DC High School Calculus Curriculum
Give your child the support they need to keep up with DC high school calculus. Our lessons cover limits, derivatives, and integrals exactly as local schools teach them.
About High School District of Columbia Calculus
The District of Columbia follows DC academic standards, organizing calculus around limits, derivatives, and integration. Students work through evaluating limits graphically and numerically, applying differentiation rules including the power, product, quotient, and chain rules, and analyzing functions using critical points and concavity. Integration covers Riemann sums, the Fundamental Theorem of Calculus, substitution, and real-world applications such as area, displacement, and average value. StudyPug provides video lessons and practice problems for every strand.
- Limits and continuity, differentiation rules, curve analysis, and integration techniques
- Video lessons covering every calculus topic from limits to definite integrals
- Practice problems and worked examples for derivatives, optimization, and integration applications
- Content aligned to DC academic standards for high school calculus
Curriculum topics by strand
Lessons and practice organized by strand and aligned to DC academic standards for high school calculus.
DC High School Calculus Topics
- Limits and continuity: Understand limits graphically and numerically, evaluate basic limits using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior.
- Derivatives and differentiation rules: Understand the derivative as rate of change and slope of a tangent line; apply the power rule, product rule, quotient rule, and chain rule; differentiate trigonometric, exponential, and logarithmic functions; and find derivatives of implicitly defined functions.
- Applications of derivatives: Find equations of tangent lines and use linear approximation; locate critical points and solve optimization problems; analyze increasing and decreasing behavior and concavity to sketch curves; solve related rates problems; and apply derivatives to velocity and acceleration.
- Antiderivatives and integration: Find antiderivatives of basic functions using initial conditions and approximate definite integrals with left, right, and midpoint Riemann sums.
- The Fundamental Theorem of Calculus and techniques: Use the FTC to evaluate definite integrals, apply the substitution method, and find area under and between curves.
- Applications of integration: Use integrals to find displacement and distance from velocity functions and calculate the average value of a function over an interval.
How StudyPug Helps DC High School Calculus Students
When a student gets stuck on a related rates problem or cannot see why the chain rule applies, StudyPug lets them replay a focused video lesson at their own pace, then work through practice problems with step-by-step explanations until the idea clicks. Every topic - from evaluating a basic limit to setting up a definite integral for area between curves - is covered in the same order DC teachers follow.
Students can also use StudyPug to prepare ahead of class, review before a test, or fill gaps from earlier units. The ability to move between limits, derivatives, and integration topics freely means a student never has to wait for help on exactly what they need right now.
Aligned to DC High School Calculus Curriculum
StudyPug content for high school calculus is built around DC academic standards, covering every major strand from limit evaluation and continuity through differentiation rules, curve analysis, and integration applications. Families can be confident that the lessons and practice problems match what students encounter in their DC high school classrooms.
Written by the StudyPug Math Team
Last updated June 5, 2026
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