12 grade
Derivative fundamentals
This test introduces the derivative as a rate of change and applies the basic rules of differentiation. Tasks cover derivatives of constant, power, linear and quadratic functions.
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Derivatives and optimisation
These tests help build a secure understanding of the topic and its solution methods. Choose a test for your grade and practise at your own pace.
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Tests for this topic
12 grade
Tangent and physical meaning of derivative
This test develops the geometric and physical interpretations of a derivative. Students form tangent equations, interpret velocity and acceleration and connect the sign of a derivative with the behaviour of a function.
12 grade
Function analysis using derivatives
This test uses the first derivative to analyse a function. Tasks include finding critical points, intervals of increase and decrease, local extrema and absolute maximum or minimum values.
12 grade
Optimisation problems
This test models geometric and economic optimisation situations. Students construct an objective function, determine its feasible domain, use derivatives to find an extremum and interpret the result in context.