Probability tree diagrams and outcomes
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Calculus
Differentiation: gradients, derivative rules and meaning
Understand the derivative as an instantaneous rate of change and use the core differentiation rules fluently.
CalculusApplications of Differentiation: stationary points, monotony and inflection
Use derivatives to classify local maxima, local minima and horizontal points of inflection.
CalculusOptimisation: modelling maximum and minimum problems
Turn a real context into a one-variable function, then use calculus to optimise it.
CalculusTangents and Normals to Curves
Find equations of tangents and normals using derivative gradients.
CalculusIntegration: anti-differentiation and standard integrals
Build fluency with indefinite integration and the role of the constant of integration.
CalculusIntegration Techniques: substitution, by parts and special cases
Choose and apply appropriate techniques for non-standard integrals.
CalculusDefinite Integrals: signed area and properties
Interpret definite integrals as signed area and use integral properties efficiently.
CalculusArea Enclosed Between Two Curves
Find intersection points and integrate upper curve minus lower curve over the correct interval.
CalculusDifferential Equations: separable equations and modelling
Solve simple differential equations and connect slope fields/solutions to modelling contexts.
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Probability tree diagrams: combined events
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Set notation and Venn diagrams
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Probability with Venn diagrams
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Independent and combined events
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Probability problem solving
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Probability worked example
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Cumulative frequency diagrams
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“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” — Radford