# MATH 110

## College Algebra

Mathematics
College of Physical and Mathematical Sciences

### Course Description

Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, systems of linear equations, permutations, combinations, binomial theorem.

### When Taught

All Semesters/Terms

### Fixed

3

### Fixed

3

### Fixed

1

### Other Prerequisites

Math 97 or equivalent (see Independent Study).

### Note

Offered by BYU Independent Study; enroll anytime throughout the year; one year to complete; additional tuition required; register at is.byu.edu.

### Title

Functions, polynomials, theory of equations, etc.

### Learning Outcome

This course prepares students to take courses in calculus, statistics, mathematics for elementary education majors, and other areas where algebra skills are required. Fluent skills in algebra are necessary for success in any area that uses mathematical analysis. The mastery of college algebra requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. College Algebra develops the concepts of graphing functions, polynomial and rational functions, exponential and logarithmic functions, conic sections, solving systems of equations, the binomial theorem, permutations, combinations, and probability. This course contributes to all the expected learning outcomes of the Mathematics BS degree. For more detailed information, visit the Math 110 Wiki page.

### Title

Exponential and Logarithmic Functions

### Learning Outcome

Exponential functionsLogarithmic functionsProperties of LogarithmsLogarithmic and exponential equationsCompound interestExponential growth and decay

### Title

Functions and their graphs

### Learning Outcome

Graph functions using horizontal and vertical shifts
Graph functions using compressions and stretches
Graph functions using reflections about the x-axis or y-axis
Form composite functions and find the domain
Determine the inverse of a function
Graph an inverse function from the graph of a function

### Title

Polynomial and Rational Functions

### Learning Outcome

Quadratic functions
Polynomial functions
Rational functions
Polynomial and rational inequalities
The real zeros of a polynomial function
Complex zeros and the Fundamental Theorem of Algebra
The Intermediate Value Theorem.
The inequalities |x-a|<b and a-b<x<a+b

### Title

Systems of Equations and Inequalities

### Learning Outcome

Solve systems of linear equations using substitution and elimination. Detect systems that have infinitely many solutions or no solutions.
Solve systems of non-linear equations using substitution and elimination, including systems with multiple solutions.

### Title

Sequences and Induction

### Learning Outcome

Find terms in a sequence using a formula and a recursive definition.
Given terms in a sequence that follow a pattern, produce a formula for the sequence.
Find a formula for terms in an arithmetic sequence and be able to add the terms of a finite arithmetic sequence.
Find a formula for the terms in a geometric sequence and be able to find the sum of finite and infinite geometric series.

### Title

Counting and Probability

### Learning Outcome

Count the number of ways in which a sequence of events can occur (the Rule of Product).
Compute probabilities based on equally likely outcomes.
Compute probabilities of complements of events and unions of disjoint events.
Compute the probability of a sequence of independent events.