OGM.13.CAL
Open Global Math Standards 2026™ · 12th Grade
Differential and Integral Calculus, Differential Equations, and Infinite Processes
Grade12th Grade
SubjectMath
Levelstrand
Child standards (8)
- OGM.13.CAL.1Understand differentiation as the limit of a difference quotient and rate of change; differentiate from first principles for integer powers, $\sin x$, and $\cos x$; interpret the derivative as the tangent slope and the second derivative as concavity and inflection points.
- OGM.13.CAL.2Differentiate algebraic, power ($x^n$), exponential ($e^{kx}, a^{kx}$), logarithmic ($\ln x$), and trigonometric functions ($\\sin kx, \\cos kx, \\tan kx$) using standard differentiation rules (product rule, quotient rule, chain rule), and find derivatives of inverse functions.
- OGM.13.CAL.3Differentiate implicitly defined relations and parametrically defined curves to find first derivatives $\frac{dy}{dx}$.
- OGM.13.CAL.4Apply differentiation to determine equations of tangents and normals, identify stationary points, local extrema, intervals of increase and decrease, solve optimization problems, and analyze connected rates of change.
- OGM.13.CAL.5Understand and apply the Fundamental Theorem of Calculus and integration as the limit of a Riemann sum; integrate standard functions $x^n$, $e^{kx}$, $\frac{1}{x}$, $\sin kx$, and $\cos kx$.
- OGM.13.CAL.6Apply advanced integration techniques including $u$-substitution, integration by parts, and partial fraction decomposition (linear denominators) to evaluate definite and indefinite integrals.
- OGM.13.CAL.7Evaluate definite integrals to calculate the area under a curve and the area enclosed between two intersecting curves.
- OGM.13.CAL.8Formulate first-order differential equations from contextual models (kinematics, population growth, Newton's law of cooling, supply-demand); solve by separation of variables to obtain general and particular solutions satisfying initial conditions, and evaluate the limitations of the model.