Mathematics: Analysis and Approaches SL
Calculus
Limits, derivatives, tangents, optimization, kinematics, integration, area, and mathematical modelling with rates of change.
Understand gradients and limits
Connect secant gradients, average rate of change, and the intuition behind limits.
Differentiate with the power rule
Differentiate polynomial and power functions using derivative notation and the power rule.
Find tangent and normal equations
Find tangent and normal gradients and equations using derivatives at a point.
Analyse increasing and decreasing intervals
Use derivatives to classify stationary points and describe increasing or decreasing behaviour.
Solve optimization problems
Model and solve maximum or minimum problems using derivatives and clear interpretation.
Use calculus in kinematics
Connect displacement, velocity, and acceleration using differentiation in motion contexts.
Integrate with the power rule
Find indefinite and definite integrals using the reverse power rule and correct constant notation.
Find area under curves
Use definite integrals to calculate signed area and interpret area under a curve.