Unit 1
Function & Algebra Readiness
- Real numbers and algebraic fluency
- Equations and inequalities
- Polynomial and rational expressions
- Radicals and rational exponents
- Function notation
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College Mathematics
MATH 114 — Precalculus
A five-credit-style precalculus pathway combining algebraic and trigonometric functions and preparing students for calculus.
Course overview
A five-credit-style precalculus pathway combining algebraic and trigonometric functions and preparing students for calculus.
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
Polynomial & Rational Functions
- Polynomial functions and zeros
- Factoring and multiplicity
- Rational functions
- Asymptotes and end behavior
- Graphing and modeling
Unit 3
Exponential & Logarithmic Functions
- Exponential functions and transformations
- Growth and decay models
- Logarithms as inverses
- Logarithmic properties
- Exponential/logarithmic equations
Unit 4
Trigonometric Foundations
- Angles and radian measure
- Unit circle
- Sine, cosine, and tangent
- Reference angles and exact values
- Basic trig applications
Unit 5
Trigonometric Functions & Graphs
- Graphs of trig functions
- Amplitude, period, and phase shift
- Inverse trig functions
- Trig modeling
- Combining algebraic and trig representations
Unit 6
Trigonometric Identities & Equations
- Pythagorean and reciprocal identities
- Sum/difference identities
- Double-angle identities
- Trig equations
- Identity verification
Unit 7
Triangles & Applications
- Right-triangle trigonometry
- Law of Sines
- Law of Cosines
- Area of oblique triangles
- Modeling with triangles
Unit 8
Polar, Parametric & Complex Connections
- Parametric equations
- Polar coordinates
- Polar graphs
- Complex numbers in polar form
- Geometric interpretation
Unit 9
Calculus Readiness
- Average and instantaneous rate of change
- Function behavior and transformations
- Algebraic/trigonometric fluency
- Model interpretation
- Precalculus-to-calculus transition
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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