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ch 1 notes - Algebra Notes Chapter 1 Exploring Expressions...

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Algebra Notes Chapter 1 – Exploring Expressions, Equations, and Functions 1.1 Variables and Expressions Variables – Symbols that are used to represent unspecified numbers. Example: S M (m times s) Algebraic Expressions – An expression consisting of one or more numbers and variables along with one or more arithmetic operations. Example: 2 - x 3 + b a s t 2 k mn 3 7 ÷ Ways in which multiplication is shown in algebra… xy y x ) ( y x ) )( ( y x y x ) ( xxy This manner is usually avoided because the multiplication symbol appears like a the variable “x” Factors – In a multiplication expression, the quantities being multiplied are called factors. Product – The result of multiplication Power – An expression of the form x n is known as a power. Base – In the expression x n , the base is x Example : 6 3 Read as six cubed or six to the third power! (6 x 6 x 6 = 216) Exponent – In the expression x n , the exponent is n So… 6 3 Base Exponent
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Evaluate – To find the value of an expression when the values of the variables are known. Example: Evaluate 3 4 (3 x 3 x 3 x 3 = 81) Word Sign Example Sum + The sum of a and b ) ( b a + Difference - The difference of a and b Or, a decreased by b ) ( b a - Product x The product of 8 and x ) 8 ( x Quotient ÷ The quotient of x and 2 2 x -------------------------------------------------------------------------------------------------------------------- - 1.2 Patterns and Sequences Sequence – A set of numbers in a specific order. Example: 2, 4, 6, 8, 10,… Terms – A number in a sequence Example: 2, 4, 6, 8, 10,… Each number is a term! Look for a pattern – A problem solving strategy often involving the use of tables to organize information so that a pattern may be determined. (See example on pages 13 and 14… sides and diagonals) Inductive Reasoning – Using patterns to make an algebraic rule (See example #4 on page 14) Rule 3n + 2 Deductive Reasoning – Uses logic to make a rule.
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