Tasks and notes for the state exam


  1. Explain the terms "primitive function", "integral function" and "definite integral" on the level of the secondary level II!
    Also deal with existence and uniqueness!
  2. Explain two different (basic) ideas that learners at the end of secondary level II should associate with the term definite integral!
    Describe and justify a learning activity that enables learners to establish relationships between these two notions!
  3. Within the context of a lesson, the main theorem of differential and integral calculus is to be elaborated and justified. Describe the main steps of the lesson and justify them from a didactical point of view!



  1.  Explain the terms prism, cylinder, pyramid and cone!
  2. Describe and discuss three different types of solid models. Use an appropriate instructional activity for each when discussing straight prisms and circular cylinders!
  3. Develop a lesson in which the volume formula of straight prisms is worked out!



  1. Explain the different algebraic representations of quadratic functions and compare them with respect to their applicability in specific problems!
  2. Design a modeling task for an extreme value problem (with solution sketch), which can be solved in the intermediate level with recourse to quadratic functions! Explain how the competence "modeling mathematically" is addressed in this task! 3.
  3. Develop a teaching unit in which the meaning of the parameter \( a \) in \( f(x)=a(x-b)^2+c \) is explained!