3 x  18
23. f(x) = x  12
24. f(x) =
Inequality Notation:
Interval Notation:
Set Notation:
________________
______________
____________________
22. f(x) =
25. f(x) =
2x  3
26. f(x) =
7 x
7x
27. f(x) =
2
6x
x 1
2
Inequality Notation:
Interval Notation:
Set Notation:
________________
______________
____________________
28. Find the solution and graph the following:
a) 1 –
3
x  x4
2
c)  1 
3 x
1
2
b) - 8 < 1 – 3(x – 2) < 13
1 3 x 5



d)
4
2
6
29. Solve the inequality and sketch the solution:
a) 10 1  2 x  5
30. Perform addition or subtraction and simplify:
3
5

a)
x2 2 x
b) 3 +
x  14
 17
2
b)
1
x
 2
x  x  2 x  5x  6
2
31. Perform the multiplication or division and simplify:
a)
3( x  y ) x  y

4
2
b)
4 y  16 4  y

5 y  15 2 y  6
32. Find the solutions to the equation algebraically. Check for extraneous solutions.
a)
x  1  3x  1
b) (x – 3)2 =
16
25
c)
x  1  ( x  7)
d)
9 x  20  x