New Jersey High School Calculus: What Students Learn
High school calculus in New Jersey builds on algebra and precalculus to introduce three major pillars: limits, derivatives, and integrals. Students aligned to the NJ Student Learning Standards for Math are expected to understand these concepts both graphically and analytically. StudyPug covers every topic with video lessons and guided practice so New Jersey students can keep up with class or get ahead.
Limits and Continuity
Calculus begins with limits — understanding what a function approaches as the input gets close to a value. Students learn to evaluate limits graphically and numerically, use substitution, and identify types of discontinuities. They also explore limits at infinity to describe the end behavior of functions.
Derivatives
Derivatives measure the rate of change of a function. New Jersey calculus students learn the power rule, product rule, quotient rule, and chain rule. They also differentiate trigonometric, exponential, and logarithmic functions, and work with implicit differentiation. Applications include finding tangent line equations, solving optimization problems, analyzing increasing and decreasing intervals, and working through related rates problems in real-world contexts.
Integrals
The second half of calculus focuses on integration. Students find antiderivatives of basic functions, approximate definite integrals using Riemann sums, and apply the Fundamental Theorem of Calculus to evaluate integrals exactly. Topics also include the substitution method, finding area under and between curves, calculating displacement and distance from velocity functions, and determining the average value of a function over an interval.
Topics Covered in This Course
- Limits graphically and numerically; substitution
- Continuity at a point; types of discontinuities
- Limits at infinity and end behavior
- Derivative as rate of change and slope of tangent line
- Power rule, product rule, quotient rule, and chain rule
- Derivatives of trigonometric, exponential, and logarithmic functions
- Implicit differentiation
- Tangent lines and linear approximation
- Critical points, local maxima and minima, optimization
- Curve sketching using first and second derivatives
- Related rates in real-world contexts
- Velocity, acceleration, and rate problems
- Antiderivatives and initial conditions
- Riemann sums: left, right, and midpoint
- Fundamental Theorem of Calculus
- Substitution method for integrals
- Area under curves and between curves
- Displacement and distance from velocity functions
- Average value of a function over an interval
How StudyPug Helps New Jersey Calculus Students
StudyPug provides video lessons broken into short, focused segments that students can pause and replay. After each lesson, practice problems reinforce the concept. Whether your child is preparing for an AP Calculus exam, catching up after a difficult unit, or just trying to finish tonight's homework, StudyPug has the right lesson ready to go — on any device, at any time.
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