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New Mexico High School Calculus Curriculum

Video lessons and practice for every Calculus topic. Aligned to New Mexico Mathematics Standards. From limits to integrals, get help with every concept.

New Mexico High School Calculus Curriculum | StudyPugHelp

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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

New Mexico High School Calculus: Topics and Skills

Calculus is one of the most important math courses high school students take. New Mexico high schoolers studying Calculus will build skills across three major areas: limits and continuity, differential calculus, and integral calculus. StudyPug covers every one of these areas with clear video lessons and targeted practice problems.

Limits and Continuity

Students begin Calculus by understanding what a limit is — both graphically and numerically. From there, they learn to evaluate limits using substitution, identify types of discontinuities, and analyze end behavior using limits at infinity. These foundational concepts are essential for everything that follows in the course.

Derivatives and Differentiation

The derivative is the core idea of differential calculus. Students learn to interpret the derivative as a rate of change and as the slope of a tangent line. StudyPug walks through every differentiation rule:

  • Power rule, product rule, quotient rule, and chain rule
  • Derivatives of trigonometric, exponential, and logarithmic functions
  • Implicit differentiation for equations not solved for y
  • Tangent line equations and linear approximation

Applications of derivatives include finding critical points, solving optimization problems, analyzing curve behavior, and solving related rates problems in real-world contexts.

Integrals and Integration

The second half of Calculus focuses on antiderivatives and integrals. Students learn to find antiderivatives of basic functions, approximate definite integrals using Riemann sums, and apply the Fundamental Theorem of Calculus. Key integration techniques and applications include:

  • Substitution method for evaluating integrals
  • Finding area under curves and between curves
  • Using integrals to find displacement and distance from velocity functions
  • Calculating average value of a function over an interval

Aligned to New Mexico Mathematics Standards

All StudyPug Calculus content is aligned to New Mexico Mathematics Standards. Whether your student is preparing for an AP Calculus exam, reviewing before a unit test, or catching up on a missed lesson, StudyPug has the right content at the right level.