ColoradoColorado High School Calculus Curriculum
Video lessons and practice for every Calculus topic. Aligned to Colorado Academic Standards Math. From limits to integrals, get help with every concept.
Colorado High School Calculus Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
Concept of Limits | Understand limits graphically and numerically; evaluate basic limits using substitution |
Continuity | Determine continuity at a point and identify types of discontinuities |
Limits at Infinity | Find limits at infinity and describe end behavior of functions |
Derivative Concept | Understand derivative as rate of change and slope of tangent line |
Derivative Rules | Find derivatives using power rule; product rule; quotient rule; and chain rule |
Derivatives of Special Functions | Find derivatives of trigonometric; exponential; and logarithmic functions |
Implicit Differentiation | Find derivatives of implicitly defined functions |
Tangent Lines | Find equations of tangent lines and use for linear approximation |
Critical Points and Extrema | Find critical points; local maxima and minima; and solve optimization problems |
Curve Analysis | Analyze increasing/decreasing behavior and concavity; sketch curves using derivatives |
Related Rates | Solve related rates problems in real-world contexts |
Motion and Rates | Apply derivatives to velocity; acceleration; and other rate problems |
Antiderivatives | Find antiderivatives of basic functions and use initial conditions |
Riemann Sums | Approximate definite integrals using left; right; and midpoint Riemann sums |
Fundamental Theorem of Calculus | Use FTC to evaluate definite integrals and find antiderivatives |
Basic Integration Techniques | Use substitution method to evaluate integrals |
Area Under Curves | Find area under curves and between curves using definite integrals |
Average Value | Calculate average value of functions over intervals using integrals |
Colorado High School Calculus: Topics and Skills
Colorado high school Calculus follows the Colorado Academic Standards Math and covers three major areas: limits and continuity, differential calculus (derivatives), and integral calculus. Each builds directly on the last, so a strong foundation in limits makes derivatives much easier to understand.
Limits and Continuity
Students start by understanding limits graphically and numerically, then learn to evaluate limits using substitution. From there, they study continuity at a point, identify types of discontinuities, and explore limits at infinity to describe end behavior of functions.
Derivatives
Differential calculus begins with the derivative as a rate of change and slope of a tangent line. Students apply the power rule, product rule, quotient rule, and chain rule, then extend to derivatives of trigonometric, exponential, and logarithmic functions. Implicit differentiation and linear approximation round out this section.
- Critical points, local maxima and minima
- Optimization problems
- Increasing/decreasing behavior and concavity
- Curve sketching using derivatives
- Related rates and real-world rate problems
- Velocity and acceleration applications
Integrals
Integral calculus covers antiderivatives, Riemann sums, and the Fundamental Theorem of Calculus (FTC). Students learn substitution, 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 Colorado Calculus Students
StudyPug has a video lesson and practice problems for every topic listed above. Students can search by topic, watch a short lesson, and immediately practice what they learned. This makes it easy to keep up with class, catch up after a tough unit, or prepare for an AP Calculus exam.