California High School Calculus Topics
This course covers all major Calculus topics taught in California high schools, aligned to the California Common Core State Standards. Students work through 19 chapters spanning limits, derivatives, and integrals.
- Understand limits graphically and numerically; evaluate basic limits using substitution
- Determine continuity at a point and identify types of discontinuities
- Find limits at infinity and describe end behavior of functions
- Understand the derivative as rate of change and slope of a tangent line
- Find derivatives using power rule, product rule, quotient rule, and chain rule
- Find derivatives of trigonometric, exponential, and logarithmic functions
- Find derivatives of implicitly defined functions
- Find equations of tangent lines and use them for linear approximation
- Find critical points, local maxima and minima, and solve optimization problems
- Analyze increasing/decreasing behavior and concavity; sketch curves using derivatives
- Solve related rates problems in real-world contexts
- Apply derivatives to velocity, acceleration, and other rate problems
- Find antiderivatives of basic functions and apply initial conditions
- Approximate definite integrals using left, right, and midpoint Riemann sums
- Use the Fundamental Theorem of Calculus to evaluate definite integrals
- Use substitution to evaluate integrals
- Find area under curves and between curves using definite integrals
- Use integrals to find displacement and distance from velocity functions
- Calculate average value of functions over intervals using integrals
How StudyPug Helps California Calculus Students
Calculus is one of the most challenging courses in high school. StudyPug breaks every topic into short, focused video lessons so students can learn at their own pace. Each lesson is followed by practice problems that mirror what students see on tests and homework assignments.
Whether your child is struggling with the chain rule, confused about Riemann sums, or preparing for an AP Calculus exam, StudyPug covers every concept aligned to what California schools teach. Students can revisit any lesson as many times as they need — no rushing, no pressure.
Calculus and California Standards
All content on this page aligns to the California Common Core State Standards for mathematics. California high school students are assessed through the CAASPP program at grade 11, but Calculus students are often also preparing for AP exams or college placement. StudyPug supports both.
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