Download Intermediate Algebra with Applications

Intermediate Algebra with
Applications
Course Outcome Summary
Information
Course Number
10-804-118
Credits
Contact Hours
4
72
Development Date
02/23/2004
Types of Instruction
Type of Instruction
Contact Hours
Credits
Classroom Presentation
72
4
Totals
72
4
Competencies, Linked Exit Learning Outcomes, and
Performance Standards
1.
Apply properties of real number systems
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
1.a.
you identify the different sets of real numbers
1.b.
you use set notations
1.c.
you find intersections and unions of sets
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Intermediate Algebra with Applications
Outcome Summary
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Current Date: 08/19/05D:\582742619.doc
1.d.
you graph real numbers on the number line
1.e.
you compare real numbers
Learning objectives
What you will learn as you master the competency:
2.
a.
Identify natural numbers, whole number, integers
b.
c.
Identify rational and irrational real numbers
Use set notation to identify the different sets of real numbers.
d.
Find the intersection of sets
e.
Find the union of sets
f.
Graph real numbers on the number line
Evaluate expressions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
2.a.
you identify additive inverse, absolute values, and reciprocals
2.b.
you add, subtract, multiply, and divide real numbers
2.c.
you substitute values for variables
2.d.
you find powers and roots of real numbers
2.e.
you apply the order of operation
2.f.
you evaluate absolute value expressions
Learning objectives
What you will learn as you master the competency:
a.
Identify additive inverse of a number
b.
Identify the absolute values of a number
c.
Apply the rules of exponents to simplify an algebraic expression
d.
Apply the order of operation to evaluate an expression
e.
Evaluate absolute value expressions
f.
Identify the powers, roots and reciprocals of real numbers
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Intermediate Algebra with Applications
Outcome Summary
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g.
3.
Perform basic arithmetic operations on signed numbers.
Solve linear equations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
3.a.
you evaluate formulas
3.b.
you find equations and formulas for a specific variable
3.c.
3.d.
you write and solve equations from given information
you solve application problems using formulas and linear equations
Learning objectives
What you will learn as you master the competency:
4.
a.
b.
Solve linear equations
Check an apparent solution to a linear equation
c.
Write an algebraic expression to describe a given verbal statement
d.
Set up and solve application problems that lead to linear equations
e.
Evaluate equations and formulas with given values
Solve linear inequalities
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
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Intermediate Algebra with Applications
Outcome Summary
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Performance will be successful when:
4.a.
you solve simple and compound linear and compound linear inequalities
4.b.
you solve absolute value equations and inequalities
4.c.
you solve word problems involving equations, absolute value, and inequalities
4.d.
4.e.
you use internal notation and set builder notations
you graph inequalities
Learning objectives
What you will learn as you master the competency:
5.
a.
b.
Solve simple linear inequalities using addition property of inequalities
Solve simple linear inequalities using multiplication property of inequalities
c.
Solve absolute value equations
d.
Solve absolute value inequalities
e.
f.
Graph inequalities
Use set builder notation to describe a solution to an inequality
Use the Cartesian coordinate system
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
5.a.
5.b.
you find the distance between two points
you find the midpoint of two points
5.c.
you find the slope given two points or the equation of the line
Learning objectives
What you will learn as you master the competency:
a.
Determine the slope of a line given two points on the line
b.
Calculate the distance between two points using the distance formula
c.
Find the midpoint of two points on a line
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Intermediate Algebra with Applications
Outcome Summary
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6.
Demonstrate graphing skills on the Cartesian coordinate plane
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
6.a.
6.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
Performance will be successful when:
6.a.
6.b.
you plot ordered pairs, read coordinates, and identify x- and y- intercepts
you graph a line, given its slope and point on the line
6.c.
you graph linear function
6.d.
you graph linear equations
Learning objectives
What you will learn as you master the competency:
7.
a.
Graph ordered pairs of numbers
b.
Identify points in the coordinate plane
c.
d.
Find the "y" intercept of a line
Find the "x" intercept of a line
e.
Describe a line using points method for graphing a line
f.
Describe a line given a point on the line and slope of the line
Analyze linear equations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
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Intermediate Algebra with Applications
Outcome Summary
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Current Date: 08/19/05D:\582742619.doc
Performance will be successful when:
7.a.
7.b.
you use slope to determine if two lines are parallel, perpendicular, or neither
you find the equation of a line, given two points of the line
7.c.
you write the equation of a line in standard, slope-intercept, or pint-slope form
Learning objectives
What you will learn as you master the competency:
a.
Find the slope"m" of a line by solving for the form "y = mx - b"
8.
b.
Identify parallel and perpendicular lines using their slopes
c.
Write the equation for a line given two points on the line
d.
e.
Write the equation for vertical lines
Write the equation for horizontal lines
f.
