West Virginia Calculus Curriculum

Video lessons and practice for every Calculus topic. Aligned to WV College Career Ready Standards Math so West Virginia students can keep up and get ahead.

West Virginia 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

West Virginia Calculus: What Students Learn

West Virginia Calculus courses follow the WV College Career Ready Standards Math and cover three major areas: limits and continuity, differential calculus, and integral calculus. Each unit builds on the one before it, so students who master early concepts find the later material much easier to handle.

Limits and Continuity

Students begin by understanding limits graphically and numerically, then learn to evaluate limits using substitution. From there, they study continuity at a point, types of discontinuities, and limits at infinity to describe end behavior of functions. These foundational skills are essential for everything that follows in Calculus.

Derivatives and Differentiation

The derivative unit introduces the concept of rate of change and the slope of a tangent line. West Virginia students learn to apply 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.

  • Power, product, quotient, and chain rules
  • Derivatives of trig, exponential, and logarithmic functions
  • Implicit differentiation
  • Tangent lines and linear approximation

Applications of Derivatives

Once students can find derivatives, they apply them to real-world problems. Topics include finding critical points, local maxima and minima, and solving optimization problems. Students also analyze increasing and decreasing behavior, concavity, and use derivatives to sketch curves. Related rates and velocity and acceleration problems round out this section.

Integrals and the Fundamental Theorem of Calculus

The integration unit starts with antiderivatives and initial conditions, then moves to Riemann sums for approximating definite integrals. The Fundamental Theorem of Calculus connects differentiation and integration. Students learn substitution, how to find area under and between curves, displacement and distance from velocity functions, and average value of a function over an interval.

  • Left, right, and midpoint Riemann sums
  • Fundamental Theorem of Calculus (Parts 1 and 2)
  • U-substitution
  • Area between curves
  • Displacement vs. distance from velocity
  • Average value of a function

How StudyPug Helps West Virginia Calculus Students

StudyPug covers every topic listed above with video lessons and practice problems aligned to WV College Career Ready Standards Math. Whether a West Virginia student is working through limits for the first time or preparing for an AP Calculus exam, StudyPug provides the step-by-step support they need to succeed.