ELEMENTARY ALGEBRA

The Department’s Educational Philosophy

The study of mathematics will enhance the ability of all students to problem solve and to reason. Through a strong standardized
departmental program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using
representations, students will develop self-confidence and a positive attitude towards mathematics.
Our curriculum matches that of the Massachusetts Mathematics Curriculum Framework , and we are philosophically aligned with the
National Council of Teachers of Mathematics Standards .

Guiding Principles
• Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of
understanding.

• Effective mathematics programs focus on problem solving and require teachers who have a deep knowledge of the discipline.

• Technology is an essential tool in a mathematics education, and all students should gain facility in using it where advantageous.

• All students should have a high-quality mathematics program.

• Assessment of student learning in mathematics should take many forms to inform instruction and learning.

• All students should understand the basic structure of mathematics.

• All students should recognize that the techniques of mathematics are reflections of its theory and structure.

• All students should gain facility in applying mathematical skills and concepts.

• All students should understand the role of inductive and deductive reasoning in mathematic and real life situations.

ELEMENTARY ALGEBRA 1-2 (SP): COURSE #326

Course Frequency: Full-year course, five times per week
Credits Offered: Five
Prerequisites: C- or higher in Elementary Algebra 1-1 (SP)

Background to the Curriculum
This course uses the Glencoe Algebra 1 text, 1996 edition, and has been updated to the 2000 edition. The Glencoe text replaced the
Holt Algebra 1 and had been used for the previous 10 years. The Glencoe text is followed quite closely since it matches both the 2000
edition of the National Council of Teachers of Mathematics Curriculum Standards and the 2000 edition of the Massachusetts State
Framework recommendations for a first-year algebra course . This course exposes students to the first year Algebra 1 curriculum and
is well aligned with national and state guidelines. Teachers bring in other material where appropriate and make minor changes as to
the specific sections taught each year, after consultation with the RDL.

Core Topics/Questions/Concepts/Skills
Simplifying expressions and solving equations
Solving everyday word problems
Using ratio, proportion, and percent
Solving equations in more than one variable
Equations of lines and graphing
Introductory statistical concepts
Solving and graphing inequalities in one and two dimensions
Factoring polynomials and solving equations by factoring
Operations on polynomials
Simplifying radical expressions and solving radical equations

Course-End Learning Objectives

Assessment
Students are generally assessed by in-class tests and quizzes, which are administered regularly throughout a marking period.
Generally, two quizzes are equivalent to a test. The students’ attitude, effort, and quality of homework preparations will also impact
their term grade to a small degree. Teachers informally assess students every day by asking pivotal questions, as well as questions
involving mechanics or concepts, and the students’ term grades may be positively affected to a small degree based on their responses.

A standardized midyear examination and final examination are administered to all students in this course in order to assess their longterm
retention of the course material.

Technology Learning Objectives Addressed in This Course
(This section is for faculty and administrative reference; students and parents may disregard.)

Materials and Resources
Teachers use other resources for supplementary ideas, such as the “Algebra with Pizzazz” series of activities. There are review
materials that closely match most tests and quizzes, as well as a close resemblance to the departmental examinations. All teachers of
the course use these materials. Teachers may also reinforce ideas by using manipulatives, such as algebra tiles , in class.

MATH 225 CALCULUS II

Course Description:
This course is a continuation of Calculus I. Topics include an introduction to differential
equations, techniques and applications of integration, L’Hopital’s Rule, improper
integrals, infinite series, conics, and parametric and polar equations.
Prerequisite: MAT 220 or its equivalent. 4 credits

Course Objectives
Upon successful completion of the course, the student will be able to define, use
correctly, and apply to solving problems the concepts and terminology in each of the
topics listed below. Upon successful completion of the course, students will:

