Genesee Course Catalog

Official Course Information

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Mathematics Courses:

MAT102 - Algebra 2
Credits: 3 Catalog Description: Topics include solving first degree inequalities, introduction to functions, linear equations in two variables and graphing, solving systems of two or three linear equations and inequalities, brief review of polynomial operations and factoring, algebraic fractions, variation, solving rational equations and proportions, rational exponents and radical expressions, complex numbers, solving radical equations, and four methods for solving quadratic equations, with emphasis on problem solving and applications throughout the course. Not open for credit to students who have credit in MAT 136 or higher. Three class hours. Prerequisite: MAT 092 or equivalent by placement. Lecture: 3 hrs. Student Performance Outcomes: The student will be able to demonstrate each of the following skills in writing on one or more tests without referring to notes, textbook, or other resources. 1. Correctly translate and solve first-degree equations and inequalities. (Minimum of 5 times) 2. Given a relation, identify if it is a function. If so, find its domain and range, and then correctly evaluate the function given a value in its domain. (Minimum of 2 times) 3. Given a linear equation, correctly graph it on a rectangular coordinate system. (Minimum of 2 times) 4. Find the equation of a line given one of the following: (Minimum of 5 times) A point on the line and the slope of the line Two points on the line A point on the line and the equation of a line parallel or perpendicular to it 5. Given a system of linear equations, correctly solve the system by graphing, substitution or the addition method. (Minimum of 4 times) 6. Given a system of inequalities, solve the system by the graphing method. (Minimum of 2 times) 7. Given two or more polynomials, correctly add, subtract, multiply or divide the expressions. (Minimum of 6 times) 8. Given two or more rational expressions, correctly add, subtract, multiply or divide the expressions. (Minimum of 6 times) 9. Given an equation involving rational expressions, correctly solve the equation. (Minimum of 2 times) 10. Given two or more radical expressions, add, subtract, multiply and divide the expressions and write the answer in simplest form. (Minimum of 6 times) 11. Given two complex numbers, add, subtract, multiply or divide the numbers and write the answer in the form a + bi. (Minimum of 6 times) 12. Given a quadratic equation, solve it by factoring, taking square roots, completing the square or using the quadratic formula. (Minimum of 6 times) This course objective has been identified as a student learning outcome that must be formally assessed as part of the College's Comprehensive Assessment Plan. All faculty teaching this course must collect the required data (see Assessing Student Learning Outcomes form) and submit the required analysis and documentation at the conclusion of the semester to the Office of Assessment and Special Projects. Content Outline: 1. REVIEW OF REAL NUMBERS (optional) 2. FIRST-DEGREE EQUATIONS AND INEQUALITIES 2.1 Solving First-degree Equations A. Solve equations using the addition or multiplication property of equations B. Solve equations using both the addition and multiplication properties C. Solve equations containing parentheses D. Solve literal equations for one of the variables 2.2 Applications: Puzzle Problems A. Solve integer problems B. Solve coin and stamp problems 2.3 Applications: Mixture and Uniform Motion Problems A. Solve value mixture problems B. Solve percent mixture problems (optional) C. Solve uniform motion problems 2.4 First-degree Inequalities A. Solve an inequality in one variable B. Solve a compound inequality C. Solve application problems 3. LINEAR FUNCTIONS AND EQUATIONS IN TWO VARIABLES 3.1 The Rectangular Coordinate System A. Graph points in a rectangular coordinate system B. Find the length and midpoint of a line segment C. Graph a scatter diagram (optional) 3.2 Introduction to Functions A. Evaluate a function 3.3 Linear Functions A. Graph a linear function by using the t-table method B. Graph an equation of the form Ax + By = C by using the t-table method C. Find x- and y-intercepts of a straight line D. Application problems 3.4 Slope of a Straight Line A. Find the slope of a line given two points B. Graph a line given a point and a slope 3.5 Finding Equations of Lines A. Find the equation of a line given a point and the slope B. Find the equation of a line given two points C. Application problems (optional) 3.6 Parallel and Perpendicular Lines A. Find parallel and perpendicular lines 3.7 Inequalities in Two Variables A. Graph the solution set of an inequality in two variables 4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES 4.