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Chapter 1 Overall Review of Chapter 1
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1.1 Expressions and Formulas
Students Will Be Able To:• Use Order of Operations to Evaluate Expressions• Use Formulas
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Review: Order of Operations
The Order of Operations is a rule used to clarify which procedures should be performed first in a given mathematical expression.
Remember there are 4 Steps of Order of Operations.
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Order of Operations
• Grouping Symbols can be used to clarify the order of operations.
• When calculating the value of an expression start with the innermost set of grouping symbols.
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Ex 1a: Simplify an Expression
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Ex 1b: Simplify an Expression
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Try this! Order of Op!
Find the value of:
3
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Use Your Calculator!
1. Simplify :
2. Describe the Procedure the calculator used to get the answer.
3. Where should parenthesis be placed so that the expression has each of the following values?
a) -10
b) 29
c) -5
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Use Your Calculator Again!
1. Evaluate:
2. Describe the Procedure the calculator used to get the answer.
3. If you removed the parenthesis, would the solution remain the same? Why or Why not?
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Ex 2: Fraction Bar!
• A fraction bar can act as a grouping symbol.
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Try this! Fraction Bar!
• Simplify:
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Remember: Terminology
• Variable: A letter that represents a number or a set of numbers.
• Algebraic expression: one or more algebraic terms in a phrase that may include variables, constants, and operating symbols (+, -, x, and ÷). It does NOT have an equal sign.
• Algebraic Equation: Includes variables, operations, and an equal sign.
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Don’t Forget!
Expressions are simplified (or evaluated)
Equations are solved. You cannot solve something that doesn’t have an equal sign.
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Ex 3: Evaluate an Expression
• Evaluate the expression if s = 2 and t = -3
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You Try!.
Evaluate the expression for x=5, y=-2, and z=-1
-9
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1-2 Properties of Real Numbers
Objectives: students will be able 1) to classify real numbers and 2) use the properties of real numbers to
evaluate expressions
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What are Real Numbers?
• Real Numbers are all the numbers we use in everyday life.
• Every Real Number will correspond to exactly one point somewhere on a Number Line.
• Real Numbers can be Rational or Irrational
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Rational Numbers
• Includes all integers, as well as all terminating or repeating decimals• Examples of rational numbers:
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Special Rational Numbers
Rational numbers can be broken down to other sub-sets.
• Integers: {…-2, -1, 0, 1, 2, …}
• Whole numbers: {0, 1, 2, …}
• Natural numbers: {1, 2, 3, …}
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Irrational Numbers
• Irrational numbers: nonterminating, nonrepeating decimals• Examples of irrational numbers:
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The Real Number Diagram
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Example 1: Name The Sets!
Name the sets of numbers to which each number belongs.
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Properties of Real Numbers
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Example 2: Simplify each expression.
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1-3 Solving Equations
Objectives: students will be able to 1) translate verbal expressions into algebraic expressions and equations,
and vice versa and 2) solve equations using the properties of equality
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Write an Algebraic Expression
Write an algebraic expression to represent each verbal expression.
a) 7 less than a number
b) Three times the square of a number
c) The cube of a number increased by 4 times the same number
d) Twice the sum of a number and 5
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Writing Verbal Sentence
Example 2: Write a verbal sentence to represent each equation.
The difference of a number and 8 is -9.
A number divided by 6 is equal to the number squared.
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Ex 3: Solve each equation.
Solve each equation.
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Ex 4: Solving Formulas
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1-5 Solving Inequalities
Objective: students will be able to solve inequalities
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Solving Inequalities v. Solving Equations
What is the difference between solving an equation and solving an inequality?
• When multiplying or dividing BOTH sides of an inequality by a negative number, the inequality sign must be reversed.
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Remember Graphing Inequalities?
• When graphing inequalities on a number line:
• When an inequality is solved, if the variable is on the left the inequality symbol will tell you which way to shade.• For example, x < 5 will result in an open circle on 5 and then
will be shaded to the left (since the arrow is pointing left). This only works when the variable is on the left hand side.
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Different Notations
• There are two different types of notation you may be asked to use when writing your solution: set-builder notation or interval notation.
• Set-builder notation
This is read as “the set of all numbers x such that x is less than 5”
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Set Builder Notations
The Set Builder Notation for x < 5 is
This is read as “the set of all numbers x such that x is less than 5”
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Interval Notation
The left number indicates the left bound of the graph, while the right number indicates the right bound.
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Parenthesis In Interval Notation
• Parenthesis are used to indicate • 1) a graph is unbounded in a certain direction• 2) a graph cannot equal a number, meaning that the graph contains an open circle
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Brackets In Interval Notation
• Brackets are used to indicate closed circles.
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Let’s practice interval notation.• Write each solution using interval notation.
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Ex 1: Solve and Graph
Example 1: Solve and graph each inequality. Write solutions in Interval Notation.
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Try These…
• Solve and Write your Solution in Interval Notation