CO High School Calculus Curriculum

Colorado High School Calculus Topics

• Limits and continuity: Understand limits graphically and numerically, evaluate limits using substitution, determine continuity at a point, identify types of discontinuities, and analyze limits at infinity and end behavior.
• Derivatives and differentiation rules: Find derivatives using 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: Write equations of tangent lines, use linear approximation, find critical points and local extrema, solve optimization problems, analyze increasing and decreasing behavior and concavity, sketch curves, solve related rates problems, and apply derivatives to velocity and acceleration.
• Antiderivatives and indefinite integrals: Find antiderivatives of basic functions and apply initial conditions to determine particular solutions.
• Definite integrals and the Fundamental Theorem of Calculus: Approximate definite integrals using left, right, and midpoint Riemann sums; use the Fundamental Theorem of Calculus to evaluate definite integrals; and apply the substitution method.
• Applications of integration: Find area under curves and between curves, determine displacement and distance from velocity functions, and calculate the average value of a function over an interval.

How StudyPug Helps Colorado High School Calculus Students

When a student gets stuck on a related rates problem or cannot follow a step in a Riemann sum approximation, StudyPug lets them go back to the exact concept at their own pace. Each video lesson focuses on one idea, works through a complete example, and is followed by practice problems so the student can confirm they understood it before moving on.

Because the lessons follow the same strand order used in Colorado classrooms, a student preparing for a unit test on integration or catching up after an absence can jump straight to the relevant section without working through unrelated material first.

Aligned to Colorado High School Calculus Curriculum

Every lesson and practice problem in this course is built around the Colorado Academic Standards for high school math. The strand structure - limits and continuity, differentiation, and integration - mirrors what Colorado students encounter in class, so the support students find on StudyPug connects directly to what their teacher is covering and what will appear on school assessments.