MI High School Calculus Curriculum

Michigan High School Calculus Topics

• Limits and Continuity: Understand limits graphically and numerically, evaluate basic limits using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior of functions.
• Derivatives and Differentiation Rules: Understand the derivative as rate of change and slope of the tangent line; find derivatives using the power rule, product rule, quotient rule, and chain rule; differentiate trigonometric, exponential, and logarithmic functions; and find derivatives of implicitly defined functions.
• Applications of Derivatives: Find equations of tangent lines and use linear approximation; locate critical points, local maxima, and minima; solve optimization problems; analyze increasing and decreasing behavior and concavity; sketch curves using derivatives; solve related rates problems; and apply derivatives to velocity, acceleration, and other rate problems.
• Integration and Applications of Integrals: Find antiderivatives of basic functions using initial conditions; approximate definite integrals using left, right, and midpoint Riemann sums; use the Fundamental Theorem of Calculus to evaluate definite integrals; apply the substitution method; find area under curves and between curves; use integrals to find displacement and distance from velocity functions; and calculate the average value of functions over intervals.

How StudyPug Helps Michigan High School Calculus Students

When a student gets stuck on a related rates problem or cannot remember how to apply the chain rule, StudyPug lets them go back to the exact concept they need. Each video lesson focuses on one idea, followed by practice problems with step-by-step solutions so the student can see where their reasoning went off track.

Michigan high school calculus moves quickly, and students often hit a wall when differentiation rules stack on top of each other or when integration techniques multiply. StudyPug gives students a place to slow down, rewatch an explanation, and build confidence before the next class or assessment.

Aligned to Michigan High School Calculus Curriculum

Every lesson and practice problem on StudyPug is organized to match the Michigan K-12 Standards for Mathematics, so the topics your student sees here are the same ones their teacher is covering in class. From the first unit on limits through the final strand on integral applications, the content stays in step with what Michigan high school calculus courses expect students to know.