Math 12 (Calculus Standard)
Course Overview
Calculus Standard is a full-year introductory course in differential and integral calculus for students pursuing college programs in science, engineering, business, or economics. Unlike the AP Calculus track, this course focuses on conceptual understanding, real-world application, and a balanced development of algebraic and graphical fluency. It is aligned with Florida B.E.S.T. benchmarks and College Board SAT/Pre-AP mathematical practices.
Students explore the foundational concepts of limits, rates of change, derivatives, and integrals with attention to units, function behavior, and visual interpretation. The course emphasizes application over formal theory and supports readiness for college placement exams and introductory calculus at the university level.
Learning Outcomes by Quarter
- Quarter 1: Review functions and graphs, explore limits and continuity, and understand instantaneous rates of change.
- Quarter 2: Learn techniques of differentiation, interpret derivatives graphically and numerically, and apply them to motion, slope, and optimization problems.
- Quarter 3: Understand the concept of area under a curve, develop the definite integral, and apply integration to real-world contexts.
- Quarter 4: Extend integral applications to volume, accumulation, and basic differential equations.
Instructional Methods
Instruction combines graph-based interpretation, conceptual lectures, real-world problem-solving, and technology integration (e.g., Desmos, GeoGebra, graphing calculators). Group investigations, lab-style modeling tasks, and cumulative review cycles are used to support retention and deepen insight. This course maintains algebraic accessibility while encouraging abstract thinking.
Assessment and Grading
| Category | Weight |
|---|---|
| Major Tests & Projects | 40% |
| Quizzes & Concept Reviews | 25% |
| Homework & Practice Sets | 20% |
| Class Engagement | 10% |
| Reflections & Portfolios | 5% |
Anchor Topics Justification
- Limits & Continuity: Establish foundational reasoning for all of calculus and prepares students for AP or college-level progression.
- Derivatives & Rate of Change: Applicable in physics, economics, biology, and business decision-making.
- Integrals & Area: Connects geometry, accumulation, and real-world application in science and engineering.
- Graphical Analysis: Promotes deep understanding of function behavior and aligns with SAT and data fluency demands.
College Board – SAT/Pre-AP Crosswalk
| Domain | Integrated Skills in Calculus Standard |
|---|---|
| Functions & Modeling | Analyzing growth, decay, and motion with graphs, tables, and equations |
| Quantitative Reasoning | Applying rates, units, and graphical interpretation in real contexts |
| Algebraic Manipulation | Using slope, difference quotients, and simplifying expressions before calculus |
| Conceptual Thinking | Explaining change, limits, and accumulation in everyday terms |
Unit Overview
| Quarter | Unit Title | Florida B.E.S.T. Benchmarks | College Board Focus Skills |
|---|---|---|---|
| Q1 | Functions, Limits & Continuity | MA.912.F.1.1, MA.912.L.1.1 | Limit behavior, graphs, local linearity |
| Q2 | Derivatives & Their Applications | MA.912.DP.1.1, MA.912.C.1.1 | Rate of change, optimization, tangents |
| Q3 | Integrals & Area Under Curves | MA.912.C.2.1, MA.912.C.2.3 | Definite integral, area interpretation |
| Q4 | Volume, Accumulation & Slope Fields | MA.912.C.2.4, MA.912.C.3.1 | Revolutions, motion, basic differential equations |
Academic Vocabulary Matrix
| Category | Key Terms | Contextual Application |
|---|---|---|
| Limits & Continuity | Limit, Asymptote, Continuity | Used to explore function behavior and rates |
| Differentiation | Derivative, Slope, Instantaneous Rate | Used in motion and optimization problems |
| Integration | Antiderivative, Area, Definite Integral | Used in modeling accumulation and displacement |
| Applied Calculus | Velocity, Maximum, Accumulation | Used in physics, business, and environmental modeling |