Advanced Calculus BC homeschool curriculum.
Your student extends calculus to series, parametric equations, polar coordinates, and vector-valued functions.
A personalized lesson from the course
The same motion can look difficult or simple depending on whether position is described with rectangular, parametric, or polar coordinates.
- Lesson
- Coordinates Are a Choice
- Goal
- Choose a representation that matches a motion question and interpret derivatives, area, or arc length in that representation.
How a lesson works
An 11-minute reading
This example lesson comes from the unit on parametric, polar, and vector motion. It moves from “Representation changes the work” to “Derivatives keep their meaning” and builds to one idea: a coordinate system is a question about what the problem wants to make easy to see.
Help inside the reading
Our Always-On Mentor stays beside “Coordinates Are a Choice” the whole way through, answering questions about any highlighted line and, during the Reading Check, clarifying a question without giving the answer away.
A check halfway through
Your child answers “Why might a parametric model be better than y = f(x) for motion?” before reading on, and the Reading Check at the end asks new questions.
A project your child hands in
Model a designed or observed path in rectangular, parametric, and polar forms, then compare which representation answers each question best.
- Task
- Use derivatives or area to make a claim about motion and explain the coordinate choice
- Hand in
- Three-representation model with graph, calculations, and coordinate-choice reflection
See the reasoning behind the answer
Your student needs to decide which representation fits a problem and explain convergence, rather than memorize another procedure. We keep earlier differentiation and integration in the practice while teaching those extensions, so weak algebra or an unfinished prerequisite stays visible. Advanced Calculus BC runs through 18 units and 72 skills, starting with limits and continuity, differentiation, and applications of differentiation.
- Cumulative mixed problem sets
- Parametric, polar, and vector analyses
- Series arguments and corrected free responses
Units and skills
Advanced Calculus BC18 units · 72 skills
Limits and continuity4 skills
- Implement an appropriate mathematical process for Limits and continuity
- Connect analytical, graphical, numerical, and verbal representations of Limits and continuity
- Justify mathematical conclusions involving Limits and continuity
- Communicate reasoning about Limits and continuity with precise notation
Differentiation4 skills
- Implement an appropriate mathematical process for Differentiation
- Connect analytical, graphical, numerical, and verbal representations of Differentiation
- Justify mathematical conclusions involving Differentiation
- Communicate reasoning about Differentiation with precise notation
Applications of differentiation4 skills
- Implement an appropriate mathematical process for Applications of differentiation
- Connect analytical, graphical, numerical, and verbal representations of Applications of differentiation
- Justify mathematical conclusions involving Applications of differentiation
- Communicate reasoning about Applications of differentiation with precise notation
Integration and accumulation4 skills
- Implement an appropriate mathematical process for Integration and accumulation
- Connect analytical, graphical, numerical, and verbal representations of Integration and accumulation
- Justify mathematical conclusions involving Integration and accumulation
- Communicate reasoning about Integration and accumulation with precise notation
Differential equations4 skills
- Implement an appropriate mathematical process for Differential equations
- Connect analytical, graphical, numerical, and verbal representations of Differential equations
- Justify mathematical conclusions involving Differential equations
- Communicate reasoning about Differential equations with precise notation
Applications of integration4 skills
- Implement an appropriate mathematical process for Applications of integration
- Connect analytical, graphical, numerical, and verbal representations of Applications of integration
- Justify mathematical conclusions involving Applications of integration
- Communicate reasoning about Applications of integration with precise notation
Parametric equations4 skills
- Implement an appropriate mathematical process for Parametric equations
- Connect analytical, graphical, numerical, and verbal representations of Parametric equations
- Justify mathematical conclusions involving Parametric equations
- Communicate reasoning about Parametric equations with precise notation
Polar coordinates4 skills
- Implement an appropriate mathematical process for Polar coordinates
- Connect analytical, graphical, numerical, and verbal representations of Polar coordinates
- Justify mathematical conclusions involving Polar coordinates
- Communicate reasoning about Polar coordinates with precise notation
Vector-valued functions4 skills
- Implement an appropriate mathematical process for Vector-valued functions
