Pre Calc - Algebra Review
Simplify.
1)
4)
! 8)
!
!
-102
2)
x 3 " 9x
5)
2
x " 7x + 12
9" x
"2
3 + x "1
!
9)
102
3)
x 2 " 2x " 8
3
2
x + x " 2x
1
3x "
x
x+5
!
6)
! 10)
Solve the following!equations:
(
)
8 * 3 + 4[2 * 21 " 4 6 ÷ 3 + 6]
448 " 8[5 + 4(1 + 3 * 2)]
2
4
7)
3+ 2
1 1
"
x 5
1
1
"
x 2 25
1" 5
1
8x + 12 + 5(2x + 3)
! 11)
2
(2x + 3)3
!
!
13)
8
7 5
x + = x "2
3
6 4
15)
5x " 9 = 6
12)
2 ( 4x + 5 ) – ( 7x – 6 ) = 11 – 3 ( 8 – 9x )
14)
1.5 ( 8.4x – 5 ) – 0.6 ( 2x – 12 ) = 14.1
16)
4 ( 3x – 2 ) – 2x = 5 ( 2x + 4 ) – 12
! 17)
2x + 1 = x + 3
18)
3x " 5 2x + 7
=
4
6
! 19)
x y z
+ + = 1, for a
a b c
20)
V = 2 ( ab + bc + ca ) , for a
22)
A = P + nrP, for P
23)
2x – 2yd = y + xd, for d
25)
4x2 + 12x + 3 = 0
26)
2x + 1 =
!
!
!
21)
5
x+2
Y=cekt, for k
!
!
24)
2x 1 # x
+
= 0 , for x
4"
2
27)
x +1
x
"
=0
x
x +1
3
Solve the following inequalities – write solutions in set and interval notation :)
29)
4
3
20y "15 # 8y "12
5
2
31)
4x – 5 ( 2x + 6 ) ≤ 18 – 6x
(
)
(
)
28)
7x – 15 – 3x < 14 – 6x + 11
30)
4y " 3
> 6" y
"7
32)
x2 – 2x – 15 < 0
33)
2x2 + 3x – 5 ≥ 0
34)
x +1
>2
2x " 3
35)
x3 + 12x2 + 32x ≥ 0
36)
| 2x + 5 | < 4
37)
| 3x – 7 | ≥ 5
!
!
!
Solve by factoring.
38)
4x4 – 17x2 + 4 = 0
39)
6x3 + 14x2 – 12x = 0
40)
2x4 – 18x2 + 40 = 0
41)
x5 – 16x = 0
42)
8x3 + 27 = 0
43)
4x3 – 8x2 – 25x + 50 = 0
Solve each quadratic equation by using the quadratic formula.
44)
2x2 + 4x – 30 = 0
45)
2x2 – 4x – 1 = 0
46)
4x2 + 4x + 1 = 0
x2 + 3x – 5 = 0
49)
3x2 + x – 4 = 0
Solve by completing the square.
47)
x2 + 4x – 7 = 0
48)
Complete the square and reduce to one of the standard forms
y – b = A(x – a)2 or x – a = A(y – b)2.
50)
y = x2 + 4x + 3
51)
3x2 + 3x + 2y = 0
Find the equation of the circle.
52)
x2 – 2x + 4y2 + 16y + 6 = 0
Use synthetic division
53)
The equation 12x3 – 23x2 – 3x + 2 = 0 has a solution x = 2. Find all other
solutions.
54)
Solve for x, the equation 12x3 + 8x2 – x – 1 = 0.
(Hint: All solutions are rational and between ± 1)