College algebra
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
Algebraic foundations
- Real numbers, exponents, radicals, and algebraic manipulation
- Linear equations, inequalities, and absolute value
Functions and graphs
- Functions: domain, range, composition, and inverses
- Graphs of functions and transformations (shifts, stretches, reflections)
- Linear functions, slope, and modeling with lines
Polynomial and rational functions
- Quadratic functions: factoring, completing the square, and the quadratic formula
- Polynomial functions: zeros, division, and the factor and remainder theorems
- Rational functions: asymptotes, domain restrictions, and partial-fraction ideas
Exponential and logarithmic functions
- Exponential functions and their properties
- Logarithmic functions; change-of-base and solving exponential/log equations
Systems and inequalities
- Systems of linear equations in two and three variables
- Systems of inequalities and linear programming (introduction)
STEM / applied
Modeling and data
- Mathematical modeling with linear, exponential, and logarithmic functions
- Regression and curve fitting with technology (calculator or software)
- Data tables, scatter plots, and choosing an appropriate model
Applied contexts
- Sequences, series, and financial mathematics (compound interest, annuities)
- Applied optimization and interpretation of solutions in context
- Dimensional analysis and unit consistency in applied problems
- Piecewise functions in science and engineering contexts
- Matrix methods for solving small linear systems (optional at this level)
Notes
Topics reflect common college algebra and precalculus-algebra syllabi at US two- and four-year institutions. Many courses combine this content with precalculus or trigonometry review.