NY High School Calculus Curriculum
Give your student the support they need to succeed in high school calculus. Lessons and practice problems covering every topic taught in New York classrooms, from limits to integration.
About High School New York math
New York follows the New York Next Generation Math Standards, which guide calculus through limits, derivatives, and integrals. This course covers evaluating limits graphically and numerically, determining continuity, finding derivatives using the power, product, quotient, and chain rules, analyzing curve behavior, solving optimization and related rates problems, and applying integration to area, displacement, and average value. StudyPug provides video lessons and practice problems for every strand.
- Strands: limits and continuity, differentiation rules and applications, antiderivatives and integration techniques, and definite integrals and their applications
- Video lessons taught step by step for every calculus topic
- Practice problems with instant feedback for each strand
- Content aligned to the New York Next Generation Math Standards
Curriculum topics by strand
Lessons and practice for every strand, aligned to the New York Next Generation Math Standards.
NY High School Calculus Topics
- Limits and continuity: Evaluate limits graphically and numerically using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior.
- Differentiation rules: 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: Write equations of tangent lines, use linear approximation, find critical points and local extrema, solve optimization problems, analyze increasing and decreasing behavior and concavity, sketch curves, and solve related rates and motion problems.
- Antiderivatives and indefinite integrals: Find antiderivatives of basic functions, apply initial conditions, and use substitution to evaluate integrals.
- Definite integrals and their applications: Approximate definite integrals using left, right, and midpoint Riemann sums, apply the Fundamental Theorem of Calculus, find area under and between curves, calculate displacement and distance from velocity functions, and determine the average value of a function over an interval.
How StudyPug Helps NY High School Calculus Students
When a student gets stuck on a limit problem or loses track of which differentiation rule to apply, StudyPug provides step-by-step video lessons that walk through each concept at a pace they can control. Practice problems follow every lesson so students can check their understanding immediately, and worked solutions show exactly where a mistake occurred.
For the more demanding topics in New York high school calculus - optimization, related rates, and integration applications - having a resource that breaks each problem into clear stages helps students build the confidence they need for in-class tests and the AP Calculus exam.
Aligned to NY High School Calculus Curriculum
Every lesson and practice problem on StudyPug is built around the New York Next Generation Math Standards, so the topics, sequencing, and skills your student works on match what their teacher covers in class. From the first unit on limits through the final applications of definite integrals, the content follows the same path as the New York high school calculus course.
Written by the StudyPug Math Team
Last updated June 5, 2026
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