Standard
Pre-calculus · High school · Math
Topics typically covered
Typical US high school Pre-calculus — aligned with Khan Academy Precalculus units and common college-prep outlines.
Functions and analysis
- Polynomial and rational functions — Analyze end behavior, asymptotes, holes, and intercepts.
- Exponential and logarithmic functions — Solve advanced exponential and log equations; apply change of base.
- Composition and inverses — Compose functions and verify inverses graphically and algebraically.
Trigonometry
- Unit circle mastery — Evaluate all six trig functions for standard angles in radians.
- Identities and equations — Prove identities and solve multi-step trig equations.
- Applications — Model with sinusoids; use laws of sines and cosines.
Vectors and matrices
- Vectors in the plane — Add vectors, find magnitude and direction, and compute dot products.
- Matrix operations — Add, multiply, and find inverses of small matrices.
- Systems with matrices — Solve linear systems using matrices and row reduction (intro).
Conic sections
- Parabolas — Write and graph parabolas with focus and directrix.
- Ellipses and hyperbolas — Identify foci, vertices, and asymptotes from standard forms.
- Applications of conics — Interpret conic models in applied settings.
Sequences, series, and induction (intro)
- Sequences and series — Work with arithmetic/geometric sequences and finite sums.
- Binomial theorem — Expand (a + b)^n using the binomial theorem.
- Mathematical induction (intro) — Prove simple statements with induction when included in the course.
Limits and continuity (intro)
- Intuitive limits — Estimate limits from graphs and tables; compute simple algebraic limits.
- Continuity — Identify continuous and discontinuous functions at a point.
Probability and combinatorics
- Counting principles — Use permutations, combinations, and the fundamental counting principle.
- Probability — Compute basic and conditional probabilities in finite sample spaces.
Related courses
Parallel materials covering overlapping topics — not the same as this course page.
- 12th Grade (Common Core)
Grade-level Common Core standards for the same band
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