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Hawaii High School Calculus Curriculum

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

Hawaii 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

Hawaii High School Calculus: Topics and Skills

Calculus is one of the most important math courses Hawaii high school students will take. It builds the foundation for college-level STEM programs and standardized tests like the AP Calculus AB and BC exams. StudyPug covers every major topic aligned to Hawaii Common Core Standards Math, so students always know they're studying the right material.

Limits and Continuity

Students begin Calculus by understanding limits graphically and numerically. They learn how to evaluate limits using substitution, identify types of discontinuities, and describe end behavior using limits at infinity. These concepts form the backbone of everything that follows in the course.

Derivatives

The derivative unit covers the definition of the derivative as a rate of change and slope of a tangent line. Students apply the power rule, product rule, quotient rule, and chain rule to find derivatives efficiently. They also differentiate trigonometric, exponential, and logarithmic functions, as well as implicitly defined functions.

  • Tangent line equations and linear approximation
  • Critical points, local maxima and minima
  • Optimization problems in real-world contexts
  • Curve sketching using increasing/decreasing behavior and concavity
  • Related rates and motion problems involving velocity and acceleration

Integrals

The integral unit introduces antiderivatives, Riemann sums, and the Fundamental Theorem of Calculus. Students learn substitution to evaluate more complex integrals and apply definite integrals to find area under and between curves.

  • Left, right, and midpoint Riemann sums
  • Using the FTC to evaluate definite integrals
  • Displacement and distance from velocity functions
  • Average value of a function over an interval

How StudyPug Supports Hawaii Calculus Students

StudyPug provides video lessons and practice problems for every topic listed above. Each lesson is short, focused, and can be paused or replayed as many times as needed. Whether your student is preparing for an AP Calculus exam, catching up after a tough test, or just trying to finish tonight's homework, StudyPug is available on any device, anytime.