Write the equation of a line in standard form
Apply properties of functions and relations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
8.a.
you distinguish the differences between relations and functions
8.b.
you find the domain and range of a relation or function
8.c.
you use function notation
8.d.
you solve applications involving functions
Learning objectives
What you will learn as you master the competency:
a.
Distinguish between relations and functions
b.
Identify types of relations and functions
c.
Find the domain and range of a function
d.
Use functional notation to manipulate, combine, and evaluate functions.
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Intermediate Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\582742619.doc
9.
Solve systems of equations and inequalities
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
9.a.
you solve systems of two linear equation by graphing, elimination, and substitution
methods
9.b.
you solve systems of three linear equations using elimination and /or substitution
methods
9.c.
you classify systems as consistent/inconsistent or dependent/ independent
9.d.
you graph absolute value inequalities
9.e.
9.f.
you solve application problems involving systems or equations
you solve applications of systems of equations
Learning objectives
What you will learn as you master the competency:
10.
a.
b.
Find an approximate graphical solution to a system of two equations
Solve a system of two equations and two unknowns by the addition-subtraction method
c.
Solve a system of equations by substitution.
d.
Solve a system of two equations having fractional coefficients, or having the unknown in
the denominator
e.
f.
Solve a system of three equations and three unknowns by addition subtraction or by
substitution.
Describe method for graping absolute value inequalities
g.
Identify systems of equation as consistent or inconsistent
h.
Identify systems of equation as dependent or independent
i.
Apply principles of systems of equations to practical problems
Apply properties of exponents
Linked Core Abilities
A.
Learn effectively
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Intermediate Algebra with Applications
Outcome Summary
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*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
10.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
10.b.
by active participation in class discussion and activities
Performance will be successful when:
10.a.
you apply product, quotient, negative, and zero exponent rules
10.b.
you apply the power rule for exponents
10.c.
you change numbers to scientific notation and vice versa
10.d.
you use scientific notation in calculations
Learning objectives
What you will learn as you master the competency:
11.
a.
Use the laws of exponents to simply and combine expression with rational exponents
b.
Use product rule for exponents
c.
Evaluate "a" raised to the zero power
d.
Use Quotient rule
e.
Evaluate "a" raised the nth power
f.
g.
Write number in scientific notation
Perform calculation using scientific notation
Perform basic operations with polynomials
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
11.a.
you identify the degree of a polynomial
11.b.
you add, subtract, multiply, and divide polynomials
11.c.
you solve application problems involving polynomials
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Intermediate Algebra with Applications
Outcome Summary
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Current Date: 08/19/05D:\582742619.doc
Learning objectives
What you will learn as you master the competency:
a.
Add, Subtract, multiply and divide polynomials
12.
b.
Identify numeric coefficients
c.
Identify degree of a polynomial
d.
e.
Use FOIL method to multiply binomial
Use Distributive Property to multiply polynomials
f.
Use special products formulas to multiply polynomials
Graph functions and relations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
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
Performance will be successful when:
12.a. you graph quadratic, radical, absolute value, and cubic functions
12.b.
you interpret rigid transformations of functions
12.c.
you recognize equations of circle in standard form
12.d.
you recognize circles in non-standard form
12.e.
you graph circles
Learning objectives
What you will learn as you master the competency:
a.
b.
Graph a function on the rectangular coordinate system
Identify transformations of functions
c.
Graph Quadratic functions
d.
Graph absolute value functions
e.
Graph cubic functions
f.
Graph a circle
g.
Identify equations of a circle in standard form
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Intermediate Algebra with Applications
Outcome Summary
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13.
Factor polynomials
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
13.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
13.b.
by active participation in class discussion and activities
Performance will be successful when:
13.a.
you calculate the greatest common factors
13.b.
13.c.
you factor trinomials
you factor by grouping and by substitution
13.d.
you factor the difference of two squares, two cubes, and the sum of two cubes
Learning objectives
What you will learn as you master the competency:
a.
Factor expressions by removing common factors
14.
b.
Factor binomials that are the difference of the two squares
c.
Factor the sum or difference of two cubes
d.
e.
Factor trinomials
Factor the perfect square trinomial
f.
Factor expressions by grouping
g.
Use factoring techniques in applications
Solve equations using factoring
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
14.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
14.b.
by active participation in class discussion and activities
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Intermediate Algebra with Applications
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Performance will be successful when:
14.a.
14.b.
you use the zero factor property
you solve quadratic and cubic equations using factoring
Learning objectives
What you will learn as you master the competency:
15.
a.
b.
Use the zero factor property to solve quadratic equations
Solve quadratic equations by factoring
c.
Solve cubic equations by factoring.
