Download Algebraic Properties

ALGEBRA/GEOMETRY REVIEW
Algebraic Properties
Commutative
Associative
Distributive
Addition
Multiplication
a+b=b+a
(a)(b) = (b)(a)
(a + b) + c = a + (b + c)
(ab)c = a(bc)
a(b + c) = ab + ac
Problems:
a) 2(x + 2) = 3x + 4
b) -5(x + 2) = 3x + 4
c) 2x + 9 = 15
d) -1 + (2/3)x = x
Powers of Ten:
100 = 1
101 = 10
102 = 100
103 = 1000
104 = 10000
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
10-4 = 0.0001
Combining:
(1 x 10a)(1 x 10b) = 1 x 10(a + b)
1x10 a
 1x10 ab
b
1x10
1
b

1
x
10
this means
1x10b
ALGEBRA/GEOMETRY REVIEW
Problems:
a) (1 x 104)(1 x 106) =
b) (1 x 103)(1 x 102) =
c) (1 x 105)(1 x 10-2) =
1x10 7

d)
1x103
1x10 7

e)
1x103
1x106

f)
8
1x10
Also note that (1
x 10a)b = 1 x 10(ab)
(example: (1 x 103)2 = 1 x 106 )
Try these problems
g) (1 x 105)2 =
h) (1 x 103)4 =
i) (1 x 10-2)2 =
j) (1 x 102)-2 =
ALGEBRA/GEOMETRY REVIEW
Geometry/Trigonometry:
Circle: (let r = radius)
circumference = 2r
area = r2
3600 in one circle
3600 = 2 radians
or
 = 180 degrees
Problems:
a) Given a circle of radius = 3.2 feet
a. find the circumference ________________
b. find the area _______________
b) If we rotate 1800 of a circle, what fraction of the area has been covered?
_____
c) If we rotate 900 of a circle, what fraction of the area has been covered?
_____
ALGEBRA/GEOMETRY REVIEW
Triangles:
A “right” triangle has ONE 900 angle.
hypotenuse
opposing
side
90

The “sine” of angle (theta) is the ratio
of the length of the opposing side to the
length of the hypotenuse.
sin  
The cosine of angle q is the ratio of the
adjacent side length to the hypotenuse length
adjacent side
cos 
hypotenuse
opposing side
hypotenuse
hypotenuse
90

adjacent side
Example:
Find the length of the opposing side (?):
?
10 feet

opposite
hypotenuse
opposite
0.6157 
10 ft
(0.6157)(10 ft )  opposite
opposite  6.157 ft
sin  
ALGEBRA/GEOMETRY REVIEW
Problems: find x (make sure your calculator is in the “degrees” mode)
a)
?
20 feet

b)
20 feet

?
c)
?
15 feet

d)
15 feet

?