North DakotaNorth Dakota High School Calculus Curriculum
Video lessons and practice for every Calculus topic. Aligned to North Dakota Mathematics Standards. Get help with limits, derivatives, and integrals anytime.
North Dakota High School Calculus Curriculum | StudyPugHelp
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 |
North Dakota High School Calculus: Topics and Skills
North Dakota high school Calculus follows the North Dakota Mathematics Standards and introduces students to the core ideas of differential and integral calculus. StudyPug covers every topic with video lessons and practice problems so students can build confidence at their own pace.
Limits and Continuity
Students begin by understanding limits graphically and numerically, evaluating limits using substitution, and identifying types of discontinuities. They also explore limits at infinity to describe the end behavior of functions.
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. They also find derivatives of trigonometric, exponential, and logarithmic functions, as well as implicitly defined functions.
Applications of Derivatives
- Equations of tangent lines and linear approximation
- Critical points, local maxima and minima, and optimization
- Increasing/decreasing behavior and concavity for curve sketching
- Related rates problems in real-world contexts
- Velocity, acceleration, and other rate-of-change applications
Integrals and Applications
Students learn antiderivatives, Riemann sums (left, right, and midpoint), and the Fundamental Theorem of Calculus. They use substitution to evaluate integrals and apply integrals to find area under and between curves, displacement, distance, and average value of functions.
StudyPug's Calculus course is built to support North Dakota students through every unit — from the first limit to the last integral.