Download Math Fundamentals NOTES

ACT Prep: Math Fundamentals (Chapter 10)
NUMBERS
Real
Imaginary
2
3
i
-2
a  bi (complex)
0
-7
3 5
8
47

2.8
5
2
Factors: integers that ______________ together to make a given product
-For example, the factors of 10 are 1, 2, ____, and _____
-A number’s factors are always ______________ than or the same as that number.
-Greatest common factor (your TI calculator will do this for you!)
Multiple: the product of an a given number and another _____________
-For example, the first four positive multiples of 5 are 5, 10, 15, 20.
-A number’s multiples are always ______________ than or the same as that number.
-Least common multiple (your TI calculator will do this for you!)
Prime: any number with only ____ distinct factors: 1 and itself
-For example, 2, 3, 5, 7, and 11 are prime numbers
Composite: a positive number that has _______ than 2 factors
*Note: the number _____ is neither prime nor composite!
*Know your rules for 0: 0 is even; 0 is neither positive nor negative; 0 raised to any power is 0.
Prime factorization: reduction of a number to its prime factors…factor trees are helpful!
24
ACT Prep: Math Fundamentals (Chapter 10)
Properties of Exponents
Property Name:
Property Rule:
Multiplication Property
a m  a n  a ( m n )
x3  x5 
Nested Power Property
(a m ) n  a mn
( y 2 )4 
Power of a Product
Property
(ab) m  a m b m
(xy) 6 
Division Property
am
 a (mn)
n
a
a n 
Negative Exponent
Property
Example:
z9

z7
1
an
x 8 
and
1

y 3
1
 an
n
a
Zero Exponent Property
a0  1

12
3.2 x

*Use your calculator well and wisely! A calculator is particularly helpful with:
- imaginary numbers.
- radicals (roots).
- converting decimals or other expressions into fractions.
- multiplying and dividing large numbers.
0
