Idaho High School Calculus Topics
This course covers all major Calculus topics taught in Idaho high schools, fully aligned to Idaho Content Standards Math. Students progress from foundational limit concepts through advanced integration techniques used in AP Calculus and college-level courses.
Limits and Continuity
Students begin by understanding limits graphically and numerically, evaluating limits using substitution, and identifying types of discontinuities. They also explore limits at infinity to describe end behavior of functions — a key skill for curve sketching later in the course.
Derivatives
The derivative unit covers the derivative as a rate of change and slope of a tangent line. Students learn to apply the power rule, product rule, quotient rule, and chain rule. Derivatives of trigonometric, exponential, and logarithmic functions are also covered, along with implicit differentiation.
Applications of Derivatives
Applications include finding equations of tangent lines, linear approximation, identifying critical points, solving optimization problems, and analyzing increasing and decreasing behavior. Students also practice curve sketching using first and second derivative tests, and solve related rates and motion problems.
Integrals
The integration unit starts with antiderivatives and initial conditions, then moves to Riemann sums for approximating definite integrals. Students apply the Fundamental Theorem of Calculus, use substitution to evaluate integrals, and find area under and between curves.
Applications of Integrals
Students use integrals to find displacement and distance from velocity functions, and calculate the average value of a function over an interval — connecting Calculus concepts to real-world physics and engineering problems.
- Limits and continuity at a point and at infinity
- Derivative rules: power, product, quotient, chain
- Derivatives of trig, exponential, and log functions
- Implicit differentiation and tangent line equations
- Optimization and curve sketching
- Related rates and motion applications
- Antiderivatives and Riemann sums
- Fundamental Theorem of Calculus
- Substitution method for integration
- Area between curves and average value of a function
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