Oxbridge
Engineering
Interview
Scripts
Oxbridge Engineering Interview Scripts
What’s the hardest thing
about preparing for an
Oxbridge interview?
More than even the difficulty of the questions themselves, many students say it’s
the unfamiliarity of the whole experience.
How can you prepare if you’ll have no idea what it will be like?
These example interview scripts are a part of our solution to this problem. We
consulted with multiple Oxbridge graduates and current Oxbridge students to
create examples of how a good student might respond to a typical interview-style
question, and how the tutor would both test and support them throughout.
We’ve also added further information on what each question is testing, how it
might be extended, how the tutor might give further hints if the candidate got
stuck at any point, and what the student does well that you might look to replicate
in your own interview.
To get the most out of these scripts, we advise you to think about how you’d
respond to the question, and to each of the tutor’s hints, comments, or further
questions, before carefully reading the student’s response, and then making sure
you understand what’s going on before you move on to the next part.
Of course, while reading a script of an interview can be very useful, it’s not the
same as having to answer the questions yourself in real time!
That’s why we’re also running live online mock interview courses and 1-1 sessions
for Oxbridge Engineering this November and December.
Oxbridge Engineering Interview Preparation Options
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
01
Oxbridge Engineering Interview Scripts
02
Introduction
Here’s an example script of a good Engineering interview. The
first and third questions are more physics-based, and the
second is more mathsbased. These questions are very relevant
for Physics, Physical Natural Sciences and Materials Science
applicants too.
Engineering interview question 1
(Mechanics)
Question: A cart is travelling along a horizontal track at a constant velocity.
What would happen to the velocity of the cart if it started raining? Assume
that the rain droplets fall perfectly vertically into the cart.
Model interview
Student: Firstly, I have two clarifying questions. Can
I ignore the effects of friction between the cart and
the track and air resistance acting on the cart?
Also, can I assume the rate of rain falling in the cart
to be constant?
Tutor: You may ignore friction, but the second
assumption is unnecessary.
Student: Hmm… My intuition is telling me that the
cart will slow down as it fills with rain if no other
external forces are acting on the cart. (Pauses to
think.) But let me verify that using momentum
conservation in the direction of the cart. I’m going
to call the mass of the cart m and the speed of the
cart v. A small interval of time δt later, the speed of
the cart is v + δv and its total mass is m +δm.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
Attempting a physics
question often requires
making the correct
simplifying assumptions.
It’s best to spell them out
at the start and give your
motivations for making them
if you can.
Oxbridge Engineering Interview Scripts
03
δm
m
m + δm
v
v +δv
(Student writes) Momentum conservation (→) to track:
mv = (m + δm )(v + δv)
mv = mv mδv + δmv + δmδv
⇒δmv + mδv =
ignore since small
0
Since I defined δm as a positive quantity, δv must
be a negative quantity. As a result, the cart has to
slow down.
Tutor: Okay, you’ve used a momentum description
to explain why the cart slows down. Could you
explain why the cart slows down in terms of forces?
If you haven’t seen ‘δm’
and ‘δv’ used in this way
before, check out our
bonus chapter online
for more information:
oxbridgeformula.co.uk/
bonus-chapter.
Student: (Pauses to think) Let me answer that by considering the fact that Impulse
= Δmomentum. I’m going to consider the momentum of the rain droplet and cart
separately during the collision: the rain droplet gains momentum in the forwards
direction and the cart loses momentum in the forwards direction. This means
that the rain droplet exerts a force backwards to the left on the cart and the cart
exerts a force forwards on the rain droplet. Physically, I think this occurs when the
rain ‘sloshes’ into the back of the cart.
Tutor: Can you be more precise about this ‘sloshing’?
Student: (Pauses.) Well, the rain impacts the cart
with no horizontal velocity. From here, two things
can happen: it is accelerated from rest to the new
speed of the cart by a horizontal friction force
acting forwards, which according to Newton’s third
law means the cart experiences a similar friction
force in the opposite direction acting backwards.
Alternatively, the rain could simply hit the back of
the cart and exert a backwards impulse on the cart.
Tutor: Thank you. That’s all on that question.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
This might seem
straightforward, but you’re
being asked to explain
something from basics
without being distracted
by details (such as the
fact the water is liquid
rather than solid). The
clarity of your explanations
matters because it
reflects the degree of your
understanding.
Oxbridge Engineering Interview Scripts
Further hints
If you’re struggling with the fact that rain is continuously falling into the cart, the
tutor might suggest something such as: ‘Suppose we think about what happens
to one raindrop…’ (You can often analyse the behaviour of a fluid by thinking about
each small part of it as a simple particle.)
They might also draw a diagram for you if you’re completely stuck to give you
something to guide your thoughts.
