MATH 197: Prelude to Calculus I

Bulletin Description

Prerequisite: First-Year Math Advising Module; Category III* and IV* placement for QR/Math.

Review of numbers and operations, exponents, and radicals. Linear, quadratic, polynomial, and rational functions. Exponential growth and exponential functions. Logarithmic functions. The transcendental number e and natural logarithms. The first semester of a year-long stretch pre-calculus course.


Math 197 is recommended for students who self-identify as wanting support or more time in taking the pre-calculus sequence.  (STEM students with category III or IV for QR/Math designations are encouraged to enroll in Math 197.)

Students may select Math 199, the one-semester version of precalculus, or the two-semester version, Math 197 & 198.  Both the one-semester version and the year-long version deal with the same topics.

Course Attributes:

Pre-requisite to Math 198. Math 198 meets the B4: Math/QR requirement.

Purpose and Goals

The purpose of this course is to prepare students for Math 198 and to succeed in calculus, specifically Math 226 and in future math and science courses.  The prerequisite for Math 226 is a C or higher in Math 198 or 199.

Goals of a Precalculus course:

•   To build understanding of specific relationships (functions) and their inverses, through problem solving and reasoning using tables, graphs and   equations, and

•.  To develop fluency in the use of algebra to solve problems.

Precalculus Classes

Success in calculus requires fluency in using algebra, but more than that, success requires you to be able to move easily back and forth among mathematical representations:  words, graphs, tables and equations.  Graphs and tables, as  way to visualize relationships (functions) and reason about them are especially important.

Learning mathematics at the level of understanding needed for calculus requires active participation in problem solving and in explaining your reasoning.  Much of the time during this class will be spent working in small groups with other students on the activities and problems with the instructor’s support.  Participation and sharing your thinking and questions with other students is the key to learning precalculus.

This means class will generally start with a short introduction to the day’s work and time for questions followed by groupwork where you work with other students to discuss and solve the problems.  Your instructor will be going from group to group to support your work and respond to questions, sometimes calling the whole class back together to clarify or share ideas. You will need to keep a record of your work each day.


Course Content Objectives





Unit 1

Functions: Exponential, linear and others

•   Recognize and move easily between representations for linear and exponential and other functions: tables, graphs, equations, situations.

•   Develop fluency transitioning between different forms of equations.

•   Solve equations graphically

about 3 weeks

Unit 2

Quadratics: Introducing Parameters and Transformations

•   Second differences and quadratic functions

•   Effects of parameters on graphs

•   Changing algebraic forms and deriving the Quadratic Formula

•   Comparing/contrasting quadratic and exponential functions

about 4 Weeks

Unit 3

New Functions from old

•   Build new functions by multiplying, dividing and taking roots of given functions, and describe their domains, ranges, and end behaviors.

•   Create linear transformations from graphs, equations and tables.

•   Compose and decompose functions.

about 3 weeks

Unit 4

Inverse Functions

•   Determine whether functions have inverses, and if so, represent the inverse of a given function using a table, an equation and a graph.

•   Logarithms as inverse exponential functions.

•   Rules of exponents to rules for logs to solving problems involving exponential funcions.

about 4 weeks

Submitted by Eric Hsu, May 16 2024