1. Find general and particular solutions of differential equations .
2. Use separation of variables to solve a simple differential equation.
3. Calculate Areas and Volumes by Integration.
4. Calculate arc length of a smooth curve.
5. Calculate the area of a surface of revolution.
6. Apply integration to various situations such as work, centers of gravity, motion, etc.
7. Use techniques of integration such as integration by parts, trigonometric substitution,
partial fractions.
8. Apply L’Hopital’s rule to indeterminate forms.
9. Evaluate improper integrals.
10. Use an appropriate test to determine the convergence or divergence of infinite
sequences and series.
11. Approximate a function with a Taylor or MacLaurin polynomial.
12. Find a power series representation of a function.
13. Find the equation of a parabola , ellipse, and hyperbola.
14. Sketch the graph of a curve defined by a set of parametric equations.
15. Understand the polar coordinate system.

Course Requirements
Students are expected to attend all scheduled classes, do the homework assigned each day
for the next class, take tests, and be active participants in the class.

Student Evaluation and Testing
Student evaluation may include in-class testing, class attendance, participation in
classwork, and homework assignments . Your instructor will make clear his/her grading
policy.

Required Text, Tools, and/or Supplies:
CALCULUS OF A SINGLE VARIABLE,
Eighth Edition, by Larson, Hostetler, Edwards
Houghton Mifflin, 2006
Graphing calculator such as the TI- 83 Plus or TI-84
Student Solutions Manual

Non-discrimination and Disability Statements:
Southern Maine Community College is an equal opportunity /affirmative action institution and
employer. For more information, please call 207-741-5798.

If you have a disabling condition and wish to request accommodations in order to have
reasonable access to the programs and services offered by SMCC, you must register with the
disability services coordinator, Mark Krogman, who can be reached at 741-5629.
(TTD 207-741-5667) Further information about services for students with disabilities and the
accommodation process is available upon request at this number.

Course Evaluation: Students may evaluate the course online and anonymously by going to
“Resources for Current Students” at the SMCC homepage and selecting “Evaluate Your
Courses.” The online course evaluation is available to students two weeks prior to the end date
of the course. Students cannot see a course grade online until the online course evaluation is
completed.

Required Course Topics, MAT 225 Chapter 5-10 as follows:

CHAPTER 5 – Logarithmic, Exponential, and Other Transcendental Functions
5.6 Inverse Trigonometric Functions: Differentiation
5.7 Inverse Trigonometric Functions: Integration
5.8 Hyperbolic Functions

CHAPTER 6 – Differential Equations
6.1 Slope Fields and Euler ’s Method
6.2 Differential Equations: Growth and Decay
6.3 Separation of Variables and Logistic Equations

CHAPTER 7 - Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
7.3 Volume: The Shell Method
7.4 Arc Length and Surfaces of Revolution
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force

CHAPTER 8 – Integration Techniques, L’Hopital’s Rule, and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integral
8.4 Trigonometric Substitution
8.5 Partial Fractions
8.6 Integration by Tables and Other Integration Techniques
8.7 Indeterminate Forms and L’Hopital’s Rule
8.8 Improper Integrals

CHAPTER 9 – Infinite Series
9.1 Sequences
9.2 Series and Convergence
9.3 The Integral Test and p-Series
9.4 Comparisons of Series
9.5 Alternating Series
9.6 The Ratio and Root Tests
9.7 Taylor Polynomials and Approximations
9.8 Power Series
9.9 Representation of Functions by Power Series
9.10 Taylor and MacLaurin Series

CHAPTER 10 – Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler ’s Laws

CHAPTER 2 – Systems of Linear Equations and Matrices
2.1 Systems of Linear Equations: An Introduction
2.2 Systems of Linear Equations: Unique Solutions, Gauss-Jordan Method
2.3 Systems of Linear Equations: Underdetermined and Overdetermined Systems
2.4 Matrices
2.5 Multiplication of Matrices
2.6 The Inverse of a Square Matrix

CHAPTER 3 – Linear Programming: A Geometric Approach
3.1 Graphing Systems of Linear Inequalities in Two Variables
3.2 Linear Programming Problems
3.3 Graphical Solution of Linear Programming Problems

