MTH 095 Intermediate Algebra

Lecture Hours: 4
Credits: 4

Introduces the study of functions with a focus on linear (including arithmetic sequences), quadratic (including an introduction to complex numbers), and exponential functions (including geometric sequences). Also covers converting rates using dimensional analysis. Uses a variety of methods including logarithms to solve equations. Explores topics using a graphing calculator (required) as well as traditional approaches.

Prerequisite: Placement into MTH 095 or higher; or completion of MTH 070 with a grade of C or better, or equivalent course as determined by instructor; or consent of instructor.
Student Learning Outcomes:

Use mathematical problem-solving techniques involving constant, linear quadratic, power, and exponential functions.
Create algebraic models of real situations using constant, linear, quadratic, power, and exponential functions.
Use inductive reasoning to develop mathematical conjectures involving constant, linear, quadratic, power, and exponential functions. Use deductive reasoning to verify conjectures and to apply mathematical theorems.
Make mathematical connections to, and solve problems from, other disciplines involving constant, linear, quadratic, power, and exponential functions.
Use oral and written skills to individually and collaboratively communicate about applications involving constant, linear, quadratic, power, and exponential functions.
Use appropriate technology to solve mathematical problems and to enhance mathematical thinking and understanding of constant, linear, quadratic power, and exponential functions.

Statewide General Education Outcomes

Use appropriate mathematics to solve problems.
Recognize which mathematical concepts are applicable to a scenario, apply appropriate mathematics and technology in its analysis, and then accurately interpret, validate, and communicate the results.

Content Outline

Qualitative Graphs
Introduction to Functions
- Independent and dependent variables
- Increasing/decreasing
- Domain and range
- Function notation
- Functions defined by graphs, data, verbal, and equations
Linear Functions
- Review of writing, graphing, and solving linear equations
- Arithmetic sequences
Quadratic Functions
- Graphing
- Radicals, simplifying radicals
- Vertex, maximum, minimum
- Quadratic formula
- Complex numbers
Exponential Functions
- Rational exponents
- Graphing
- Finding equations
- Logarithms base 10 and base e
- Solving exponential equations with logarithms
- Geometric sequences
Power Functions
- Direct variation
- Inverse variation
Modeling with functions
- Real life data
- Scatter grams
- Regression
- Estimating and predicting
- Model breakdown
Dimensional Analysis
- Converting measures of rate