Grade 12
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.
Tests by topic
Derivatives and optimisation
These tests help build a secure understanding of each topic and its solution methods. Choose a test for your school level and work at your own pace.
Tests by topic
Tests for this topic
Grade 12
Tangent Lines and the Physical Meaning of the 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.
Grade 12
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.
Grade 12
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.