To get you started, the tutor might ask ‘What quantities are conserved when a
raindrop hits the cart?’ or ‘What force does a raindrop experience when it hits the
cart?’ To give less away, they could instead ask something such as ‘If you’re sitting
in the cart, what do you see happen when a raindrop falls into it?’—inviting you
to think about either the forces involved, or the ‘before’ and ‘after’ states of the
raindrop.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
04
Oxbridge Engineering Interview Scripts
Extending the question
To extend the question, you could be asked to find an equation for the velocity
of the cart as a function of time, given that the rain falls at a constant rate
(hint: if you take the equation (δm)v + m(δv) = 0 and send δm and δv to 0, you
dv
v
get dm
m ’ where v and M are both functions of time.) The scenario could also
be altered in several ways:
•
The rain falls at an angle
•
The cart starts full of water, which leaks out of a hole at the bottom
•
The cart starts full of water, which leaks out of a hole at the back.
What is the question testing?
This question is primarily designed to assess your physical intuition and whether
you can connect that intuition to physical principles such as conservation of
momentum.
Many students will be confused as to whether momentum is indeed conserved.
To deal with this problem, it’s important to specify exactly what system you’re
dealing with, and to make sure you don’t change that system halfway through.
For example, you can either define your system as the cart itself, in which case
momentum is not conserved, or you can define your system as the cart plus rain
droplet, in which case momentum is conserved.
Related topics from university
This question is an example of a collision problem in mechanics; the study of
collisions comprises a large portion of a first-year Mechanics course.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
05
Oxbridge Engineering Interview Scripts
06
Engineering interview question 2
(Differential Equations)
Some interviewers will test you on your maths skills using a physics question,
but others will test you on these separately. Graph sketching and calculus are
common themes in Engineering maths questions.
Question: (The interviewer verbally explains, aided by pen and paper.) A
dy
y
differential equation of the form dx f x can often be more easily solved
y
using a substitution of the form y = u (x) x (i.e. u(x) = ), where u is a function of x.
x
dy
y . Differentiating the substitution y = u(x)x
Let’s take a simple example: x
dx
dy
du
dy
u x
y by
yields
, but dividing both sides of our initial equation x
dx
dx
dx
du
dy
u. Then either x is 0 (which is a trivial
u , so we get u x
x gives us
dx
dx
du
solution) or
is 0. So, the non-trivial solution is: y = cx.
dx
Please could you use this method to solve
(x 2 y)
dy
dx
x y?
Some interview questions
will be of this form, in which
the interviewer shows you
a technique, gives you an
example, and asks you to
apply that technique to a
more difficult question.
Model interview
Student: Okay, I see how in your example we have
du
x
0 , but I’m not sure how you got from there to
dx
y = cx.
Tutor: Well, if
Always ask when you’re
unsure!
du
0, u is simply a constant c.
dx
Student: Ah, I see now, so substituting y = u(x)x gives y = cx.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
Oxbridge Engineering Interview Scripts
07
Tutor: Great! So how about this new equation I’ve given you?
y
Student: I don’t immediately see where I will get a x from, but I think I should
dy
divide through by x + 2y to give me dx
x y .
x 2 y (Pauses to think.)
Maybe I could divide the numerator and denominator by x. That would give me
dy
dx
x y
x x .
du
x y Ah yes, and substituting in u I’ll get: u x dx
x 2x
want to group the u’s together, so I should get: x
du
dx
1 u .
I suppose that I
1 2u
2
2u 2u 1
. However, I’m not
1 2u
sure if I know how to solve this?
Tutor: What form do you want it to be in to be able to solve it?
Student: (Thinks.) Some function of u times
du
some function of x?
dx
Tutor: Or…?
Student: Some function of x times
dx
some
du
function of u? Oh, I see I can do that. I think I should have
1 dx
x du
1 2u
, which I
1 2u 2u2
think I should be able to integrate… (pauses.) I’m not sure how I would deal with
1 2u
, though?
1 2u 2u2
Tutor: What does the numerator look like? Look at the denominator.
Student: (Pauses for a few seconds.) Oh yes, the
numerator is like the denominator differentiated,
1
ln (1 2u 2 u2) c , and I can
so I must get: ln(x)
2
rearrange and substitute to get…
Tutor: That’s good, we can leave that there; I think
you understand how to get to an answer.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
If you substitute for u
and rearrange, you’ll
get to the equation
2
2
x + 2xy + 2y + k, for k a
positive constant. However,
interviewers will sometimes
move on if they’ve seen
you do the most interesting
or difficult part of the
question.
