Session 05-09 - Oral Exam Practice I

Section 05: Differential Calculus

Dr. Nikolai Heinrichs & Dr. Tobias Vlćek

Welcome

Why Practice the Oral Exam?

Talking about mathematics is a skill of its own.

  • Students who do not pass the written Feststellungsprüfung sit an oral examination
  • The oral rewards understanding: can you explain the maths, not just compute it?
  • Explaining out loud also deepens your written-exam skills
  • From now on, we practice this regularly - today is round one

The full format is explained in our oral exam guide - we walk through it together today.

The Format at a Glance

Two topics, two very different situations

Block A Block B
Preparation 30 min, with notes None - spontaneous
Subject One area, announced A different area
Your job Present in free speech Discuss an impulse question

Follow-up questions come at three levels: [I] reproduce · [II] apply · [III] evaluate and justify.

How Today Works

Roles and Rotation

You work in groups of three

  • Candidate: receives a Block A sheet, prepares 30 minutes, then presents
  • Examiner: runs the exam with the examiner key (follow-ups + Block B impulse)
  • Observer: takes notes - clarity, structure, correct vocabulary - and gives feedback
  • After each round, roles rotate, with a fresh topic set

Being the examiner is secretly the best practice: you must judge why an answer is right.

Timing for Today

  • Preparation: 30 minutes (candidate prepares, examiner reads the key)
  • Exam conversation: ~20 minutes (Block A presentation + follow-ups, then Block B)
  • Feedback: 10 minutes in the group
  • Then rotation, and after the coffee break, the final round

During preparation the candidate may use notes they create now - no books, no phones, exactly like the real oral.

Today’s Topic Sets

Sets 09 and 10 - handed out in class

  • Set 09: Cost & profit analysis (cubic cost) · Probability (binomial)
  • Set 10: Exponential function analysis · Cost & profit (break-even, profit maximum)
  • Both mirror the recurring written mock-exam problems - nothing new, just spoken

The numbers are deliberately calculator-light. The focus is what you compute and why.

What Good Answers Sound Like

Speaking Mathematics

Structure beats speed

  • Name the goal first: “To find the break-even point, I set revenue equal to cost.”
  • Use the correct terms: derivative, zero, factor, marginal cost - not “the thing”
  • Justify steps: “I can divide by \(x\) here because \(x = 0\) is not in the domain.”
  • Interpret results: a number without a unit and a sentence is only half an answer

When You Get Stuck

  • Say what you do know: “This is a quadratic, so I expect up to two solutions.”
  • Think aloud - examiners reward a visible reasoning process
  • Ask for the question to be rephrased rather than staying silent
  • A corrected error counts far more than a lucky guess

Coffee Break - 15 Minutes

Final Round

Round Three

Rotate roles one last time

  • The remaining group member becomes the candidate
  • Examiner and observer swap as well
  • Use your feedback notes from the first two rounds: what should this candidate try to do better?

Wrap-Up

Key Takeaways

  • The oral exam is a conversation, not an interrogation
  • Structure + vocabulary + justification = a strong answer
  • Weaknesses you noticed today are your study list for the next round
  • We will practice again after the integral-calculus mock

Next Session Preview

Session 06-01: Antiderivatives & Indefinite Integrals

  • We review the mock exam and start Section 06: Integral Calculus
  • Integration as the reverse of differentiation

Preparation

Rework one Block A topic from today in writing - the same problem, silent and precise.