CHAPTER 4 - Linear Programming: An Algebraic Approach
4.1 The Simplex Method: Standard Maximization Problems
4.2 The Simplex Method: Standard Minimization Problems
4.3 The Simplex Method: Nonstandard Problems – Using SOLVER in EXCEL

CHAPTER 5 – Mathematics of Finance
5.1 Compound Interest
5.2 Annuities
5.3 Amortization and Sinking Funds
5.4 Arithmetic and Geometric Progressions

CHAPTER 6 – Sets and Counting
6.1 Sets and Set Operations
6.2 The Number of Elements in a Finite Set
6.3 The Multiplication Principle
6.4 Permutations and Combinations

CHAPTER 7 – Probability
7.1 Experiments, Sample Spaces, and Events
7.2 Definition of Probability
7.3 Rules of Probability
7.4 Use of Counting Techniques in Probability
7.5 Conditional Probability and Independent Events
7.6 Bayes’ Theorem

Learning Outcomes for Introductory Algebra

Course Description:
For students with limited algebra experience . Curriculum will include solving algebraic
equations, operations with polynomials, and extensive factoring of polynomials . Graphical
solutions for linear and quadratic equations will be explored , including slope, intercepts, and
inequalities. Culminating material will include solving rational, radical, and systems of
equations

Chapter 7 Objectives: Algebraic Expressions
Objective: (7.1) Evaluate Algebraic Expression by Substitution
Objective: (7.1) Translate Phrase to Algebraic Expression
Objective: (7.2) Use < or > to Make True Statement
Objective: (7.2) Find Absolute Value
Objective: (7.3) Add Three or More Numbers
Objective: (7.3) Solve Apps : Addition of Real Numbers
Objective: (7.4) Subtract Two Real Numbers and Simplify
Objective: (7.4) Simplify Combination of Additions and Subtractions
Objective: (7.4) Solve Apps: Addition and Subtraction of Real Numbers
Objective: (7.5) Multiply Two Real Numbers
Objective: (7.6) Divide Integers
Objective: (7.6) Divide Real Numbers
Objective: (7.7) Simplify Fraction Expression
Objective: (7.7) Use Distributive Laws to Multiply Expressions
Objective: (7.7) Use Distributive Laws to Factor Expression
Objective: (7.7) Collect Like Terms
Objective: (7.8) Find an Equivalent Expression Without Parentheses
Objective: (7.8) Remove Parentheses and Simplify
Objective: (7.8) Simplify Expression with Nested Parentheses

Chapter 8 Objectives: Solving Equations
Objective: (8.1) Solve Equation Using Addition Principle
Objective: (8.1) Solve Equation Fractions (Addition Principle)
Objective: (8.2) Solve Equation Using Multiplication Principle
Objective: (8.2) Solve Equation Fractions (Multiplication Principle)
Objective: (8.3) Solve Equation Using Both Principles
Objective: (8.3) Collect Terms and Solve Equation
Objective: (8.3) Remove Parentheses, Collect Terms, and Solve
Objective: (8.4) Solve Formula for Specified Letter
Objective: (8.5) Solve Percent Problem : Amount
Objective: (8.5) Solve Percent Problem: Base
Objective: (8.5) Solve Percent Problem: Percent Number
Objective: (8.5) Solve Apps: Using Percents
Objective: (8.6) Solve Apps: Numbers
Objective: (8.6) Solve Apps: Other
Objective: (8.7) Solve Inequality Using Addition Principle
Objective: (8.7) Solve Inequality Using Multiplication Principle
Objective: (8.7) Solve Inequality Using Both Principles
Objective: (8.8) Solve Apps: Miscellaneous

