Florida High School Calculus: Topics and Skills
Calculus is one of the most important math courses Florida high school students will take. It builds directly on algebra, precalculus, and trigonometry, introducing powerful new tools for analyzing change and accumulation. StudyPug covers every topic your student will encounter, with video lessons and practice aligned to Florida's B.E.S.T. Standards for Mathematics.
Limits and Continuity
Calculus begins with limits. Students learn to understand limits graphically and numerically, evaluate basic limits using substitution, and determine continuity at a point. They also learn to identify types of discontinuities and find limits at infinity to describe the end behavior of functions.
Derivatives
The derivative is the heart of differential calculus. Florida Calculus students learn to interpret the derivative as a rate of change and as the slope of a tangent line. They apply the power rule, product rule, quotient rule, and chain rule to find derivatives efficiently. Topics also include derivatives of trigonometric, exponential, and logarithmic functions, as well as implicit differentiation.
Applications of Derivatives
Knowing how to find a derivative is only the beginning. Students use derivatives to find equations of tangent lines, perform linear approximation, locate critical points, and solve optimization problems. Curve sketching using increasing/decreasing behavior and concavity helps students connect algebra to visual reasoning. Related rates and applications to velocity and acceleration round out this section.
Integrals and the Fundamental Theorem of Calculus
Integral calculus introduces antiderivatives, Riemann sums, and the Fundamental Theorem of Calculus. Students approximate definite integrals using left, right, and midpoint Riemann sums, then learn to evaluate them exactly. The substitution method extends the range of integrals students can solve.
Applications of Integration
Students apply integrals to find the area under a curve and between curves. They also use integrals to find displacement and distance from velocity functions, and calculate the average value of a function over an interval. These real-world applications show students why calculus matters beyond the classroom.
- Limits graphically, numerically, and analytically
- Continuity and types of discontinuities
- Limits at infinity and end behavior
- Derivatives using power, product, quotient, and chain rules
- Derivatives of trig, exponential, and logarithmic functions
- Implicit differentiation
- Tangent lines and linear approximation
- Optimization and critical points
- Curve sketching with first and second derivative tests
- Related rates and motion problems
- Antiderivatives and basic integration
- Riemann sums and definite integrals
- Fundamental Theorem of Calculus
- Substitution method for integrals
- Area under and between curves
- Displacement, distance, and average value
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