NH High School Calculus Curriculum

NH High School Calculus Topics

• Limits and continuity: Understand limits graphically and numerically, evaluate limits using substitution, determine continuity at a point, identify types of discontinuities, and analyze end behavior using limits at infinity.
• Derivatives and differentiation rules: Interpret the derivative as rate of change and slope of a tangent line; apply 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: Write equations of tangent lines and use linear approximation; find critical points, local maxima, and minima; solve optimization problems; analyze increasing and decreasing behavior and concavity; sketch curves; solve related rates problems; and apply derivatives to velocity and acceleration.
• Antiderivatives and indefinite integrals: Find antiderivatives of basic functions and apply initial conditions to determine particular solutions.
• Definite integrals and the Fundamental Theorem of Calculus: Approximate definite integrals using left, right, and midpoint Riemann sums; use the Fundamental Theorem of Calculus to evaluate definite integrals and connect differentiation and integration.
• Integration techniques and applications: Apply substitution to evaluate integrals; find area under curves and between curves; determine displacement and distance from velocity functions; and calculate the average value of a function over an interval.

How StudyPug Helps NH 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 lesson they need rather than waiting until the next class. Each topic is broken into short video lessons followed by practice problems with step-by-step solutions, so a student can work through a gap in understanding the same evening they spot it.

New Hampshire students preparing for end-of-course tests or the AP Calculus exam can use StudyPug to review every strand at their own pace, returning to limits and continuity, derivatives, or integration techniques as many times as necessary to build confidence before the test.

Aligned to NH High School Calculus Curriculum

StudyPug content for high school Calculus is built around the NH Model Competencies, the standards that guide what New Hampshire math teachers are expected to cover. Every strand in this course - from evaluating limits to calculating area between curves using definite integrals - reflects the scope and sequence that New Hampshire students follow in class, so lessons on StudyPug reinforce rather than replace what teachers assign.