Curriculum Map

Precalculus

Master trigonometric functions, identities, polar coordinates, vectors, conic sections, sequences, limits, and parametric equations. Desmos visualizations for every major concept. TEKS §111.42 aligned.

14 Units

Early Units (Foundation)

Building Skills

Advanced Concepts

Capstone/Synthesis

Functions: Analysis and Transformation

Review and extend function families, master transformations including shifts, reflections, and stretches, and analyze piecewise-defined functions to build the analytical foundation for Precalculus.

4-5 days

Polynomial and Rational Analysis

Analyze polynomial and rational functions through end behavior, zeros and multiplicity, the Rational Zero Theorem, and asymptotic behavior to develop fluency in curve sketching without a calculator.

5-6 days

Exponential and Logarithmic Functions

Develop fluency with exponential and logarithmic functions, their properties and graphs, the natural logarithm, solving equations involving exponentials and logs, and modeling real-world growth and decay.

5-6 days

Trigonometric Functions

Build trigonometric functions from the unit circle, master radian measure, graph sine, cosine, and tangent with transformations, and connect periodic functions to real-world phenomena.

5-6 days

Trigonometric Identities

Master the fundamental trigonometric identities — Pythagorean, reciprocal, quotient, sum/difference, double-angle, and half-angle — and develop proof-writing skills for verifying identities.

5-6 days

Trigonometric Applications

Apply trigonometry to solve oblique triangles using the Law of Sines and Law of Cosines, compute triangle areas with trigonometric formulas, and model real-world measurement problems.

4-5 days

Polar Coordinates and Complex Numbers

Explore the polar coordinate system, graph polar equations including roses, limacons, and cardioids, and convert fluently between polar and rectangular representations.

4-5 days

Vectors

Represent quantities with magnitude and direction using vectors, perform vector operations, compute dot products, and apply vectors to problems in force and motion.

4-5 days

Conic Sections

Analyze parabolas, ellipses, and hyperbolas in standard form, graph each conic section, understand eccentricity, and explore applications from satellite orbits to architecture.

5-6 days

Sequences and Series

Analyze arithmetic and geometric sequences, compute partial and infinite sums, explore convergence, and encounter mathematical induction as a proof technique.

5-6 days

Parametric Equations

Describe curves using parametric equations, eliminate the parameter to find rectangular equations, and model motion including projectile trajectories.

4-5 days

Introduction to Limits

Develop the concept of a limit intuitively and algebraically, evaluate limits using multiple techniques, analyze limits at infinity, and connect limits to continuity.

5-6 days

Rates of Change and Area Preview

Distinguish average from instantaneous rate of change, develop the tangent line concept using limits, and preview the area problem through Riemann sums.

4-5 days

Precalculus Capstone

Synthesize all Precalculus topics by comparing function families, modeling complex real-world scenarios, and building the conceptual bridges to calculus.

4-5 days

Learning Progression

This course is designed to be taken sequentially. Earlier units establish foundational concepts that later units build upon. While you can explore units in any order, following the numbered sequence provides the most coherent learning experience.