High School Calculus AB Course Syllabus (Texas TEKS-Aligned)

Course Overview

This course follows the Texas Essential Knowledge and Skills (TEKS) for Calculus, focusing on the concepts, applications, and methods of differential and integral calculus. It prepares students for college-level calculus by emphasizing conceptual understanding, behavioral modeling of functions, and multi-representational approaches (algebraic, graphical, numerical, and verbal). [1, <* href="https://www.google.com/goto?url=CAESrAEB7keqTTR5Gsc78uGjsMzVpZJipu_lPPx6zqXGJSqO0TP7HgN51hiDnFwBXtAQ3QOdQCv9Y5cYownXA0YID8F6QqV20IcEG-Oa_GOYjUeea4kJxtgpU2srVixg3l-TGDn_rU-CNX14zfLZMgkuZaCEGeGu7QuZP5h-LD3y6AoZDxZmsYd2YvLb5NWqkHxfkc8tVdUvUUxb8oGUjm7QTpoQM6Cvt9T7Q9CncXgX">2, <* href="https://www.google.com/goto?url=CAESiwEB7keqTaMRHc8d3oY2sNKUNsNsnU1aXlowdppbzWAbjKzUkQZwZxIhig1FLeHH2uen9be37bw6JCgbgXAV7lVFqEfKF96A1BDH4lyoz8OHgoq92Ac0_DekdpnNZMqCzNMYdS1pEDF9f4VAEzfOf60SaRK63bNz1uKP_094-U_fsjPOX8jTVGLxKBSx">3]

Grading Period 1: Limits, Continuity, and Foundations

• TEKS Focus: §111.45.(c)(1) Mathematical process standards; §111.45.(c)(2) Limits and continuity.
• Core Concepts:
  • Graphical and numerical estimation of limits.
  • Algebraic properties and evaluation of limits.
  • One-sided limits and limits involving infinity.
  • Definition and conditions of continuity at a point and over an interval.
  • The Intermediate Value Theorem (IVT). [1, <* href="https://www.google.com/goto?url=CAESaQHuR6pN6eAUVUr-fqFJfZxONTnQEVlvFMCh4o8VrXNAn6hrvEdmLkMPH3fi6iLNO7vRqjhCdXoPXFMrT0RQyCTTZ5DwFryCT6BWsotLSYB5mHLqwJ5ZXWnwWEdjKoYm4Rh0uW9mu-mdnQ==">2]

Grading Period 2: Introduction to the Derivative

• TEKS Focus: §111.45.(c)(3) Derivatives and their applications.
• Core Concepts:
  • Average vs. instantaneous rates of change.
  • Defining the derivative as a limit and as a tangent line slope.
  • Differentiability and its relationship to continuity.
  • Basic derivative rules (Power, Product, Quotient, and Constant Multiple rules).
  • Derivatives of trigonometric, exponential, and logarithmic functions.
  • The Chain Rule and implicit differentiation. [1, <* href="https://www.google.com/goto?url=CAESTgHuR6pNNGT9iCABWMNHY7jpoR9-5g8AjUkTqaOYDfzDsgYlKUPDmPIAbiPYych6MaLC3ZUqozllIgV521xaHou7dOEGxvKQsfQYDIyRqw==">2]

Grading Period 3: Applications of the Derivative

• TEKS Focus: §111.45.(c)(3) Derivatives and their applications.
• Core Concepts:
  • The Mean Value Theorem (MVT) and Extreme Value Theorem (EVT).
  • Justifying behavior of functions using first and second derivatives (Intervals of increase/decrease, concavity).
  • Locating relative (local) and absolute (global) extrema.
  • Optimization problems.
  • Related rates of change. [1, <* href="https://www.google.com/goto?url=CAESTgHuR6pNAEmYsg-iImwDyKRB-7xqJ7XrKpqU4qDZf-Zcbd9_lUZ48DT1EKYAJFuy5NsT0pr6lqksKIo3wB6AJqMc71tMKSrajsFNZBqL8w==">2]

Grading Period 4: Introduction to Integration and Accumulation

• TEKS Focus: §111.45.(c)(4) Integrals and their applications.
• Core Concepts:
  • Definite integrals modeled as area under a curve.
  • Approximating area using Riemann sums (left, right, midpoint) and trapezoidal sums.
  • The Fundamental Theorem of Calculus (Parts 1 and 2).
  • Antiderivatives and indefinite integration.
  • Integration techniques, including u-substitution. [1, <* href="https://www.google.com/goto?url=CAESVwHuR6pNLMuYqXe5q8e_ln8LgRQRUWzaCl4Bqvd5IE-CwRpB8eeyZQ8DSCacDmc5MLTiBSbCX-2R9U0bKMdT6ZzbXB8P4PrRZt8pIJ2F8N4FUBOzSXejFA==">2, <* href="https://www.google.com/goto?url=CAESXQHuR6pN0gjHF-vcN6R2o6t2_3idNF6p3oaRA5MoD90NJtOr7UCx9hqOLm877-V8VDk8-5DUgZ4IeSSzv_B2VWqn8jpafRYB5lJgQTsQdUZ7OuwXqQMspMN7V11QWg==">3]

Grading Period 5: Applications of Integration & Differential Equations

• TEKS Focus: §111.45.(c)(4) Integrals and their applications.
• Core Concepts:
  • Accumulation functions and net change.
  • Area between two curves.
  • Volumes of solids with known cross-sections.
  • Volumes of solids of revolution (Disk and Washer methods).
  • Introduction to differential equations and slope fields.
  • Separable differential equations and exponential growth models. [1, <* href="https://www.google.com/goto?url=CAESYQHuR6pN90ZCkf2nyIG7mzJjbZUQLHvSxYuc3X_uVx5k4xp5pymnj2v7C55w262DiIAcvMJhzAbZNRxwlX9sxMWcwDstgr7cNCJGArLjSdUyAYprHjwOODboEKOGJCgCjf0=">2]

Grading Period 6: Comprehensive Review and Exam Preparation

• TEKS Focus: Integration of all previously covered standards [§111.45.(c)(1)-(4)].
• Core Concepts:
  • Synthesis of limits, derivatives, and integrals.
  • Practice with multiple-choice and free-response question formats.
  • Application of theorems to contextual, analytical, and tabular problems.
  • Final course evaluations and diagnostic review. [1]