Unit 1
Algebraic Foundations
- Real numbers and algebraic properties
- Factoring and polynomial operations
- Rational expressions and restrictions
- Radicals and rational exponents
- Equation-solving strategy
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College Mathematics
MATH 112 — College Algebra
A college algebra roadmap focused on elementary functions, equations, inequalities, graphs, and real-world modeling.
Course overview
A college algebra roadmap focused on elementary functions, equations, inequalities, graphs, and real-world modeling.
Math Aficionado uses this structure as a tutoring roadmap: lessons can be paced around the student's current level, school sequence, assignments, and assessment goals rather than forcing every student through the same timetable.
Units & topics
Unit 2
Equations & Inequalities
- Linear equations and inequalities
- Absolute-value equations and inequalities
- Quadratic equations
- Polynomial equations
- Radical and rational equations
Unit 3
Functions & Function Notation
- Defining functions
- Domain and range
- Function notation and evaluation
- Piecewise functions
- Transformations and combinations
Unit 4
Polynomial & Rational Functions
- Polynomial graphs and end behavior
- Zeros, multiplicity, and factors
- Rational functions and asymptotes
- Graph transformations
- Solving polynomial and rational inequalities
Unit 5
Exponential Functions
- Exponential growth and decay
- Transformations of exponential functions
- Compound interest and continuous growth
- Exponential equations
- Modeling with exponential functions
Unit 6
Logarithmic Functions
- Logarithms and inverse relationships
- Logarithmic properties
- Graphs and transformations
- Exponential and logarithmic equations
- Applications of logarithmic models
Unit 7
Systems & Function Combinations
- Linear systems
- Nonlinear systems
- Composition of functions
- Inverse functions
- Interpreting multiple representations
Unit 8
Modeling & Mathematical Reasoning
- Building models from data
- Selecting an appropriate function family
- Parameter interpretation
- Checking model limitations
- Communicating and justifying conclusions
Curriculum reference: University of Wisconsin–Madison Guide / Department of Mathematics. The page is an independent tutoring roadmap and is not an official course page of the source institution.
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