SC High School Calculus Curriculum

SC 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 find limits at infinity to describe end behavior.
• Derivatives and differentiation rules: Grasp the derivative as rate of change and slope of a tangent line, then apply the power rule, product rule, quotient rule, and chain rule to a wide range of functions including trigonometric, exponential, and logarithmic forms.
• Implicit differentiation and linear approximation: Find derivatives of implicitly defined functions and use tangent line equations for linear approximation.
• Applications of derivatives: Locate critical points, local maxima and minima, 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 basic integration: Find antiderivatives of basic functions using initial conditions and use the substitution method to evaluate integrals.
• Definite integrals and the Fundamental Theorem of Calculus: Approximate definite integrals with left, right, and midpoint Riemann sums, then use the Fundamental Theorem of Calculus to evaluate them exactly.
• Area, displacement, and average value: Find area under curves and between curves, calculate displacement and distance from velocity functions, and determine the average value of a function over an interval.

How StudyPug Helps SC High School Calculus Students

When a student gets stuck on a related rates problem or cannot follow the steps in a chain rule example, StudyPug lets them replay a focused video lesson and then work through practice problems with immediate feedback. Every lesson is organized by strand, so finding the right explanation takes seconds rather than a full textbook search.

Students preparing for the AP Calculus exam or simply trying to keep pace with a demanding South Carolina high school course can move at their own speed, revisiting limits one evening and working ahead on integration the next without losing their place.

Aligned to SC High School Calculus Curriculum

All StudyPug calculus content is built around the South Carolina College- and Career-Ready Standards, covering the same strands and sequencing that South Carolina teachers follow in the classroom, so lessons connect directly to what students see on tests and assignments.