Chapter 9 Objectives: Graphs of Linear Equations
Objective: (9.1) Solve Apps: Circle, Bar, Line Graphs
Objective: (9.1) Plot Points Associated with Ordered Pairs
Objective: (9.1) Determine Quadrant of Point
Objective: (9.1) Find Coordinates of Point on Graph
Objective: (9.2) Determine If Ordered Pair Is a Solution
Objective: (9.2) Use Ordered Pairs to Determine Another Solution
Objective: (9.2) Determine Coordinates of y-Intercept
Objective: (9.2) Graph Linear Equation
Objective: (9.2) Solve Apps: Graphs of Linear Equations
Objective: (9.3) Find Intercepts from Graph of Linear Equation
Objective: (9.3) Find Intercepts of Linear Equation
Objective: (9.3) Find Intercepts and Graph Equation
Objective: (9.3) Graph x=a or y=b Equation
Objective: (9.3) Write Equation from x=a or y=b Graph
Objective: (9.4) Find Slope from Graph
Objective: (9.4) Graph Line and Find Slope Given Two Points
Objective: (9.4) Find Slope from Pair of Points
Objective: (9.4) Solve Apps: Find Slope/Pitch/Grade
Objective: (9.4) Solve Apps: Find Rate of Change from Graph
Objective: (9.4) Find Slope from Equation

Chapter 10 Objectives: Polynomials; Operations
Objective: (10.1) Identify Meaning of Exponential Notation
Objective: (10.1) Evaluate Expression with Zero or One as Exponent
Objective: (10.1) Evaluate Expression with Exponent
Objective: (10.1) Evaluate Geometric Formula with Exponent
Objective: (10.1) Change Negative Exponent to Positive
Objective: (10.1) Change Positive Exponent to Negative
Objective: (10.1) Use Product Rule to Multiply with Exponents
Objective: (10.1) Use Quotient Rule to Divide with Exponents
Objective: (10.2) Use Power Rule to Simplify a Product
Objective: (10.2) Use Power Rule to Simplify Quotient
Objective: (10.2) Convert Decimal Notation to Scientific Notation
Objective: (10.2) Solve Apps: Convert to Scientific Notation
Objective: (10.2) Convert Scientific Notation to Decimal Notation
Objective: (10.2) Multiply or Divide Using Scientific Notation
Objective: (10.2) Solve Apps: Scientific Notation
Objective: (10.3) Evaluate a Polynomial
Objective: (10.3) Solve Apps: Evaluate a Polynomial
Objective: (10.3) Identify Terms of Polynomial
Objective: (10.3) Identify Like Terms of Polynomial
Objective: (10.3) Identify Coefficients in Polynomial
Objective: (10.3) Collect Like Terms to Simplify Polynomial
Objective: (10.3) Arrange Polynomial in Descending Order
Objective: (10.3) Collect Like Terms and Arrange in Descending Order
Objective: (10.3) Identify the Degree of a Polynomial
Objective: (10.3) Identify Missing Terms in Polynomial
Objective: (10.3) Write Missing Terms in Polynomial in Two Ways
Objective: (10.3) Classify Polynomial
Objective: (10.4) Add Polynomials
Objective: (10.4) Simplify the Opposite of a Polynomial
Objective: (10.4) Subtract Polynomials
Objective: (10.4) Use Polynomials to Represent Perimeter or Area
Objective: (10.5) Multiply Monomials
Objective: (10.5) Multiply Monomial and Polynomial
Objective: (10.5) Multiply Two Binomials
Objective: (10.5) Draw Rectangles Illustrating Multiplication
Objective: (10.5) Multiply Two Polynomials
Objective: (10.6) Multiply Two Binomials Using FOIL
Objective: (10.6) Multiply Sum and Difference of Two Terms
Objective: (10.6) Square a Binomial
Objective: (10.6) Multiply Mentally
Objective: (10.6) Compare Squares
Objective: (10.6) Multiply Polynomials to Find Area of Rectangles
Objective: (10.7) Evaluate Polynomial in Several Variables
Objective: (10.7) Solve Apps: Evaluate Polynomial
Objective: (10.7) Identify Coefficients and Degrees of Terms
Objective: (10.7) Identify Degree of Polynomial
Objective: (10.7) Collect Like Terms
Objective: (10.7) Add Polynomials in Several Variables
Objective: (10.7) Subtract Polynomials in Several Variables
Objective: (10.7) Multiply Polynomials in Several Variables
Objective: (10.8) Divide Polynomial by Monomial
Objective: (10.8) Divide Polynomial by Binomial

