South Carolina High School Calculus Curriculum Overview
Calculus is one of the most important math courses South Carolina high school students will take. It builds directly on algebra, pre-calculus, and trigonometry skills, introducing powerful tools for analyzing change and accumulation. StudyPug covers every major topic in high school Calculus, aligned to SC College Career Ready Standards.
Limits and Continuity
Students begin by understanding limits graphically and numerically, evaluating basic limits using substitution, and determining continuity at a point. They also learn to identify types of discontinuities and describe end behavior of functions using limits at infinity. These foundational concepts are essential for everything that follows in Calculus.
Derivatives
The derivative unit is at the heart of high school Calculus. South Carolina students learn to:
- Understand the derivative as a 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
- Find derivatives of implicitly defined functions
- Write equations of tangent lines and use linear approximation
Applications of Derivatives
Once students understand how to find derivatives, they apply them to real problems. This includes finding critical points, local maxima and minima, and solving optimization problems. Students also analyze increasing and decreasing behavior, concavity, and learn to sketch curves using derivative information. Related rates problems and applications to velocity and acceleration are also covered.
Integrals and the Fundamental Theorem of Calculus
The second half of Calculus focuses on integration. Students find antiderivatives of basic functions, approximate definite integrals using left, right, and midpoint Riemann sums, and apply the Fundamental Theorem of Calculus to evaluate definite integrals. The substitution method is introduced for more complex integrals.
Applications of Integrals
Students use integrals to solve real-world problems including:
- Finding area under curves and between curves
- Calculating displacement and distance from velocity functions
- Finding the average value of a function over an interval
StudyPug makes each of these topics approachable with short video lessons, worked examples, and practice problems, so South Carolina students can build confidence at every step of their Calculus course.
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