- Connect analytical, graphical, numerical, and verbal representations of Vector-valued functions
- Justify mathematical conclusions involving Vector-valued functions
- Communicate reasoning about Vector-valued functions with precise notation
Infinite sequences and series4 skills
- Implement an appropriate mathematical process for Infinite sequences and series
- Connect analytical, graphical, numerical, and verbal representations of Infinite sequences and series
- Justify mathematical conclusions involving Infinite sequences and series
- Communicate reasoning about Infinite sequences and series with precise notation
Mathematical justification4 skills
- Implement an appropriate mathematical process for Mathematical justification
- Connect analytical, graphical, numerical, and verbal representations of Mathematical justification
- Justify mathematical conclusions involving Mathematical justification
- Communicate reasoning about Mathematical justification with precise notation
Cumulative free response4 skills
- Implement an appropriate mathematical process for Cumulative free response
- Connect analytical, graphical, numerical, and verbal representations of Cumulative free response
- Justify mathematical conclusions involving Cumulative free response
- Communicate reasoning about Cumulative free response with precise notation
Multiple quantitative representations4 skills
- Implement an appropriate mathematical process for Multiple quantitative representations
- Connect analytical, graphical, numerical, and verbal representations of Multiple quantitative representations
- Justify mathematical conclusions involving Multiple quantitative representations
- Communicate reasoning about Multiple quantitative representations with precise notation
Graph construction and interpretation4 skills
- Implement an appropriate mathematical process for Graph construction and interpretation
- Connect analytical, graphical, numerical, and verbal representations of Graph construction and interpretation
- Justify mathematical conclusions involving Graph construction and interpretation
- Communicate reasoning about Graph construction and interpretation with precise notation
Written mathematical justification4 skills
- Implement an appropriate mathematical process for Written mathematical justification
- Connect analytical, graphical, numerical, and verbal representations of Written mathematical justification
- Justify mathematical conclusions involving Written mathematical justification
- Communicate reasoning about Written mathematical justification with precise notation
Advanced Calculus BC cumulative assessment4 skills
- Implement an appropriate mathematical process for Advanced Calculus BC cumulative assessment
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus BC cumulative assessment
- Justify mathematical conclusions involving Advanced Calculus BC cumulative assessment
- Communicate reasoning about Advanced Calculus BC cumulative assessment with precise notation
Advanced Calculus BC exam-mode practice4 skills
- Implement an appropriate mathematical process for Advanced Calculus BC exam-mode practice
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus BC exam-mode practice
- Justify mathematical conclusions involving Advanced Calculus BC exam-mode practice
- Communicate reasoning about Advanced Calculus BC exam-mode practice with precise notation
Advanced Calculus BC reflection and transfer4 skills
- Implement an appropriate mathematical process for Advanced Calculus BC reflection and transfer
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus BC reflection and transfer
- Justify mathematical conclusions involving Advanced Calculus BC reflection and transfer
- Communicate reasoning about Advanced Calculus BC reflection and transfer with precise notation
Questions parents ask
How does Advanced Calculus BC prepare my student for AP Calculus BC?
- Advanced Calculus BC follows the AP Calculus BC framework unit by unit, as its skill tree shows. Your teen explains and applies the ideas in written responses and projects, so the work shows which skills are secure and which need more practice.
How does a homeschooler register for an AP exam?
- An AP coordinator at an AP-authorized local school arranges registration. Use College Board’s homeschool exam guidance to find a host school. That school sets its deadlines and outside-student policies; its coordinator orders the exam, collects fees, and tells your child where and when to test.
Which course title goes on a homeschool transcript?
- Advanced Calculus BC, not AP Calculus BC. The AP designation requires College Board Course Audit authorization of the course, which framework alignment does not give. We generate the transcript with that title, ready for you to sign as homeschool administrator.
How can AP scores earn college credit?
- Colleges award credit under their own AP score policies. College Board reports scores on a 1–5 scale, separately from our coursework grades; check the college’s required score and whether it grants credit, placement, or both.
Advanced Calculus BC, with the teaching and records handled
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