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method A. Solve a system of linear equations by graphing B. Solve a system of linear equations by substitution C. Solve investment problems (optional) 4.2 Solving Systems of Linear Equations by the Addition Method A. Solve a system of two linear equations in two variables by the addition method B. Solve a system of three linear equations in three variables by addition method 4.3 Solving Systems of Equations by Using Determinants (optional) 4.4 Application Problems A. Solve rate-of-wind or rate-of-current problems B. Solve application problems 4.5 Solving Systems of Linear Inequalities A. Graph the solution set of a system of linear inequalities 5. POLYNOMIALS 5.1 Exponential Expressions A. Multiply monomials B. Divide monomials and simplify expressions with negative exponents C. Write a number using scientific notation D. Solve application problems (optional) 5.2 Introduction to Polynomials A. Evaluate polynomial functions B. Add or subtract polynomials 5.3 Multiplication of Polynomials A. Multiply a polynomial by a monomial B. Multiply two polynomials C. Multiply polynomials that have special products D. Solve application problems 5.4 Division of Polynomials A. Divide polynomials using long division B. Divide polynomials using synthetic division C. Evaluate a polynomial using synthetic division (optional) 5.5 Factoring Polynomials A. Factor a monomial from a polynomial B. Factor by grouping C. Factor a trinomial of the form x2 + bx + c D. Factor ax2 + bx + c 5.6 Special Factoring A. Factor the difference of two perfect squares or a perfect-square trinomial B. Factor the sum or difference of two perfect cubes C. Factor a trinomial that is quadratic in form D. Factor completely 5.7 Solving Equations by Factoring A. Solve an equation by factoring B. Solve application problems 6. RATIONAL EXPRESSIONS 6.1 Multiplication and Division of Rational Expressions A. Find the domain of a rational function B. Simplify a rational function C. Multiply rational expressions D. Divide rational expressions 6.2 Addition and Subtraction of Rational Expressions A. Rewrite rational expressions in terms of a common denominator B. Add or subtract rational expressions 6.3 Complex Fractions A. Simplify a complex fraction 6.4 Ratio and Proportion A. Solve a proportion B. Solve application problems 6.5 Rational Equations A. Solve a fractional equation B. Solve work problems C. Solve uniform motion problems (optional) 6.6 Variation A. Solve variation problems 7. RADICAL EXPRESSIONS 7.1 Rational Exponents and Radical Expressions A. Simplify expressions with rational exponents B. Write exponential expressions as radical expressions and vice versa C. Simplify radical expressions that are roots of perfect powers 7.2 Operations on Radical Expressions A. Simplify radical expressions B. Add or subtract radical expressions C. Multiply radical expressions D. Divide radical expressions 7.3 Solving Equations Containing Radical Expressions A. Solve a radical equation B. Solve application problems 7.4 Complex Numbers A. Simplify a complex number B. Add or subtract complex numbers C. Multiply complex numbers D. Divide complex numbers 8. QUADRATIC EQUATIONS 8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots A. Solve a quadratic equation by factoring B. Write a quadratic equation given its solutions C. Solve a quadratic equation by taking square roots 8.2 Solving Quadratic Equations by Completing the Square A. Solve a quadratic equation by completing the square (Limit examples to those with a Lead Coefficient of One.) 8.3 Solving Quadratic Equations by Using the Quadratic Formula A. Solve quadratic equations by using the quadratic formula 8.4 Solving Equations that are Reducible to Quadratic Equations (optional) 8.5 Quadratic Inequalities and Rational Inequalities (optional) 8.6 Applications of Quadratic Equations A. Solve application problems Grading: The student's final grade (A, B, C, D, or F) will be based on a comprehensive final exam, unit tests, quizzes, homework assignments, and student participation, according to a formula determined by the instructor. Effective Term: Fall 2002

