Download Elementary Algebra with Applications

Elementary Algebra with
Applications
Course Outcome Summary
Information
Course Number
10-804-110
Credits
Contact Hours
3
54
Development Date
02/23/2004
Types of Instruction
Type of Instruction
Contact Hours
Credits
Classroom Presentation
54
3
Totals
54
3
Competencies, Linked Exit Learning Outcomes, and
Performance Standards
1.
Perform basic operations with real numbers
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
1.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
1.b.
by active participation in class discussion and activities
Your performance will be successful when:
1.a.
you add, subtract, multiply, and divide real numbers
1.b.
you evaluate numerical expressions using exponents
1.c.
you evaluate expressions containing parenthesis
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
1.d.
you evaluate expressions using the order of operations
1.e.
you evaluate algebraic expressions
Learning objectives
What you will learn as you master the competency:
2.
a.
Combine positive and negative numbers
b.
c.
Divide positive and negative numbers
Apply the laws of exponents to simplifying expressions with exponents.
d.
Apply the order of operations to arithmetic operations
e.
Simplify expression by removing grouping symbols
f.
Evaluate equations and formulas with given variables.
Solve linear equations
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
2.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
2.b.
by active participation in class discussion and activities
Your performance will be successful when:
2.a.
you identify like terms
2.b.
you solve one step linear equations
2.c.
you solve linear equations with the variable on one side of the equation
2.d.
you solve linear equations with the variable on both sides of the equation
2.e.
you solve factional equations
2.f.
you rearrange formulas
Learning objectives
What you will learn as you master the competency:
a.
Identify a term
b.
Identify a numeric coefficient
c.
Identify a variable
d.
Combine like terms
e.
Solve simple linear equations by addition or subtraction
f.
Solve simple linear equations by multiplication or division
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
3.
g.
Solve simple linear equations by multiple steps of addition, subtraction, multiplications
and division
h.
Solve fractional equations
i.
Solve literal equations for a selected variable.
Use formulas to solve problems
Linked Core Abilities
*
*
Learn effectively
Think critically and creatively
Performance Standards
You will demonstrate your competence:
3.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
3.b.
by active participation in class discussion and activities
Your performance will be successful when:
3.a.
you solve proportions
3.b.
you solve application problems using proportions
3.c.
you solve equations for a specified variable
3.d.
you find the value of a variable in a given formula
Learning objectives
What you will learn as you master the competency:
4.
a.
b.
Set up simple ratios
Set up direct proportions
c.
Solve direct proportions by cross multiplication
d.
Solve practical problems using direct proportion
e.
f.
Solve equations for specified variable
Substitute given values into equations and formulas
g.
Solve equations with given values
Use the rules of exponents
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
Performance Standards
You will demonstrate your competence:
4.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
4.b.
by active participation in class discussion and activities
Your performance will be successful when:
4.a.
you simplify expressions using positive exponents
4.b.
you simplify expressions using negative exponents
4.c.
you use exponents to express a number in a scientific notation
4.d.
you change a number from scientific notation to decimal notation
Learning objectives
What you will learn as you master the competency:
a.
Apply the rules of exponents to simplifying expressions with positive exponents
5.
b.
Apply the rules of exponents to simplifying expressions with negative exponents
c.
Write real numbers in scientific notation
d.
Convert between scientific notation and decimal notation
Perform operations with polynomials
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
5.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
5.b.
by active participation in class discussion and activities
Your performance will be successful when:
5.a.
you perform addition of polynomials
5.b.
you perform subtraction of polynomials
5.c.
you perform multiplication of polynomials
5.d.
you perform division of polynomials
Learning objectives
What you will learn as you master the competency:
a.
Combine like terms
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
6.
b.
Multiply monomial by a monomial
c.
d.
Multiply monomial by a polynomial
Multiply polynomial by a polynomial
e.
Use FOIL method to multiply polynomials
f.
Use special products formulas to multiply polynomials
g.
h.
Divide monomial by a monomial
Divide monomial by a polynomial
i.
Divide polynomial by a polynomial
Apply factoring methods
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
6.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
6.b.
by active participation in class discussion and activities
Your performance will be successful when:
6.a.
you find the greatest common factor
6.b.
you factor binomials
6.c.
you factor trinomials
6.d.
you factor polynomials with four terms
6.e.
you factor polynomials completely
Learning objectives
What you will learn as you master the competency:
a.
b.
Find the greatest common factor for a real number
Find the greatest common factor for a monomial
c.
Factor expressions by removing common factors
d.
Factor binomial that are the difference of the two squares
e.
