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Calculus

Wisconsin High School Calculus Curriculum

Video lessons and practice for every Calculus topic. Aligned to Wisconsin Standards for Math. Get help with limits, derivatives, and integrals anytime.

Wisconsin High School Calculus Curriculum | StudyPugHelp

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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 Wisconsin

Calculus is one of the most important math courses Wisconsin high school students take. It introduces the ideas of limits, derivatives, and integrals — tools that describe how things change and accumulate. StudyPug covers every major Calculus topic with video lessons and practice problems aligned to Wisconsin Standards for Math.

Limits and Continuity

Students start by understanding limits graphically and numerically. They learn to evaluate limits using substitution, identify types of discontinuities, and analyze end behavior of functions as they approach infinity. These foundational ideas are essential for everything that follows in Calculus.

Derivatives

The derivative section covers the definition of the derivative as a rate of change and slope of a tangent line. Students learn differentiation rules including the power rule, product rule, quotient rule, and chain rule. They also find derivatives of trigonometric, exponential, and logarithmic functions, as well as implicitly defined functions.

Applications of Derivatives

Once students can find derivatives, they apply them to real problems. Topics include finding equations of tangent lines, linear approximation, identifying critical points, solving optimization problems, analyzing increasing and decreasing behavior, and sketching curves. Students also solve related rates problems and connect derivatives to velocity and acceleration.

Integrals

The integral section begins with antiderivatives and moves into Riemann sums for approximating definite integrals. Students use the Fundamental Theorem of Calculus to evaluate definite integrals and apply the substitution method to more complex integrals.

Applications of Integrals

Students use integrals to find areas under curves and between curves, calculate displacement and distance from velocity functions, and find the average value of a function over an interval. These applications connect Calculus to physics, engineering, and other real-world contexts.

  • Limits and continuity — graphical, numerical, and algebraic approaches
  • Derivatives — all major differentiation rules and function types
  • Optimization, curve sketching, and related rates
  • Antiderivatives, Riemann sums, and the Fundamental Theorem of Calculus
  • Area, displacement, and average value using definite integrals