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
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