MAT102 - Algebra 2

Credits: 3

Catalog Description: Topics include solving first degree inequalities, introduction to functions, linear equations in two variables and graphing, solving systems of two or three linear equations and inequalities, brief review of polynomial operations and factoring, algebraic fractions, variation, solving rational equations and proportions, rational exponents and radical expressions, complex numbers, solving radical equations, and four methods for solving quadratic equations, with emphasis on problem solving and applications throughout the course. Not open for credit to students who have credit in MAT 136 or higher. Three class hours. Prerequisite: MAT 092 or equivalent by placement.

Lecture: 3 hrs.

Student Performance Outcomes:
The student will be able to demonstrate each of the following skills in writing on one or more tests without referring to notes, textbook, or other resources.

1. Correctly translate and solve first-degree equations and inequalities. (Minimum of 5 times)

*2. Given a relation, identify if it is a function. If so, find its domain and range, and then correctly evaluate the
function given a value in its domain. (Minimum of 2 times)

3. Given a linear equation, correctly graph it on a rectangular coordinate system. (Minimum of 2 times)

4. Find the equation of a line given one of the following: (Minimum of 5 times)
A point on the line and the slope of the line
Two points on the line
A point on the line and the equation of a line parallel or perpendicular to it

5. Given a system of linear equations, correctly solve the system by graphing, substitution or the addition method. (Minimum of 4 times)

6. Given a system of inequalities, solve the system by the graphing method. (Minimum of 2 times)

7. Given two or more polynomials, correctly add, subtract, multiply or divide the expressions. (Minimum of 6 times)

8. Given two or more rational expressions, correctly add, subtract, multiply or divide the expressions. (Minimum of 6 times)

9. Given an equation involving rational expressions, correctly solve the equation. (Minimum of 2 times)

10. Given two or more radical expressions, add, subtract, multiply and divide the expressions and write the answer in simplest form. (Minimum of 6 times)

11. Given two complex numbers, add, subtract, multiply or divide the numbers and write the answer in the form a + bi. (Minimum of 6 times)

12. Given a quadratic equation, solve it by factoring, taking square roots, completing the square or using the quadratic formula. (Minimum of 6 times)

*This course objective has been identified as a student learning outcome that must be formally assessed as part of the College's Comprehensive Assessment Plan. All faculty teaching this course must collect the required data (see Assessing Student Learning Outcomes form) and submit the required analysis and documentation at the conclusion of the semester to the Office of Assessment and Special Projects.

Content Outline:
1. REVIEW OF REAL NUMBERS (optional)

2. FIRST-DEGREE EQUATIONS AND INEQUALITIES
2.1 Solving First-degree Equations
A. Solve equations using the addition or multiplication property of equations
B. Solve equations using both the addition and multiplication properties
C. Solve equations containing parentheses
D. Solve literal equations for one of the variables
2.2 Applications: Puzzle Problems
A. Solve integer problems
B. Solve coin and stamp problems
2.3 Applications: Mixture and Uniform Motion Problems
A. Solve value mixture problems
B. Solve percent mixture problems (optional)
C. Solve uniform motion problems
2.4 First-degree Inequalities
A. Solve an inequality in one variable
B. Solve a compound inequality
C. Solve application problems

3. LINEAR FUNCTIONS AND EQUATIONS IN TWO VARIABLES
3.1 The Rectangular Coordinate System
A. Graph points in a rectangular coordinate system
B. Find the length and midpoint of a line segment
C. Graph a scatter diagram (optional)
3.2 Introduction to Functions
A. Evaluate a function
3.3 Linear Functions
A. Graph a linear function by using the t-table method
B. Graph an equation of the form Ax + By = C by using the t-table method
C. Find x- and y-intercepts of a straight line
D. Application problems
3.4 Slope of a Straight Line
A. Find the slope of a line given two points
B. Graph a line given a point and a slope
3.5 Finding Equations of Lines
A. Find the equation of a line given a point and the slope
B. Find the equation of a line given two points
C. Application problems (optional)
3.6 Parallel and Perpendicular Lines
A. Find parallel and perpendicular lines
3.7 Inequalities in Two Variables
A. Graph the solution set of an inequality in two variables

