Dual Enrollment Program Support Course: Pre-Calculus

This support course (high school credit only) is designed to be taught in the fall semester preceding Math 1431 Business Calculus (dual enrollment) in the spring semester.

Course Details

High School Code: 160348
High School Credit: 1/2 Carnegie Unit
Grade Levels: 12th, 11th
Course Offered: Fall

Topics and Objectives

Chapter and section numbers refer to Calculus for Business, Economics, Life, and Social Sciences, 14e (Barnett, Ziegler, Byleen).

Homework: Basic Number Concepts

(18 exercises)

Multiply and divide fractions
Add and subtract fractions
Simplify using order of operations
Graph inequalities on number lines and write them as intervals

Homework: Exponents and Radicals

(19 exercises)

Use properties of exponents
Simplify radicals
Use radicals and rational exponents

Homework: Linear Equations

(25 exercises)

Solve linear equations
Write linear equations
Graph linear equations
Solve systems of linear equations in two variables

Homework: Quadratic Equations

(18 exercises)

Factor trinomials
Solve quadratic equations using the square root property
Solve quadratic equations by factoring
Solve quadratic equations using the quadratic formula

Homework: Other Types of Equations

(14 exercises)

Solve equations with variable(s) in the denominator
Solve equations with radical
Solve equations of quadratic type

Homework: Functions: Domain, Range, and Evaluation

(29 exercises)

Determine whether sets, mappings, or tables define a function
Determine whether a graph defines a function
Find the domain and range of functions
Find function values from a graph
Evaluate functions
Find the average rate of change of a function, and graph the associated secant line
Find the difference quotient of a function

Homework: Functions: Properties of Functions

(22 exercises)

Find the domain of a function
Determine whether an equation defines a function and, if so, find the domain
Find the value of a function
Identify the graph of a function
Use a graph to find where a function is increasing, decreasing, or constant
Use a graph to find if a function is even or odd
Use a graph to locate local maxima and local minima
Find local maxima and minimum
Determine where a function is increasing or decreasing
Find the average rate of change of a function

Homework: Graphs of Basic Functions and Polynomials

(21 exercises)

Find the equation of lowest degree that has a given graph and intercepts
Analyze graphs of basic functions
Graph piecewise-defined functions
Graph and analyze quadratic functions
Sketch and analyze the graphs of polynomial functions
Describe the end behavior of the graph of a polynomial function
Factor polynomial functions and sketch their graphs
Find a polynomial function with real coefficients which satisfies given conditions

Homework: Functions: Transformations and Compositions

(23 exercises)

Graph functions using transformations
Find composite functions
Find the domain of composite functions
Decompose functions

Homework: Rational Expressions

(21 exercises)

Divide rational expressions using long division
Simplify rational expressions
Add and subtract rational expressions
Simplify complex rational expressions
Rationalize numerators and denominators

Homework: Rational Functions

(20 exercises)

Simplify complex rational expressions
Solve rational equations
Find equations of asymptotes and graph rational functions
Sketch graphs of rational functions and estimate function values

Homework: Exponential Functions