Download P.1 Algebraic Expressions, Mathematical Models, and Real Numbers

P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
Exponential Notation: If n is a counting number, then 𝑏 𝑛 = 𝑏 ∙ 𝑏 ∙ 𝑏 ∙ … ∙ 𝑏 with b appearing as a factor n
times.
Evaluation Expressions
-
Substitute a number in for each variable in the expression and solve using the order of
operations!
Parentheses
Exponents
Multiplication Division
Addition
Subtraction
Set: a collection of objects whose contents can be clearly determined.
Elements: the objects in a set
Roster Method: { } with commas to separate elements
Set-Builder Notation: elements are described but not listed
Ex. Set notation: {x| x is a counting number less than 6}
Roster Method: {1, 2, 3, 4, 5}
Intersection of Sets: a set containing all elements that are in both set A and set B
A∩B = {x| x is an element of A AND x is an element of B}
Empty or Null Set: A set with no elements
Union of Sets: a set containing in A or B or both
A ∪ B= {x| x is an element of A OR x is an element of B}
Real Number: a number that is either rational or irrational rather than imaginary.
Subsets of Real Numbers
Rational Numbers: All numbers that you can write as a quotient of integers (a/b); includes
terminating and repeating decimals!
Natural Numbers: Counting numbers (1, 2, 3…)
Whole Numbers: Natural numbers and 0 (0, 1, 2, 3…)
Integers: Natural numbers, their opposites and 0! (…-2, -1, 0, 1, 2…)
Rational Numbers: Fractions, repeating/terminating decimals ( ½ , 0.222, 1)
Irrational Numbers: Decimal representations that neither terminate nor repeat- cannot be
written as quotients or integers (π, √2)
Properties of Real Numbers (zero is the additive inverse for real numbers, and zero is the only real
number that has no multiplicative inverse)
Let a, b, and c represent real numbers
Property
Closure
Commutative
Associative
Identity
Inverse
Distributive
Addition
a + b is a real number
a+b=b+a
(a + b) +c = a + (b + c)
a + 0 =a, 0 +a = a
0 is the additive identity
a + (-a) = 0
a(b + c) = ab + bc
Absolute Value: the distance from zero on the number line
|x| = x if 0 ≤ x
|x| = -x if 0 > x
Multiplication
ab is a real number
ab = ba
(ab)c = a(bc)
a ∙ 1= a, 1∙ a = a
1 is the multiplicative identity
a ∙ (1/a) = 1