Download Algebra Worksheet

Algebra Worksheet
September 15, 2012
Name:
Section No:
1. Numbers and Their Disguises
1) Simplify the expression:
1
1
1
+ 1
3 4
2
3
2) Simplify the expression:
(x2 y
(y 3 x
3 )2
2) 2
3) Simplify:
3
(4x6 ) 2
4) Simplify:
(81x2
4y 2 )
1
2
5) Compute the following expression in scientific notation, rounded to
three digits:
a) (1.35 ⇥ 103 ) ⇥ (4.452 ⇥ 107 )
b)
5.24 ⇥ 105
1.02 ⇥ 106
6) Represent the following sets of numbers using interval and number
line notation:
a) 1  x < 15
b)
2x2
c)
5<x
3
7) Simplify if possible:
a) ( 1, 5) \ [3, 1)
b) ( 1, 2) \ [ 2, 1)
c) [3, 5] \ (10, 1)
1
2. Completing the Square
1) Complete the square for the following expressions:
a) f (x) = x2
8x + 12
b) g(s) = s2 + 3s
6
2) Find the center and radius of the circles represented by the following
equations:
a) x2 + y 2
4x
2y = 11
b) 2x2 + 2y 2 + 4x + 8y
20 = 0
3. Solving Equations
1) Solve for x:
2y 2 x
y2
(1 + 3y) = x
2) One thousand dollars was invested, partly at 6% annual simple interest and partly at 4%. The total interest earned in the first year
was $52. How much was invested at 6%?
3) Find the solutions, both real and complex:
x2
+ 2x
3
1=0
4) Find the solutions, both real and complex:
x2 + 2x = 4
5) Find the real solutions to:
1
x
4
+
1
4
= 2
x+4
x
16
6) Find all real solutions to:
3
x
3
=2
x+2
4. Logarithmic Functions
1) Evaluate:
log 1 64 =
4
2) Solve for x:
42x
3
= 16
3) Solve for x:
log2 x + log2 (x
2) = 3
4) Solve for x:
ex
2 +2x
3
=1
5) Solve for x:
ln t
ln t2 = 5
5. Inverse Trigonometric Functions
Evaluate the following:
1) sin
1
2) cos
1
(
1
)=
2
( 1) =
3) sin(sin
1
(0.1)) =
4⇡
)) =
3
3⇡
5) tan 1 (tan( )) =
4
4) sin
1
(sin(
6. Changing the Form of a Function
1) Factor:
6x2 y + 3xy + 9xy 2
2) Factor:
x2
2x
24
3) Factor:
x3
x
4) Rationalize and Simplify:
3
p
x
7
5) Extract as much as you can from the square root:
p
4x2 + 8x2
7. Simplifying Algebraic Expressions
Let f (x) = x2 + 3x.
1) Compute:
f (x + h)
2) Simplify:
f (x + h)
h
f (x)
3) Simplify:
1
1
1
x
1
(x+h)2
1
x2
x
4) Simplify:
h
5) Simplify:
x+
1
x+
1
x+ x1
8. Trigonometric Functions
(1) Evaluate
(a)
sin
⇣ 7⇡ ⌘
cos
⇣ 5⇡ ⌘
(b)
(c)
cos
(d)
2
2
⇣ 9⇡ ⌘
2
⇣
⌘
⇣⇡
+ 2k⇡
sin 101⇡
(2) Assuming k is a whole number, evaluate the following.
(a)
sin
(b)
cos
2
⇣ e⇡
2
⌘
+ 2k⇡
⌘
9. Exponential Functions
(1) Simplify
(a)
e(x)3
(b)
e2x
ex
(c)
e2x
ex
(d)
p
3
1
1
e2x
10. Miscellaneous
(1) Find the inverse of the following functions if they exists.
(a)
1 + 2x
f (x) =
3x 5
(b)
ex
f (x) =
1 + 2ex
(2) Simplify
(a)
⇣
⌘
sin tan 1 (3x)
(b)
sin
1
⇣
cos(2x)
⌘