MATHS 111: Pre-Calculus Algebra (3 hours)

MATH 111: Pre-Calculus Algebra (3 hours)
Syllabus
1. Prerequisite: MATH 108, appropriate score on the SAT/ACT, or appropriate score on the mathematics
placement test, or permission of the department chairperson. Not open to students who have credit in
MATH 132 or MATH 161 or MATH 165. Core Transfer Library: Mathematics (IMA 1601)
2. Course Description: Reviews fundamental concepts of algebra; covers functions and their graphs,
linear, power, quadratic, exponential, logarithmic, polynomial, and rational functions.
3. Course Objectives: The purpose of the course is to foster conceptual understanding and strategic
competence in algebra. Specifically, students in this course will—
• Review the basic ideas of expressions and equations, and understand the differences between them.
• Review the rules for manipulating expressions, particularly the distributive law, and provide a
rationale for expanding, factoring, combining like terms, and manipulations of algebraic fractions.
• Review the rules for transforming equations, laying a foundation for more complicated methods of
solving equations.
• Examine functions described by algebraic expressions, graphs, tables, and verbal descriptions.
• Use rate of change to characterize linear functions.
• Review rules for exponents, including fractional exponents, and rules for manipulating expressions
involving radicals.
• Explore power functions, relate the basic properties of a power function to the properties of the
exponent, use the law of exponents to change the form of power functions, and use equations to
model applications.
• Identify the domain and range of functions and explore composite and inverse functions.
• Examine piecewise-defined functions.
• Examine quadratic functions and their graphs, consider different forms of quadratic expressions—
standard, factored, and vertex—and show how each form reveals a different property of the function
it defines.
• Use factoring and completing the square, which leads to the quadratic formula, to solve quadratic
equations.
• Explore exponential functions.
• Explore logarithmic functions with base 10 and base e, as inverses of exponential functions, and to
solve exponential equations.
• Recognize the graphs of linear, power, exponential, and logarithmic functions.
• Consider the form of polynomial expressions, including the factored form, to see what each form
reveals about different properties of polynomial functions.
• Examine the long-run behavior of polynomials.
• Investigate the graphical and numerical behavior of rational functions.
• Examine factored form and the quotient form of rational functions, and consider horizontal, vertical,
and slant asymptotes.
4. Rationale: The purpose of the course is to prepare students for calculus. An important goal of this
course is to refocus the teaching and learning of mathematics on concepts as well as procedures. The
approach of this course is to foster conceptual understanding and strategic competence in algebra, in
addition to procedural fluency. Fluency—the ability to carry out procedures such as expanding,
factoring, and solving equations—is important, but too often students do not see the purpose or the
structure of the procedures. Conceptual understanding and strategic competence in algebra mean being
able to read algebraic expressions and equations in real-life contexts, not just manipulate them, and
being able to make choices of which form or which operation will best suit the context. They also mean
being able to translate back and forth between symbolic representations and graphical, numerical, and

verbal ones. The goal is to bring students’ understanding of mathematics to a higher level. The focus
on interpreting algebraic form, supported by graphical and numerical representations, enables students to
obtain a deeper understanding of the mathematics (McCallum, Connally, Hughes-Hallett, et al., 2010).
5. Course Content: Key concepts of algebra; rules for expressions and equations and reasons for them;
linear, power, quadratic, exponential and logarithmic functions, expressions, and equations; rules for
exponents and reasons for them; domain, range, composing and decomposing functions, inverse
functions, piecewise-defined functions; functions and their graphs; polynomial and rational functions.
6. Course Format: The course format is typically lecture and discussion. Students are expected to attend
class regularly, participate in class discussion, read the text, and complete assigned homework.
7. Methods of Evaluating Student Performance: Student performance is measured by three one-hour
exams, with each worth 100 points, and a departmental final exam worth 160 points. In addition, each
instructor is responsible for 100 points based on quizzes, homework, attendance and/or other factors.
8. Textbook: Intermediate & Pre-Calculus Algebra (Custom combination of Algebra: Form and Function
(McCallum et al.) and Functions Modeling Change (Connally et al.). Suggested order of Topics:
Algebra: Form and Function—Chapters 1, 2, 3, 4
Functions Modeling Change—Chapter 1
Algebra: Form and Function—Chapters 6, 7, 8, 9
Functions Modeling Change—Chapters 2, 4, 5,
Algebra: Form and Function—Chapters 12, 13
[Summer 2011: R. Bremigan, K. Roebuck, R. Rufatto, S. Stump, & E. Whittern; Summer 2012: Freshman
Sequence, R. Rufatto, Chair; Fall 2014, UPC, R. Pierce, Chair]