Engineering interview problems
Forces, circuits and estimates from first principles. Type your thinking, take a hint when you are stuck, then answer the follow-ups.
The problems
Will the ladder slip?
FreeA uniform ladder leans against a smooth wall, with its foot on rough ground. What stops it sliding down? How steep must it be so that it does not slip?
Try it freePower to ride a bike
In the rehearsalEstimate the power a cyclist needs to ride at 10 m/s on a flat road with no wind.
A plank on its edge
In the rehearsalA wooden plank 200 mm wide and 25 mm thick spans a stream. Is it stiffer laid flat, or on its edge? By how much?
An endless ladder of resistors
In the rehearsalA ladder circuit repeats forever: each section has a 1 Ω resistor along the top rail, then a 1 Ω rung across to the bottom rail. What is the resistance between the two terminals at the start?
Milk first or last?
In the rehearsalYou pour a hot cup of tea and want to drink it as hot as possible in ten minutes. Should you add the cold milk now, or just before you drink?
A banked track
In the rehearsalA car drives round a circular track of radius 100 m, banked at 10° to the horizontal. At what speed does it need no friction at all to stay on its path?
The longest straw
In the rehearsalWhat is the longest vertical straw you could drink water through, however hard you suck?
A bouncing ball
In the rehearsalA ball is dropped from 2 m and each bounce reaches 80% of the height before. How far does it travel in total before it stops?
Rehearse all 8
Hints, follow-ups and Mia's marks on every attempt, until 31 December.
Oxbridge Interview Rehearsal: two subjects
£199 once. No VAT is charged.
Rehearse every problem in two subjects you choose, with hints, follow-ups and Mia's marks, until your interviews.
- All 8 problems in each of your two subjects, chosen after you pay
- Hints when you are stuck, then the tutor's follow-up questions
- Mia's marks on every attempt: thinking aloud, using hints, checking, reasoning
- Your next problem picked from your weakest skill
- Every attempt saved, with re-attempts side by side
Access until 31 December 2026. Choose your subjects after paying. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right.Oxbridge Interview Rehearsal: all subjects
£299 once. No VAT is charged.
Every problem in all seven subjects, for joint courses and for practising beyond your own subject.
- All 56 problems: Maths, Computer Science, Engineering, Physics, Economics, Law and PPE
- Hints when you are stuck, then the tutor's follow-up questions
- Mia's marks on every attempt: thinking aloud, using hints, checking, reasoning
- Your next problem picked from your weakest skill
- Every attempt saved, with re-attempts side by side
Access until 31 December 2026. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right.What the universities say
“You may be asked to explore unfamiliar ideas, think through problems aloud or consider new perspectives.”
University of Oxford: Interviews“Students do make mistakes, and that's fine”
“It's not assumed that a less-talented student will need more help on any given problem”
University of Oxford: Sample interview questions“we may ask you to solve a problem and talk us through your thought processes”
Oxford Mathematical Institute: Interviews“Our tutors are not mind readers, so if you don't say anything our tutors can't tell what you are thinking!”
Oxford Computer Science: How to apply“the people interviewing you are interested in how you work out your answers and how you think”
University of Cambridge: Preparing for your interview