MichiganMichigan High School Calculus Curriculum
Video lessons and practice for every Calculus topic. Aligned to Michigan Mathematics Standards. From limits and derivatives to integrals and real-world applications.
Michigan 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 |
Michigan High School Calculus: Topics and Skills
Michigan high school Calculus courses cover three major areas: limits and continuity, differential calculus, and integral calculus. StudyPug provides video lessons and practice problems for all 19 chapters, so students never fall behind on a topic.
Limits and Continuity
Students start by understanding limits graphically and numerically, evaluating them using substitution, and identifying different types of discontinuities. Limits at infinity and end behavior of functions are also covered — essential skills before moving into derivatives.
Derivatives
The derivative unit covers the power rule, product rule, quotient rule, and chain rule. Students also learn derivatives of trigonometric, exponential, and logarithmic functions, as well as implicit differentiation. Applications include finding tangent lines, linear approximation, critical points, and local maxima and minima.
- Optimization problems using critical points
- Curve sketching using increasing/decreasing behavior and concavity
- Related rates in real-world contexts
- Velocity, acceleration, and rate problems
Integrals
The integral unit introduces antiderivatives, Riemann sums (left, right, and midpoint), and the Fundamental Theorem of Calculus. Students learn substitution, area under and between curves, displacement and distance from velocity functions, and average value of a function over an interval.
Aligned to Michigan Mathematics Standards
All StudyPug Calculus content is aligned to Michigan Mathematics Standards. Whether your child is in a standard high school Calculus course or preparing for the AP Calculus AB or BC exam, StudyPug covers every topic they need.