Math 12 (Calculus Honors)

Course Overview

Calculus Honors is a rigorous, college-preparatory course designed to provide students with a comprehensive introduction to differential and integral calculus. This non-AP advanced course mirrors the conceptual and applied depth of AP Calculus AB, offering a foundation for students pursuing STEM majors. The curriculum is aligned with Florida B.E.S.T. benchmarks and the College Board’s core calculus themes: limits, derivatives, integrals, and the Fundamental Theorem of Calculus.

Students develop strong analytical reasoning through symbolic manipulation, graph analysis, modeling, and structured problem-solving. Emphasis is placed on connecting representations: numerical, graphical, algebraic, and verbal. Applications include physics, economics, biology, and real-world motion and accumulation models.

Learning Outcomes by Quarter

• Quarter 1: Explore limits, continuity, and the concept of instantaneous rate of change. Analyze function behavior graphically and algebraically.
• Quarter 2: Master differentiation rules and apply derivatives to optimization, motion, and curve sketching.
• Quarter 3: Develop an understanding of integration as accumulation. Use definite integrals to calculate area and solve problems involving displacement and net change.
• Quarter 4: Explore applications of integrals, basic differential equations, volume by revolution, and the Fundamental Theorem of Calculus.

Instructional Methods

Instruction includes inquiry-based exploration, guided problem-solving, graphical technology (Desmos, GeoGebra, graphing calculators), and student-led explanation. Students work through advanced modeling tasks, derivation of formulas, and real-world case studies. Conceptual understanding is reinforced through multiple representations and frequent feedback.

Assessment and Grading

Category	Weight
Major Tests & Honors Projects	40%
Quizzes & Advanced Problem Sets	25%
Homework & Written Explanations	15%
Participation & Academic Discourse	10%
Portfolio & Reflection Journals	10%

Anchor Topics Justification

• Limits & Continuity: Critical for establishing the logical structure of calculus and understanding instantaneous behavior.
• Differentiation & Applications: Applies to velocity, slope, economics, biology, and physics contexts.
• Integration & Area Models: Builds conceptual understanding of accumulation and net change in a function.
• Fundamental Theorem & Modeling: Unifies differential and integral calculus and prepares for AP/college-level study.

College Board – Pre-AP/Calculus AB Alignment

Domain	Integrated Skills in Calculus Honors
Limits & Continuity	Analyzing function behavior at endpoints, jumps, and infinite limits
Differentiation	Product/quotient rules, chain rule, implicit differentiation, tangent lines
Integration	Riemann sums, net area, accumulation models
Mathematical Communication	Explaining calculus concepts verbally and in writing with clarity

Unit Overview

Quarter	Unit Title	Florida B.E.S.T. Benchmarks	College Board Focus Skills
Q1	Limits, Continuity & Intro to Derivatives	MA.912.L.1.1, MA.912.C.1.1	Concept of the derivative, limit laws
Q2	Differentiation Techniques & Applications	MA.912.C.1.2, MA.912.C.1.3	Product/quotient rule, optimization, curve analysis
Q3	Integrals & Accumulation Functions	MA.912.C.2.1, MA.912.C.2.3	Area under curve, net change theorem
Q4	FTC, Volume, Slope Fields & Models	MA.912.C.3.1, MA.912.C.3.3	Fundamental Theorem of Calculus, solids of revolution

Academic Vocabulary Matrix

Category	Key Terms	Contextual Application
Limits & Behavior	Continuity, Asymptote, Local Behavior	Used to describe the shape and motion of graphs
Derivatives	Chain Rule, Inflection Point, Critical Value	Used in motion analysis and curve sketching
Integrals	Definite Integral, Area, Riemann Sum	Used to quantify displacement and accumulation
Theorems & Modeling	Fundamental Theorem, Slope Field, Optimization	Used in advanced modeling, physics, and business applications