Chapter 11 Objectives: Polynomials; Factoring
Objective: (11.1) Factor Monomial
Objective: (11.1) Factor Out Largest Common Factor
Objective: (11.1) Factor Out a Binomial Factor
Objective: (11.1) Factor by Grouping
Objective: (11.2) Factor Trinomial x^2 + bx + c
Objective: (11.2) Factor Trinomial in Two Variables
Objective: (11.2) Factor Trinomial with Fractions or Decimals
Objective: (11.3) Factor ax^2 + bx + c
Objective: (11.3) Factor Trinomial with Higher Powers
Objective: (11.3) Factor Trinomial in Two Variables
Objective: (11.4) Factor Using ac Method (Middle Term Split)
Objective: (11.4) Factor Using ac Method
Objective: (11.5) Recognize Trinomial Square
Objective: (11.5) Factor Trinomial Square
Objective: (11.5) Recognize Difference of Squares
Objective: (11.5) Factor Difference of Squares
Objective: (11.6) Factor Binomial
Objective: (11.6) Factor Trinomial
Objective: (11.6) Factor Polynomial
Objective: (11.6) Factor Polynomial with Binomial Factor
Objective: (11.7) Solve Using Principle of Zero Products
Objective: (11.7) Solve by Factoring and Principle of Zero Products
Objective: (11.7) Find x-Intercepts of Graphs
Objective: (11.7) Use Graph to Solve Quadratic Equation
Objective: (11.8) Solve Apps: Numbers
Objective: (11.8) Solve Apps: Geometry
Objective: (11.8) Solve Apps: Other

Chapter 12 Objectives: Rational Expressions and Equations
Objective: (12.1) Determine Where Rational Expression is Not Defined
Objective: (12.1) Multiply Rational Expression by Form of One
Objective: (12.1) Simplify Rational Expression by Factoring
Objective: (12.1) Multiply Rational Expressions
Objective: (12.2) Find Reciprocal of Rational Expression
Objective: (12.2) Divide Rational Expressions
Objective: (12.3) Find LCM of Numbers
Objective: (12.3) Add Fractions
Objective: (12.3) Find LCM of Algebraic Expression
Objective: (12.4) Add Rational Expressions ( Common Denominator )
Objective: (12.4) Add Rational Expressions (Opposite Denominators)
Objective: (12.4) Add Rational Expressions (Unlike Denominators)
Objective: (12.5) Subtract Rational Expressions (Common Denominator)
Objective: (12.5) Subtract Rational Expressions (Opposite Denominators)
Objective: (12.5) Subtract Rational Expressions (Unlike Denominators)
Objective: (12.5) Simplify Combined Operations
Objective: (12.6) Solve Rational Equation I
Objective: (12.6) Solve Rational Equation II
Objective: (12.7) Solve Apps: Work
Objective: (12.7) Solve Apps: Motion
Objective: (12.7) Find Ratio
Objective: (12.7) Solve Proportion Problem
Objective: (12.7) Solve Geometry Proportion
Objective: (12.8) Simplify Complex Rational Expression

Chapter 13 Objectives: Graphs, Slope, and Applications
Objective: (13.1) Find Slope and y-Intercept of Line
Objective: (13.1) Find Equation Given Slope and Intercept
Objective: (13.1) Find Equation Given Slope and Point
Objective: (13.1) Find Equation Given Pair of Points
Objective: (13.1) Solve Apps: Use Slope
Objective: (13.2) Draw Line Given Slope and y-Intercept
Objective: (13.2) Graph Line Using Slope and y-Intercept
Objective: (13.3) Determine if Lines are Parallel or Perpendicular
Objective: (13.4) Decide if Ordered Pair is Solution to Inequality
Objective: (13.4) Graph Linear Inequality
Objective: (13.5) Find Direct Variation Equation
Objective: (13.5) Solve Apps: Direct Variation
Objective: (13.5) Find Inverse Variation Equation
Objective: (13.5) Solve Apps: Inverse Variation

