Mathematics: Applications and Interpretation HL
Calculus and numerical methods
AI HL calculus, accumulated change, optimisation, differential equations, numerical methods, and technology-supported interpretation.
Optimise models using derivatives
Differentiate an applied model and use a stationary point to optimise a quantity.
Interpret rates of change
Use derivatives to interpret instantaneous rates in context.
Approximate area using the trapezoidal rule
Use tabulated values and the trapezoidal rule to approximate accumulated change.
Solve separable differential equations
Separate variables, integrate, and use an initial condition in applied models.
Use Euler method for differential equations
Use step size and gradient information to approximate a solution value.
Integrate rates for accumulated change
Integrate a rate model to calculate total change over an interval.
Estimate derivatives with central differences
Use nearby function values to estimate an instantaneous rate of change.
Apply Simpson rule estimates
Use Simpson rule with three ordinates to estimate an integral.
Estimate logistic half-capacity time
Solve a logistic model for the time when the response reaches half its carrying capacity.