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High School Calculus

Alaska High School Calculus Curriculum

Video lessons and practice for every High School Calculus topic. Aligned to Alaska Mathematics Standards. Master limits, derivatives, and integrals.

Alaska 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 Topics Covered

StudyPug's High School Calculus course covers every major topic Alaska students encounter, from foundational limit concepts to advanced integration techniques. Each chapter is broken into focused lessons so students can target exactly what they need help with.

  • Limits: Understand limits graphically and numerically, evaluate using substitution, and analyze end behavior at infinity.
  • Continuity: Determine continuity at a point and identify types of discontinuities in functions.
  • Derivatives: Apply the power rule, product rule, quotient rule, and chain rule to find derivatives efficiently.
  • Derivative Applications: Find tangent line equations, solve optimization problems, analyze curve behavior, and work through related rates problems.
  • Special Derivatives: Differentiate trigonometric, exponential, logarithmic, and implicitly defined functions.
  • Integrals: Find antiderivatives, apply the Fundamental Theorem of Calculus, and use substitution to evaluate integrals.
  • Integration Applications: Calculate area under and between curves, find displacement and distance from velocity functions, and compute average values over intervals.

How StudyPug Helps Alaska Calculus Students

Calculus is one of the most challenging courses in high school. StudyPug breaks every topic into short, clear video lessons that students can watch at home, pause when needed, and replay as many times as it takes to understand. After each lesson, practice problems help lock in the concepts.

Whether a student is struggling with derivatives or preparing for an AP Calculus exam, StudyPug provides the support they need — aligned to Alaska Mathematics Standards — so no topic gets left behind.

Calculus Skills That Carry Forward

Mastering high school calculus opens doors to college-level math, engineering, physics, and economics. The skills built in this course — logical reasoning, problem-solving, and mathematical precision — are foundational for any STEM path. StudyPug makes sure Alaska students build those skills one clear lesson at a time.