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High School Calculus

South Dakota High School Calculus Curriculum

Video lessons and practice for every High School Calculus topic. Aligned to South Dakota Math Standards so students stay on track.

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ID

Standard

StudyPug Topic

Concept of Limits

Understand limits graphically and numerically; evaluate basic limits using substitution

Continuity

Determine continuity at a point and identify types of discontinuities

Limits at Infinity

Find limits at infinity and describe end behavior of functions

Derivative Concept

Understand derivative as rate of change and slope of tangent line

Derivative Rules

Find derivatives using power rule; product rule; quotient rule; and chain rule

Derivatives of Special Functions

Find derivatives of trigonometric; exponential; and logarithmic functions

Implicit Differentiation

Find derivatives of implicitly defined functions

Tangent Lines

Find equations of tangent lines and use for linear approximation

Critical Points and Extrema

Find critical points; local maxima and minima; and solve optimization problems

Curve Analysis

Analyze increasing/decreasing behavior and concavity; sketch curves using derivatives

Related Rates

Solve related rates problems in real-world contexts

Motion and Rates

Apply derivatives to velocity; acceleration; and other rate problems

Antiderivatives

Find antiderivatives of basic functions and use initial conditions

Riemann Sums

Approximate definite integrals using left; right; and midpoint Riemann sums

Fundamental Theorem of Calculus

Use FTC to evaluate definite integrals and find antiderivatives

Basic Integration Techniques

Use substitution method to evaluate integrals

Area Under Curves

Find area under curves and between curves using definite integrals

Average Value

Calculate average value of functions over intervals using integrals

High School Calculus in South Dakota

South Dakota high school calculus students cover a wide range of topics — from understanding limits graphically and numerically to evaluating definite integrals using the Fundamental Theorem of Calculus. StudyPug provides video lessons and practice problems for every chapter, aligned to South Dakota Math Standards.

Limits and Continuity

Students begin by exploring limits graphically and numerically, using substitution to evaluate basic limits. From there, they identify types of discontinuities, determine continuity at a point, and analyze limits at infinity to describe end behavior of functions.

Derivatives

The derivative unit covers the core rules South Dakota calculus students need: the power rule, product rule, quotient rule, and chain rule. Students also find derivatives of trigonometric, exponential, and logarithmic functions, as well as implicitly defined functions. Practical applications include finding tangent line equations and using linear approximation.

Applications of Derivatives

  • Finding critical points, local maxima, and minima
  • Solving optimization problems in real-world contexts
  • Analyzing increasing and decreasing behavior and concavity
  • Curve sketching using first and second derivative tests
  • Solving related rates problems
  • Applying derivatives to velocity and acceleration

Integrals

The integral unit introduces antiderivatives of basic functions, Riemann sums (left, right, and midpoint), and the Fundamental Theorem of Calculus. Students learn the substitution method and apply integrals to find area under curves, area between curves, displacement, distance, and the average value of a function over an interval.

How StudyPug Helps South Dakota Calculus Students

Whether students need homework help or want to get ahead, StudyPug's video lessons make every calculus topic approachable. Each lesson is 5–15 minutes and broken into short segments students can pause and replay. Practice problems after each lesson help reinforce understanding of derivatives, integrals, and limits — all aligned to what South Dakota schools teach.