Calculus Honors Study Guide
6 units with lessons, worked examples, graphs, and practice PDFs.
Units
Limits and Continuity
The vocabulary the rest of calculus is written in. A limit describes approach rather than arrival, which is why it can exist where the function does not.
5 lessons · Practice PDFs →
The Derivative and Differentiation Rules
The derivative is defined as a limit and then made practical by rules. Building it from the difference quotient once is what makes the rules feel like shortcuts rather than magic.
4 lessons · Practice PDFs →
Applications of Differentiation
Where the rules become arguments. Extremes, shape, optimization, and related rates all ask the student to justify a conclusion from derivative evidence.
5 lessons · Practice PDFs →
Integrals and the Fundamental Theorem
The integral arrives twice: as an accumulation built from Riemann sums, and as the reverse of differentiation. The Fundamental Theorem is what joins the two.
4 lessons · Practice PDFs →
Applications of Integration
The graded skill is the setup, not the antiderivative. Almost every lost mark here comes from the diagram, the slice, or the choice of variable.
4 lessons · Practice PDFs →
Techniques of Integration and Differential Equations
The honors extension. Recognising which technique an integrand calls for is the skill; differential equations then turn integration back into modeling.
4 lessons · Practice PDFs →
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