Precalculus
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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$1,162 · Precalculus · 18 tutoring hrs
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Topics typically covered
Standard syllabus
Functions and algebra review
- Functions: domain, range, composition, and inverses
- Polynomial and rational functions; zeros and asymptotes
- Exponential and logarithmic functions; laws of logarithms
- Transformations of functions: shifts, stretches, and reflections
- Piecewise-defined functions and absolute value
Trigonometry and analytic geometry
- The unit circle; radian measure and arc length
- Trigonometric functions and their graphs
- Trigonometric identities and equations
- Law of sines and law of cosines
- Conic sections: parabolas, ellipses, and hyperbolas (standard forms)
Sequences and limits
- Arithmetic and geometric sequences and series
- Binomial theorem and Pascal's triangle (introduction)
- Introduction to limits and continuity (informal)
- Polar coordinates and parametric equations (where covered)
STEM / applied
Modeling and technology
- Exponential growth and decay models (population, finance, half-life)
- Logarithmic scales and semi-log plots
- Trigonometric models: periodic phenomena and harmonic motion
- Regression with technology; fitting exponential and power models
- Vector basics in R²: magnitude, direction, and components
Preparation for calculus
- Rate of change and average vs instantaneous velocity (preview)
- Tangent lines and secant slopes (graphical introduction)
- Optimization problems with polynomial and rational models
- Systems of equations and inequalities in applied settings
Notes
Topics reflect common precalculus syllabi at US colleges and universities. Some programs integrate trigonometry across two semesters or combine precalculus with college algebra.