A.1 Algebra Review
Precalculus Introduction
Aug 17­10:58 AM
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A.1 Algebra Review
Precalculus is the course that brings
together all of your previous
mathematical learning to prepare you
for calculus.
Calculus is the "bridge" to many careers
involving mathematics, science,
technology and computers.
Aug 17­11:01 AM
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A.1 Algebra Review
This Precalculus class consists of college
algebra, trigonometry and analytical
geometry.
Before we begin the study of college
algebra we are going to review
intermediate algebra and geometry.
Aug 17­10:58 AM
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A.1 Algebra Review
A.1 Algebra Review
Objectives:
• Evaluate Algebraic Expressions
• Determine the Domain of a Variable
• Graph Inequalities
• Find Distance on the Real Number Line
• Use the Laws of Exponents
• Evaluate Square Roots
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A.1 Algebra Review
Definitions:
Set: A collection of objects or numbers.
Elements: The objects or numbers of a set.
Notation: The symbols we use to write in a mathematical language.
Example: D = {x | x > 0}
Read as: The set of all x such that x is greater than zero.
Empty Set(Null Set): A set that contains no elements.
Denoted by: ∅
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A.1 Algebra Review
Skills Review:
Example 1: Evaluating Expressions
Evaluate if x = 3 & y = -1
3y
2 - 2x
Answer: 3
4
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A.1 Algebra Review
PHS
Skills Review:
Example 2: Finding the domain in expressions.
Hint: The domain is the values of x that make the expression true.
Find the domain:
A. 3x
D: x = All real numbers ( R )
B.
3
x
D: x ≠ 0
C.
3
x-1
D: x ≠ 1
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A.1 Algebra Review
Skills Review:
Example 3: Graphing inequalities on a number line
Describe a number line.
Graph the following inequalities:
Hint: The book uses ( ) for open circles and [ ] for closed circles.
A. -3 < x < 2
­5
­4
­3
­2
­1
0
1
2
3
4
5
­5
­4
­3
­2
­1
0
1
2
3
4
5
­5
­4
­3
­2
­1
0
1
2
3
4
5
B. -3 < x < 2
C. -3 < x < 2
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A.1 Algebra Review
Skills Review:
Example 4: Absolute Value - the distance from the origin
Find the absolute value:
A. |-3| =
B. |15| =
C. |-6 - 2| =
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A.1 Algebra Review
Skills Review:
Example 5: Exponents
Simplify
A.
x5y-2
x 3y
B.
-2
( )
x-3
3y-1
C.
[-4(-2)-2]0
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A.1 Algebra Review
Skills Review:
Example 6: Square Roots
Simplify
A.
49
B.
4
25
C.
( 5 )2
D.
(-2)2
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A.1 Algebra Review
Homework:
page 959 (12, 16, 19, 20, 23, 26, 33, 36,
45, 47, 57, 60, 65, 73, 77, 85, 87)
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