Evaluate rational expressions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
15.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
15.b.
by active participation in class discussion and activities
Performance will be successful when:
15.a. you identify and simplify rational expressions
15.b.
you find domain of rational expressions
15.c.
you add, subtract, multiply, and divide rational expressions
15.d.
you simplify complex fractions
Learning objectives
What you will learn as you master the competency:
a.
Rewrite rational expression involving negative exponents
b.
c.
Find the domain of a rational expression
Simplify rational expressions
d.
Multiply rational expressions
e.
Add rational expressions
f.
Subtract rational expressions
g.
Divide polynomial by a monomial
h.
Divide polynomial by a polynomial
i.
Divide using synthetic division
j.
Divide Complex Fractions
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Intermediate Algebra with Applications
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16.
Solve equations involving rational expressions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
16.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
16.b.
by active participation in class discussion and activities
Performance will be successful when:
16.a. you solve application equations using proportions
16.b.
you solve application equations by clearing the equation of factors
16.c.
you check solution for extraneous roots
Learning objectives
What you will learn as you master the competency:
17.
a.
Solve rational equations with constant denominators
b.
Solve rational equations with variable denominators
c.
d.
Check solution to rational equations for reasonableness
Solve practical problems using rational equations
Evaluate radical expressions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
17.a.
17.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
Performance will be successful when:
17.a.
you convert radical notations to exponential expressions and vice-versa
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Intermediate Algebra with Applications
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17.b.
you simplify radicals
17.c.
17.d.
you apply rules of exponents with positive and negative rational exponents
you add, subtract, multiply, and divide radicals
Learning objectives
What you will learn as you master the competency:
18.
a.
b.
Find the nth root of a number
Simplify a radical expression
c.
Convert exponential expression to radial expressions
d.
Convert radial expression to exponential expressions
e.
f.
Add radical
Subtract radical
g.
Multiply radicals
h.
Divide radicals
i.
j.
Simplify rational expression using the rules of exponents
Find the conjugate of a rational expression
Solve radical equations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
18.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
18.b.
by active participation in class discussion and activities
Performance will be successful when:
18.a.
18.b.
you simplify radicals with numerical values
you simplify radical with algebraic terms
18.c.
you interpret a graph of a radical equation
Learning objectives
What you will learn as you master the competency:
a.
Simplify radical expression using the properties of radical
b.
Simplify radial expression using rationalization techniques
c.
Evaluate graph of a radical equation
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Intermediate Algebra with Applications
Outcome Summary
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Current Date: 08/19/05D:\582742619.doc
19.
Operate within the complex number system
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
19.a.
19.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
Performance will be successful when:
19.a.
19.b.
you identify complex numbers
you simplify radicals that include complex numbers
19.c.
you add, subtract, multiply, and divide complex numbers
Learning objectives
What you will learn as you master the competency:
a.
Simplify radicals having negative radicands
20.
b.
Calculate the sums, differences of complex numbers
c.
Calculate the product of complex numbers
d.
e.
Calculate the quotient of complex numbers
Simplify complex numbers
Solve quadratic equations
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
20.a.
20.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
Performance will be successful when:
20.a.
you use square root principle and quadratic formula
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Intermediate Algebra with Applications
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20.b.
you use the Pythagorean Theorem to solve problems involving right triangles
20.c.
you solve application problems involving quadratic equations
Learning objectives
What you will learn as you master the competency:
21.
a.
Apply the quadratic formula to solutions of quadratic equations
b.
c.
Solve quadratic equations by completing the square
Apply the Pythagorean Theorem to solve problems involving right triangles
d.
Solve practical problem involving quadratic equations.
Use Algebra functions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
Competence will be demonstrated:
21.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
21.b.
by active participation in class discussion and activities
Performance will be successful when:
21.a. you add, subtract, multiply, and divide functions
21.b.
you find composites of functions
21.c.
you identify one-to-one functions
21.d.
you find and graph inverse functions
Learning objectives
What you will learn as you master the competency:
22.
a.
Form the composite of two functions
b.
Find the domain of a composite function
Apply properties of exponential and logarithmic functions
Linked Core Abilities
A.
Learn effectively
*
Think critically and creatively
Performance Standards
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Intermediate Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\582742619.doc
Competence will be demonstrated:
22.a.
by completing assignments, quizzes, lab work, and tests with a satisfactory score as
detailed in the grading scale
22.b.
by active participation in class discussion and activities
Performance will be successful when:
22.a.
you identify, graph and evaluate exponential functions
22.b.
you rewrite exponential equations as logarithmic and vice-versa
22.c.
you use properties of logarithmic equations
22.d.
you solve exponential and logarithmic equations
22.e.
you solve applied problems involving exponential and logarithmic equations
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Intermediate Algebra with Applications
Outcome Summary
Development Date: 02/23/2004
Current Date: 08/19/05D:\582742619.doc