Session 05-09 - Oral Exam Practice I
Section 05: Differential Calculus
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
. . .
Rework one Block A topic from today in writing - the same problem, silent and precise.