Study Guide Chapter 1
Quest  Friday, 9/16
**REVIEW CLASS NOTES FROM 9/6 and 9/15**
Variable:
letters or symbols used to represent unspecified numbers
Algebraic Expression:
one or more numbers and variables, along with one or more
arithmetic operation
Numerical Expression:
only include constants (opposite of a variable)
Sequence:
a numerical pattern
Term:
each number or item in a sequence
Order of Operations: PEMDAS
1. Parenthesis
Start with the inner most set of parenthesis and work out
2. Exponents
3. Multiply
Divide
GROUPED; Work from left to right
4. Addition
Subtraction
GROUPED; Work from left to right
**Multiplication/Division are grouped together and done as they appear from left to right.
Addition/Subtraction are also grouped and done after M/D
10 + 12 + 4 * 3
10 + 12 + 12
=34
**Start with the inner most set of parenthesis and work out
( 8 * 2 + (12 – 7 ) ) -1
( 8 * 2 + 5) -1
(16 + 5) -1
21 – 1
= 20
Vinculum
 Formal name for the dividing bar or fraction bar
 treat as a parenthesis during PEMDAS
 the vinculum tells you to divide when the numerator & denominator have been
simplified
SEE BACK
Open Sentences
Equation:
sentence with an equal sign
Open Sentence:
an equation with 1 or more variables
Solving an Open Sentence: the process of finding a replacement for the variable that results
in a true sentence
Solution:
the replacement(s) that creates the true sentence
Example:
Find the solution set for x if the replacement set is {2,3,4,5,6}
4x + 3 = 15
4(2) + 3 = 15
8 + 3 = 15
11 = 15
4 x + 3 = 15
4 (3) + 3 = 15
12 + 3 = 15
15 = 15
To find solution we substitute values
from the replacement set into the
equation to see if it’s true
x = 2 is not a solution / not true
x = 3 true
Shown as {3}
A solution set can contain no items, one item, or multiple items from the replacement set.
Set:
a collection of objects or numbers
Elements:
each number or object in a set
Replacement Set:
the set of all replacement values
Solution Set:
the set of all replacements which make the equation true
Example:
X=7*7+2
10 + 7
X = 49 + 2
10 + 7
X = 51
17
X=3
Writing expressions using exponents:
Example:
Write 5*5*5*n*n*n*n*n
Solution:
Writing Algebraic Expressions:
Example:
Write an Algebraic Statement for the following:
Three less than twice a number
Solution: 2x - 3