Advanced Calculus AB homeschool curriculum.
Your student studies limits, derivatives, and integrals through graphs, calculations, and applications.
A personalized lesson from the course
A changing quantity can ask both how fast it is moving now and how much has accumulated; derivatives and integrals answer related but different questions.
- Lesson
- Two Questions, One Changing System
- Goal
- Use a derivative to interpret local behavior and an accumulation function to answer a second question about the same system.
How a lesson works
An 11-minute reading
This example lesson comes from the unit on derivatives, accumulation, and model interpretation. It moves from “Local change needs a unit” to “Accumulation answers a different question” and builds to one idea: calculus becomes coherent when the local story and the accumulated story remain connected to the same quantity.
Help inside the reading
Our Always-On Mentor stays beside “Two Questions, One Changing System” 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 can a rate and an accumulated total not be used interchangeably?” before reading on, and the Reading Check at the end asks new questions.
A project your child hands in
Use a rate model for people entering a service queue to explain both a momentary surge and the total load over a time window.
- Task
- Use derivatives and accumulation to make a staffing recommendation with assumptions visible
- Hand in
- Annotated calculus model with local-rate interpretation, accumulation, and recommendation
See the reasoning behind the answer
Your student learns to explain a derivative as an instantaneous rate and an integral as accumulated change. We teach those connections through limits, graphs, numerical estimates, and written arguments. Each submission is graded right away, and the written feedback shows whether they understand the calculus behind a result, including its units and meaning, rather than only following a differentiation rule. Advanced Calculus AB runs through 18 units and 72 skills, starting with limits and continuity; differentiation fundamentals; and composite, implicit, and inverse differentiation.
- Mixed calculator and no-calculator work
- Graphical, numerical, analytical, and verbal explanations
- Corrected free-response sets with complete justification
Units and skills
Advanced Calculus AB18 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
Differentiation fundamentals4 skills
- Implement an appropriate mathematical process for Differentiation fundamentals
- Connect analytical, graphical, numerical, and verbal representations of Differentiation fundamentals
- Justify mathematical conclusions involving Differentiation fundamentals
- Communicate reasoning about Differentiation fundamentals with precise notation
Composite, implicit, and inverse differentiation4 skills
- Implement an appropriate mathematical process for Composite, implicit, and inverse differentiation
- Connect analytical, graphical, numerical, and verbal representations of Composite, implicit, and inverse differentiation
- Justify mathematical conclusions involving Composite, implicit, and inverse differentiation
- Communicate reasoning about Composite, implicit, and inverse differentiation with precise notation
Contextual applications of differentiation4 skills
- Implement an appropriate mathematical process for Contextual applications of differentiation
- Connect analytical, graphical, numerical, and verbal representations of Contextual applications of differentiation
- Justify mathematical conclusions involving Contextual applications of differentiation
- Communicate reasoning about Contextual applications of differentiation with precise notation
Analytical applications of differentiation4 skills
- Implement an appropriate mathematical process for Analytical applications of differentiation
- Connect analytical, graphical, numerical, and verbal representations of Analytical applications of differentiation
- Justify mathematical conclusions involving Analytical applications of differentiation
- Communicate reasoning about Analytical 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
Multiple representations4 skills
- Implement an appropriate mathematical process for Multiple representations
- Connect analytical, graphical, numerical, and verbal representations of Multiple representations
- Justify mathematical conclusions involving Multiple representations
- Communicate reasoning about Multiple representations 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
Calculator-active reasoning4 skills
- Implement an appropriate mathematical process for Calculator-active reasoning
- Connect analytical, graphical, numerical, and verbal representations of Calculator-active reasoning
- Justify mathematical conclusions involving Calculator-active reasoning
- Communicate reasoning about Calculator-active reasoning 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 AB cumulative assessment4 skills
- Implement an appropriate mathematical process for Advanced Calculus AB cumulative assessment
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus AB cumulative assessment
- Justify mathematical conclusions involving Advanced Calculus AB cumulative assessment
- Communicate reasoning about Advanced Calculus AB cumulative assessment with precise notation
Advanced Calculus AB exam-mode practice4 skills
- Implement an appropriate mathematical process for Advanced Calculus AB exam-mode practice
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus AB exam-mode practice
- Justify mathematical conclusions involving Advanced Calculus AB exam-mode practice
- Communicate reasoning about Advanced Calculus AB exam-mode practice with precise notation
Advanced Calculus AB reflection and transfer4 skills
- Implement an appropriate mathematical process for Advanced Calculus AB reflection and transfer
- Connect analytical, graphical, numerical, and verbal representations of Advanced Calculus AB reflection and transfer
- Justify mathematical conclusions involving Advanced Calculus AB reflection and transfer
- Communicate reasoning about Advanced Calculus AB reflection and transfer with precise notation
Questions parents ask
How does Advanced Calculus AB prepare my student for AP Calculus AB?
- Advanced Calculus AB follows the AP Calculus AB 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 AB, not AP Calculus AB. 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 AB, with the teaching and records handled
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