Oxbridge Engineering Interview Scripts
Further hints
x y
before, you might not recognise that
x 2y
both the numerator and denominator are made up of terms of the same degree,
y
y
which means that it can be written in terms of x . For example if u = x , then
x3 2x 2 y 4y 3 1 2 u 4u3
. The interviewer could prompt you by saying something
3x2 y xy 2
3u u 2
If you’ve not seen something such as
y
such as: ‘How would you get a x in there? ’ or ‘How could you rearrange that
fraction? ’ Hopefully, you’ll be familiar with taking reciprocals in a differential
equation from the A-Level Maths syllabus. If not, the interviewer could prompt you
with: ‘Would it be easier if the variables were switched around?’, or ‘Would it be
1 2u
?’
easier to integrate
1 2u 2u 2
Extending the question
A question such as this can be easily extended by thinking of more difficult
examples of applying the same technique. (Can you think of your own?) An
dy
y x 2 y 2’,
interesting extension may be a question such as: ‘Solve x
dx
which requires you to recall the derivative of arctan (x).
What is the question testing?
This question is testing your calculus skills, but more broadly your ability to
y
spot patterns (e.g. opportunities to get x terms) and to apply a new technique
to a case you haven’t seen before. This is an important skill because one of
the differences between university and A Level is that often you receive only a
couple of examples of a technique in lectures, and other important examples are
introduced via problem/example sheets, so you have to figure out how they work
on your own.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
08
Oxbridge Engineering Interview Scripts
09
Related topics from university
Techniques for solving differential equations are taught in the Mathematics
module in the Oxford Engineering course and the Mathematical Methods module
at Cambridge. Differential equations crop up naturally in everything from circuit
theory to fluid dynamics, so having a full toolbox of techniques to solve them is
essential.
Engineering interview question 3
(Circuits)
1V
Question: What is the potential difference over
each resistor in this circuit, if they all have the
same resistance?
1
2
4
3
Model interview
1V
Student: Over resistor 1, it will be 1V. The total
potential difference over the other three will be
1
1V, and they’re all the same, so it’s
over each of
3V
them.
Tutor: Okay. Suppose I add this symbol to the
circuit? Do you know what that means?
1
2
4
3
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
Oxbridge Engineering Interview Scripts
Student: It’s a ground. I don’t really know what it
does to the circuit though. I don’t think it can have
a resistance, or produce an emf.
10
More precisely spelling out
the limits of your knowledge
is better than just saying
you don’t know what to do.
Tutor: In this case, we’ll think of it as setting the
potential of the point it attaches to 0—the same as
the negative terminal of the cell. Does that make
sense?
Student: I think so.
Tutor: In that case, if I attach it as shown, what is
the potential difference over each resistor now?
Student: I think resistor 1 is 1V because it’s the
same as before. And the potential difference over
the other three also should still be 1V, ‘because
they form a loop with resistor 1.
Tutor: Yes, exactly.
Student: But now I’m not sure what happens. Can a
current even flow through that part of the circuit if
it’s grounded?
Tutor: Yes there can be current in that part of the
circuit. Do you think that will help you find the
potential differences?
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
It’s common to face
questions in which the tutor
changes the situation you’re
analysing to make it harder;
one great way to reply is
to identify what hasn’t
changed.
Oxbridge Engineering Interview Scripts
11
Student: I was thinking I could use Ohm’s law, but I
don’t really know about the current either. I think I
should at least start with resistor 2 because the
other two will follow from it. Is there another rule I
could use?
Even when you’re unsure,
you can try to come up with
plans and useful questions.
Tutor: Here’s one way of thinking about it: the bottom end of resistor 2 is
connected directly to ground. What is the other end connected to?
Student: Resistor 1 and the cell.
Tutor: Which part of the cell?
Student: The positive terminal. Okay, so it’s similar to going from 1V to 0V. So the
potential difference over resistor 2 is 1V. And that means the potential difference
over the other two has to be 0… is that right?
Tutor: Does it make sense for the other two to be 0?
Student: Actually, yes, because it’s as though the potential is 0V at both ends.
Tutor: Exactly. Let’s expand a little bit. Where else could I attach the ground to
the circuit, and what would the potential difference over each resistor be in each
case?
Student: I think you can attach it in these ways…
1V
A.
1
2
2
4
2
3
1
4
3
G.
4
3
1
4
1V
2
1V
E.
1
F.
4
3
1V
2
1
1
3
D.
1V
C.
1V
B.
1V
1
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
2
4
2
4
These pictures are for
illustration only—in practice,
you should indicate by
pointing to the tutor’s
diagram rather than waste
time redrawing the circuit.
2
4 Scripts
2
Oxbridge Engineering
Interview
3
3
1V
F.
12
4
1V
G.
