# Math 110 College Algebra

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College Algebra.

(3:3:0)

F, W, Sp, Su

### Prerequisite

Math 97 or equivalent.

### Description

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

## Desired Learning Outcomes

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 (see learningoutcomes@byu.edu).

### Prerequisites

Students are expected to have completed a high school course in algebra 2 or intermediate algebra. These prerequisite courses are not taught at BYU. Students should be able to graph and solve linear equations. Students should be able to graph and solve quadratic equations by factoring and the quadratic formula.

### Minimal learning outcomes

Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts. Previous final exams (see http://math.byu.edu/~wright/Math%20110/Math110.html) give specific examples of the level of understanding that is expected.

1. Functions and their graphs
• 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 and graph an inverse function from the graph of a function
2. Polynomial and Rational Functions
• Polynomial functions
• Rational functions
• Polynomial and rational inequalities
• The real zeros of a polynomial function
• Complex zeros and the Fundamental Theorem of Algebra
3. Exponential and Logarithmic Functions
• Exponential functions
• Logarithmic functions
• Properties of Logarithms
• Logarithmic and exponential equations
• Compound interest
• Exponential growth and decay
4. Conic Sections
• Graph parabolas, ellipses, and hyperbolas
• Find the equation of parabolas, ellipses, and hyperbolas
• Discuss the equation of conic sections to find vertices, foci, asymptotes, and the directrix
• Work with conic sections that are not centered at the origin
5. Systems of Equations and Inequalities
• Solve systems of linear equations using substitution and elimination
• Solve systems of non-linear equations using substitution and elimination
• Decompose rational functions using partial fractions
6. Sequences and Induction
• Find terms in a sequence using a formula and a recursive definition
• 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
• Prove statements using mathematical induction
7. Counting, Probability, and the Binomial Theorem
• Work with operations on sets such as union, intersection and complement and count the number of elements in a set
• Compute permutations and combinations
• Evaluate binomial coefficients and expand binomials using the Binomial Theorem
• Compute probabilities of equally likely outcomes

### Textbooks

Possible textbooks for this course include (but are not limited to):