4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
4.1 Solving Systems of Linear Equations by Graphing and by the Substitution
Method
A. Solve a system of linear equations by graphing
B. Solve a system of linear equations by substitution
C. Solve investment problems (optional)
4.2 Solving Systems of Linear Equations by the Addition Method
A. Solve a system of two linear equations in two variables by the addition
method
B. Solve a system of three linear equations in three variables by addition method
4.3 Solving Systems of Equations by Using Determinants (optional)
4.4 Application Problems
A. Solve rate-of-wind or rate-of-current problems
B. Solve application problems
4.5 Solving Systems of Linear Inequalities
A. Graph the solution set of a system of linear inequalities

5. POLYNOMIALS
5.1 Exponential Expressions
A. Multiply monomials
B. Divide monomials and simplify expressions with negative exponents
C. Write a number using scientific notation
D. Solve application problems (optional)
5.2 Introduction to Polynomials
A. Evaluate polynomial functions
B. Add or subtract polynomials
5.3 Multiplication of Polynomials
A. Multiply a polynomial by a monomial
B. Multiply two polynomials
C. Multiply polynomials that have special products
D. Solve application problems
5.4 Division of Polynomials
A. Divide polynomials using long division
B. Divide polynomials using synthetic division
C. Evaluate a polynomial using synthetic division (optional)
5.5 Factoring Polynomials
A. Factor a monomial from a polynomial
B. Factor by grouping
C. Factor a trinomial of the form x2 + bx + c
D. Factor ax2 + bx + c
5.6 Special Factoring
A. Factor the difference of two perfect squares or a perfect-square trinomial
B. Factor the sum or difference of two perfect cubes
C. Factor a trinomial that is quadratic in form
D. Factor completely
5.7 Solving Equations by Factoring
A. Solve an equation by factoring
B. Solve application problems

6. RATIONAL EXPRESSIONS
6.1 Multiplication and Division of Rational Expressions
A. Find the domain of a rational function
B. Simplify a rational function
C. Multiply rational expressions
D. Divide rational expressions
6.2 Addition and Subtraction of Rational Expressions
A. Rewrite rational expressions in terms of a common denominator
B. Add or subtract rational expressions
6.3 Complex Fractions
A. Simplify a complex fraction
6.4 Ratio and Proportion
A. Solve a proportion
B. Solve application problems
6.5 Rational Equations
A. Solve a fractional equation
B. Solve work problems
C. Solve uniform motion problems (optional)
6.6 Variation
A. Solve variation problems

7. RADICAL EXPRESSIONS
7.1 Rational Exponents and Radical Expressions
A. Simplify expressions with rational exponents
B. Write exponential expressions as radical expressions and vice versa
C. Simplify radical expressions that are roots of perfect powers
7.2 Operations on Radical Expressions
A. Simplify radical expressions
B. Add or subtract radical expressions
C. Multiply radical expressions
D. Divide radical expressions
7.3 Solving Equations Containing Radical Expressions
A. Solve a radical equation
B. Solve application problems
7.4 Complex Numbers
A. Simplify a complex number
B. Add or subtract complex numbers
C. Multiply complex numbers
D. Divide complex numbers

8. QUADRATIC EQUATIONS
8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots
A. Solve a quadratic equation by factoring
B. Write a quadratic equation given its solutions
C. Solve a quadratic equation by taking square roots
8.2 Solving Quadratic Equations by Completing the Square
A. Solve a quadratic equation by completing the square (Limit examples to those with a Lead Coefficient of One.)
8.3 Solving Quadratic Equations by Using the Quadratic Formula
A. Solve quadratic equations by using the quadratic formula
8.4 Solving Equations that are Reducible to Quadratic Equations (optional)
8.5 Quadratic Inequalities and Rational Inequalities (optional)
8.6 Applications of Quadratic Equations
A. Solve application problems

Grading:
The student's final grade (A, B, C, D, or F) will be based on a comprehensive final exam, unit tests, quizzes, homework assignments, and student participation, according to a formula determined by the instructor.

Effective Term: Fall 2002