AR High School Calculus Curriculum

Arkansas High School Calculus Topics

• Limits Graphically and Numerically: 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.
• The Derivative as Rate of Change: Understand the derivative as rate of change and slope of tangent line.
• Differentiation Rules: Find derivatives using the power rule, product rule, quotient rule, and chain rule.
• Derivatives of Transcendental Functions: Find derivatives of trigonometric, exponential, and logarithmic functions.
• Implicit Differentiation: Find derivatives of implicitly defined functions.
• Tangent Lines and Linear Approximation: Find equations of tangent lines and use them for linear approximation.
• Optimization: Find critical points, local maxima and minima, and solve optimization problems.
• Curve Sketching: Analyze increasing and 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 the FTC to evaluate definite integrals and find antiderivatives.
• Integration by Substitution: Use the substitution method to evaluate integrals.
• Area Between Curves: Find area under curves and between curves using definite integrals.
• Displacement and Distance: Use integrals to find displacement and distance from velocity functions.
• Average Value of Functions: Calculate the average value of functions over intervals using integrals.

How StudyPug Helps Arkansas High School Calculus Students

When a student gets stuck on a derivative rule or cannot see why a Riemann sum approximation works, StudyPug lets them go back to exactly the concept causing trouble. Short, focused video lessons walk through each step, and practice problems let students check their understanding before the next class.

Parents can track progress and see which strands their student has covered, making it easy to focus extra time on optimization, related rates, or any other area that needs more work before a test.

Aligned to Arkansas High School Calculus Curriculum

Every lesson and practice problem on StudyPug is built around the Arkansas Mathematics Standards, so the sequence your student sees here mirrors what their Arkansas teacher covers in class. Families can trust that the content is relevant to what is actually being taught and assessed at their school.