Chapter 14 Objectives: Systems of Equations
Objective: (14.1) Decide if Ordered Pair is Solution of System
Objective: (14.1) Solve System by Graphing
Objective: (14.2) Solve System by Substitution: One Variable Alone
Objective: (14.2) Solve System by Substitution
Objective: (14.2) Solve Apps: Substitution Method
Objective: (14.3) Solve System by Elimination with No Multiplication
Objective: (14.3) Solve System Using Elimination and Multiplication
Objective: (14.4) Solve Apps: Solve System of Equations I
Objective: (14.4) Solve Apps: Solve System of Equations II
Objective: (14.4) Solve Apps: Solve System of Equations: Mixtures
Objective: (14.5) Solve Apps: Motion Problems Using d = rt

Chapter 15 Objectives: Radical Expressions and Equations
Objective: (15.1) Find Square Roots of Number
Objective: (15.1) Find Principal Square Root
Objective: (15.1) Find Square Root Using Calculator
Objective: (15.1) Solve Apps: Find Square Root
Objective: (15.1) Identify the Radicand
Objective: (15.1) Decide If Radical Represents Real Number
Objective: (15.1) Simplify Radical Expression
Objective: (15.2) Simplify Radical Expression
Objective: (15.2) Simplify Radical Expressions with Powers
Objective: (15.2) Multiply Radical Expressions and Simplify
Objective: (15.3) Divide Radical Expressions
Objective: (15.3) Simplify Square Roots of Quotients
Objective: (15.3) Rationalize Denominator of Radical Expression
Objective: (15.4) Add or Subtract Radical Expressions
Objective: (15.4) Multiply Binomial Radical Expressions
Objective: (15.4) Rationalize Binomial Denominator
Objective: (15.5) Solve Radical Equation (Multiply Once)
Objective: (15.5) Solve Radical Equation (Multiply Twice)
Objective: (15.5) Solve Apps: Radical Equations
Objective: (15.6) Find Third Side of Right Triangle (Picture Given)
Objective: (15.6) Find Third Side of Right Triangle (No Picture)
Objective: (15.6) Solve Apps: Right Triangles

Chapter 16 Objectives: Quadratic Equations
Objective: (16.1) Write Quadratic Equation in Standard Form
Objective: (16.1) Solve Quadratic Equation with Factor of Variable
Objective: (16.1) Solve Quadratic Equation by Factoring
Objective: (16.1) Solve Rational Equation by Factoring
Objective: (16.1) Solve Apps: Diagonals
Objective: (16.2) Solve Quadratic of Type ax^2 = p
Objective: (16.2) Solve Quadratic of Type (x + c)^2 = d
Objective: (16.2) Solve Quadratic by Completing the Square
Objective: (16.2) Solve Apps: ax^2 = p
Objective: (16.3) Solve Equation Using Quadratic Formula
Objective: (16.3) Approximate Solutions to Quadratic Equation
Objective: (16.4) Solve Formula for Letter: Rational Expression
Objective: (16.4) Solve Formula for Letter: Square Roots
Objective: (16.4) Solve Formula for Letter: Quadratic Equation
Objective: (16.5) Solve Apps: Geometry
Objective: (16.5) Solve Apps: Speed
Objective: (16.6) Find Vertex of Graph of Quadratic Equation
Objective: (16.6) Graph Quadratic Equation
Objective: (16.6) Find x-intercepts of Quadratic Equation
Objective: (16.7) Decide If Correspondence Is a Function
Objective: (16.7) Find Value of Function for Input Value
Objective: (16.7) Solve Apps: Function Value
Objective: (16.7) Graph Function
Objective: (16.7) Determine If Graph Is of Function
Objective: (16.7) Solve Apps: Functions and Graph