CA High School Calculus Curriculum
Give your student the support they need to succeed in California high school calculus. Every topic from limits to integration is covered and aligned to what their class actually teaches.
About High School California math
California high school calculus follows the California Mathematics Standards, built around a progression from limits and continuity through differentiation and integration. This course covers limits graphically and numerically, derivatives using the power, product, quotient, and chain rules, implicit differentiation, optimization, curve sketching, antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, substitution, and applications to area and motion. StudyPug provides video lessons and practice problems for every strand.
- Strands: Limits and Continuity, Derivatives and Differentiation, Applications of Derivatives, Integrals and Integration
- Video lessons with step-by-step explanations for every calculus topic
- Practice problems and worked examples aligned to California Mathematics Standards
- Progress tracking to keep up with what California high school classes cover
Curriculum topics by strand
Find lessons and practice for every topic, aligned to California Mathematics Standards for high school calculus.
CA 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 find limits at infinity to describe end behavior.
- Derivatives and Differentiation: Understand the derivative as rate of change and slope of the tangent line; find derivatives using the power, product, quotient, and chain rules; 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; solve related rates problems; and apply derivatives to velocity, acceleration, and other rate problems.
- Antiderivatives and Integration: Find antiderivatives of basic functions using initial conditions; approximate definite integrals with left, right, and midpoint Riemann sums; apply the Fundamental Theorem of Calculus; use substitution to evaluate integrals; find area under and between curves; determine displacement and distance from velocity functions; and calculate the average value of a function over an interval.
How StudyPug Helps CA High School Calculus Students
When a student gets stuck on a concept like implicit differentiation or the substitution method, StudyPug lets them rewatch the relevant lesson as many times as needed and then work through practice problems with step-by-step explanations to build real understanding before the next class.
Every lesson follows the California Mathematics Standards, so students are always working on content that connects directly to what their teacher is covering - whether that is curve sketching, related rates, or evaluating definite integrals using the Fundamental Theorem of Calculus.
Aligned to CA High School Calculus Curriculum
StudyPug content is built around the California Mathematics Standards for high school calculus, covering the same progression of limits, differentiation, and integration that California students encounter in class, so every lesson and practice problem reinforces what schools in California actually teach.
Written by the StudyPug Math Team
Last updated June 5, 2026
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