Factor the sum and difference of two squares
f.
Factor prefect square trinomial
g.
Factor by grouping
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
7.
Perform basic operations with rational expressions
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
7.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
7.b.
by active participation in class discussion and activities
Your performance will be successful when:
7.a.
you reduce rational expressions to lowest terms
7.b.
7.c.
you multiply rational expressions
you divide rational expressions
7.d.
you add rational expressions
7.e.
you subtract rational expressions
7.f.
you simplify complex fractions
Learning objectives
What you will learn as you master the competency:
8.
a.
Reduce rational expression to lowest terms
b.
c.
Multiply rational expressions
Divide rational expressions
d.
Find common denominators of rational expressions
e.
Add and subtract rational expressions
f.
Simplify complex fractions
Solve rational equations
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
8.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
8.b.
by active participation in class discussion and activities
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
Your performance will be successful when:
8.a.
you solve rational equations using proportions
8.b.
you solve rational equations by clearing the equation of fractions
8.c.
you determine if roots are extraneous roots
Learning objectives
What you will learn as you master the competency:
9.
a.
Use fractional notation to express ratios
b.
Apply cross product rule to solve proportions
c.
d.
Identify lowest common denominator of an equation
Apply to distributive property to simplifying rational equations
e.
Test solution to find extraneous roots
Graph algebraic equations
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
9.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
9.b.
by active participation in class discussion and activities
Your performance will be successful when:
9.a.
you plot ordered pairs on the X-Y axes
9.b.
you graph lines on the X-Y axes
9.c.
you find a slope of a line given two points
9.d.
9.e.
you determine the slope and the Y-intercept given the equation of the line
you graph the solution to quadratic equations
9.f.
you determine equations of lines
Learning objectives
What you will learn as you master the competency:
a.
Define the rectangular coordinate system
b.
Determine if an ordered pair is a solution to an equation of two variables
c.
Identify linear equations
d.
Describe methods of finding and plotting ordered pair solutions for graphing a line.
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
10.
e.
Apply two point slope formula to finding the slope of a line
f.
g.
Write linear equations in slope intercept form
Identify the slope of an equation in the the slope intercept form
h.
Identify the y intercept of an equation in the slope intercept form
i.
Find the equation of a line given the slope and y intercept
j.
k.
Find the equation of a line given a point on the line and the slope
Plot quadratic eeuqatiosn by finding and plotting order pair solutions
Solve systems of equations
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
10.a.
10.b.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
by active participation in class discussion and activities
Your performance will be successful when:
10.a.
10.b.
you determine the solution to a system by graphing
you determine the solution to a system using the addition-subtraction method
10.c.
you determine the solution using the substitution method
Learning objectives
What you will learn as you master the competency:
11.
a.
Review methods of graphing linear eqyations
b.
Identify the point of intersection of graphs of a linear system.
c.
Use substitution method to solve a system of linear equations
d.
e.
Use the addition method to solve a system of linear equations
Use the subtraction method to solve a system of linear equations
Perform basic operations with roots and radicals
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
Performance Standards
You will demonstrate your competence:
11.a. by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
11.b.
by active participation in class discussion and activities
Your performance will be successful when:
11.a.
you simplify radicals using numerical values
11.b.
you simplify radicals using algebraic terms
11.c.
you use pythagorean theorem to solve problems
11.d.
you simplify distance formula
Learning objectives
What you will learn as you master the competency:
a.
Find the roots of perfect squares
12.
b.
Simplify square roots containing variables
c.
Find higher order roots of real numbers
d.
Use the product rule to simplify square roots
e.
Use the quotient rule to simplify square roots
f.
Simplify radicals containing variables
g.
h.
Simplify hight order roots
Solve problem in the form of the Pythagorean equations
i.
Find the distance between two points using the distance formula
Solve quadratic equations
Linked Core Abilities
*
Learn effectively
*
Think critically and creatively
Performance Standards
You will demonstrate your competence:
12.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
12.b.
by active participation in class discussion and activities
Your performance will be successful when:
12.a.
you solve quadratics by factoring
12.b.
you solve quadratics by completing the square
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc
12.c.
you solve quadratics by using the quadratic formula
12.d.
you identify the number of roots for any quadratic equation by using the discriminant
Learning objectives
What you will learn as you master the competency:
a.
Use square root property to solve quadratic equations
b.
c.
Use factoring techniques to solve quadratic equations
Use completing the square to solve quadratic equations
d.
Use the quadratic formula to solve quadratic equations
e.
Use the discriminant to find the number of solutions to a quadratic equation
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Elementary Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\840993399.doc