UT High School Calculus Curriculum
Give your teen the support they need to keep up with Utah high school calculus. Our lessons follow the Utah Core Standards, covering limits, derivatives, and integration from the ground up.
About High School Utah calculus
Utah high school math follows the Utah Core Standards, which organize calculus content around conceptual understanding, procedural fluency, and real-world application. This course works through limits and continuity, differentiation rules and their applications, and integral calculus including Riemann sums, the Fundamental Theorem of Calculus, and area between curves. StudyPug provides video lessons, worked examples, and practice problems for every strand of the Utah Core Standards Introductory Calculus course.
- Strands: limits and continuity, differentiation, derivative applications, and integral calculus
- Video lessons and step-by-step worked examples for every topic
- Practice problems with instant feedback aligned to Utah Core Standards
- Optimization, related rates, and real-world rate-of-change applications
Curriculum topics by strand
Find lessons and practice for every Introductory Calculus strand, aligned to the Utah Core Standards.
UT High School Calculus Topics
- Limits and continuity: understand limits graphically and numerically, evaluate limits using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior.
- Differentiation rules: interpret the derivative as rate of change and slope of the tangent line; apply the power, product, quotient, and chain rules; differentiate trigonometric, exponential, and logarithmic functions; and differentiate implicitly defined functions.
- Derivative applications: find equations of tangent lines, use linear approximation, locate critical points, solve optimization problems, analyze increasing and decreasing behavior, examine concavity, sketch curves, and solve related rates and motion problems involving velocity and acceleration.
- Integral calculus: find antiderivatives of basic functions, approximate definite integrals using left, right, and midpoint Riemann sums, apply the Fundamental Theorem of Calculus, use substitution, find area under and between curves, and calculate displacement, distance, and average value of a function.
How StudyPug Helps Utah High School Calculus Students
When a student gets stuck on a derivative rule or a Riemann sum, StudyPug lets them go back to the exact concept that caused the problem. Every strand in the Utah Core Standards Introductory Calculus course has its own focused video lessons and practice problems, so a student can rewatch an explanation, try a problem, and check their work without waiting for the next class.
Parents can track which topics a student has completed and where they need more practice. Whether a student is working ahead, catching up, or preparing for an end-of-course assessment, StudyPug gives them a clear path through every calculus strand covered in Utah high school.
Aligned to Utah High School Calculus Curriculum
Every lesson and practice problem on StudyPug is built around the Utah Core Standards for Introductory Calculus. The content sequence follows the same order Utah classrooms use, moving from limits and continuity through differentiation and its applications to integral calculus, so what students see on StudyPug matches what their teacher covers in class.
Written by the StudyPug Math Team
Last updated June 5, 2026
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