1
1
2
4
3
2
4
3
Student: Wait, actually A, B and C are the same, and E, F and G are also the same,
because where the junctions are doesn’t affect the potential. So there are only
three more ways.
Tutor: Okay, and what happens for each resistor?
Student: In E, F and G, nothing changes from when there was no ground. And in A,
B and C, I think the potential difference over any of them is 0, because it’s 0 either
side. I suppose I have to calculate what happens in D. Let’s see: resistor 1 will still
get 1V. Resistor 4 will get 0V. And the other two are the same, so they both get 0.5V.
Is that right?
Tutor: Yes, that’s right. Let’s look at a final example. (Draws a new diagram)
1V
1
2
4
3
5
7
6
Tutor: Please could you find the potential
difference over each resistor again? They are still all
identical.
Student: Okay. Resistor 1 still gets 1V. I think that 4, 6 and 7 all get 0V because the
potential at either end is 0—wait, no. There’s a path through 2, 3 and 4 to the cell,
and a path through 2, 3, 7 and 6 to ground. Can I say the total potential difference
over 2 and 5 is 1V, and they’re the same, so they get half each?
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
Oxbridge Engineering Interview Scripts
13
Tutor: The total potential difference is 1V, but they
are positioned differently with respect to the rest
of the circuit, so we can’t conclude they get half
each.
Student: (Annotating the diagram.) Okay, so let’s
say it’s V2 for resistor 2 and 1—V2 for resistor 5. And
let’s write resistances V3 and V4 for resistors 3 and 4.
Well, V4 is 1 – V2 – V3, so I can simply use that. And
resistors 6 and 7 both get half of V3 – (1 – V2)
because the bottom 3 are in parallel with resistor 3.
And I can try to count the potential differences
around different loops to get some equations… Hm,
actually, I think I used all the loops already.
Don’t be afraid to introduce
your own notation
It’s much better to
announce your next step
and analyse why it failed,
than to attempt it in your
head and have nothing to
say when it doesn’t work.
Tutor: What other rules about potential differences
have you considered?
Student: I thought about Ohm’s law before. Maybe
I could use that again, because there’s a separate
rule for splitting currents at a junction. But it means
I have to work out all the currents.
Tutor: Let’s look at one junction—which might be useful?
Student: The one between resistors 1 and 2… No, that doesn’t work because I don’t
know the total current. I could work it out by finding the total resistance.
Tutor: That would work, but can we find a quicker way?
Student: I could look at the junction between resistors 2 and 5. Using the current
rule,
V V 1 V
I get:
.
R R
R
2
3
2
That means V3 is 2V2 – 1, so V4 is 2 – 3V2 .
And looking at the junction between 4 and 7, I get:
V V V (1 V ) .
R R
2R
Plugging in the values of V3 and V4, I have 2 – 3V2 = 2V2 – 1 + ½ (3V2 – 2).
4
3
3
2
8.
(Does some working out on paper.) And that means V =
. And I can get the rest
13
using that…
2
Tutor: Okay, well done. No need to do all the algebra. Let’s leave it there.
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
Oxbridge Engineering Interview Scripts
Further hints
The tutor may demonstrate how to calculate potential differences in the presence
of a ground if the student is struggling at first. They also may prompt you to recall
Kirchhoff’s laws for voltage and current.
In the last part, they might ask you ‘What paths can current follow?’ or ‘What paths
are there that join the positive terminal of the cell to points of zero potential?’
Extending the question
The tutor might opt to extend this question in several ways:
•
The ground could be moved around the last circuit in the same way it was
moved around the first one.
•
For one of the circuits, you could be asked to find the current through any
resistor or the cell, or the power dissipated in any resistor or the whole circuit.
•
You could be asked a more conceptual question about what a ground is and
why it might be added to a circuit, especially if you have seen it used before.
What is the question testing?
The question aims to assess whether you know and can apply Kirchhoff’s laws—
as well as whether you can be systematic in the way you process information
to avoid becoming lost. It helps to be able to fluently and implicitly use the laws
rather than write out an equation each time. Finally, you’re being tested on your
ability to handle the presence of an unfamiliar component (the ground).
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
14
Oxbridge Engineering Interview Scripts
Related topics from university
Circuits and electronics are an essential part of the first-year courses at both
Oxford and Cambridge. You’ll also be able to specialise in Electrical Engineering
later in your degree if you wish. The concept of ‘ground’ occurs in slightly different
ways in DC and AC systems. You’ll see the latter a lot more at uni than at A Level,
because handling varying voltages and currents introduces several complications,
and because AC systems appear in so many important applications.
Oxbridge Engineering Interview Preparation Options
Find out about interview preparation courses and mock
interview at: http://oxbridgeformula.co.uk/interview-preparation
15