MontanaMontana High School Calculus Curriculum
Video lessons and practice for every High School Calculus topic. Aligned to Montana Math Content Standards. Get help with limits, derivatives, and integrals anytime.
Montana 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 |
High School Calculus in Montana
Montana high school calculus follows the Montana Math Content Standards, preparing students for college-level mathematics and STEM pathways. The course spans foundational concepts like limits and continuity through differentiation, integration, and their applications in real-world problems.
Limits and Continuity
Students begin by understanding limits graphically and numerically, evaluating them using substitution, and identifying types of discontinuities. They also explore limits at infinity to describe end behavior of functions — skills that underpin all of calculus.
Derivatives
Differentiation is a core unit in high school calculus. Students learn the power rule, product rule, quotient rule, and chain rule, then extend these to trigonometric, exponential, and logarithmic functions. Implicit differentiation and tangent line equations round out this section.
Applications of Derivatives
Montana calculus students apply derivatives to find critical points, local maxima and minima, and solve optimization problems. Curve sketching, related rates, and velocity and acceleration problems show students how derivatives describe real-world change.
Integrals and the Fundamental Theorem of Calculus
The integration unit covers antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, and substitution. Students use definite integrals to find area under curves, area between curves, displacement, distance, and average value of a function.
- Limits and continuity
- Differentiation rules and techniques
- Applications of derivatives: optimization and related rates
- Riemann sums and definite integrals
- Integration techniques and applications