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Precalculus Math

All Precalculus skills, each with a clear explanation and code-verified practice. Aligned to Common Core.

N-CN

Complex Numbers in Polar Form — r(cos θ + i sin θ)Multiply and Divide Complex Numbers in Polar Form De Moivre's Theorem — Powers and Roots of Complex Numbers

N-VM

Vectors — Components, Addition, and Scalar Multiplication Dot Product of Vectors — Magnitude and Angle Between Vectors Matrix Addition, Subtraction, and Scalar Multiplication Matrix Multiplication — 2×2 and 2×1 Cases 2×2 Matrix Inverse and Determinant

A-APR

Polynomial Theorems — Rational Root and Fundamental Theorem Partial Fraction Decomposition

F-IF

Evaluate and Graph Piecewise Functions End Behavior and Asymptotes of Rational Functions Introduction to Limits — Evaluating Limits Numerically and Algebraically Limits at Infinity — Horizontal Asymptotes via Limits Continuity — Definition and Types of Discontinuity Explain the Concept of a Limit

F-BF

Inverse Trig Functions — Evaluate arcsin, arccos, arctan Compose Functions with Their Inverses — f(f⁻¹(x)) = x

F-TF

Sum and Difference Identities — sin(A±B), cos(A±B)Double-Angle and Half-Angle Identities Solve Trigonometric Equations on [0, 2π]Law of Sines — Solve Oblique Triangles Law of Cosines — Solve SAS and SSS Triangles Area of a Triangle Using Trig — (1/2)ab sin C

G-GPE

Parabola — Standard Form and Focus-Directrix Ellipse — Standard Form, Foci, and Key Features Hyperbola — Standard Form, Foci, and Asymptotes Parametric Equations — Graph and Convert to Rectangular

F-LE

Logistic and Exponential Models — Fit and Predict Solve Logarithmic Equations

S-MD

Expected Value — Discrete Probability Distributions Binomial Distribution — Probability and Expected Value Geometric Distribution — First Success Probability Normal Distribution Probability Calculations

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