A classic set of 99 Maths Interview questions, covering a whole gamut of topics. 

Feature!! Mathematical Pathways for A Level Mathematics Students

​Find functions fun? Like getting maths right? Want to understand how the world, in all its numerical sophistication, really works? If that’s the case, a degree in mathematics (or a related area like Actuarial Sciences, Operational Research, etc…) might just be for you. It is rewarding in itself, and full of potential and options for the future. Here is some information to help you along the way.

Some Key Points

  1. There are many different flavours of Mathematics at University, depending on your other interests. You can be more theoretical, more applied, more stats-y, more about optimisation… it’s worth exploring these options.
  2. It’s an easy degree to combine with geography, history, business studies, politics, economics, finance, econometrics, philosophy, computing, modern languages – to name but a few options! Each of these pathways will allow you to keep developing different skills along the way. It is important to read course descriptions carefully. Chat you your maths teacher if you’d like to explore this further.
  3. There are some maths degrees you won’t have heard of… Applied courses such as Actuarial Studies are extremely interesting and open up really interesting, specialised and lucrative career paths, even though few school-age people have ever heard of them.
  4. You don’t need Further Maths. If you are enjoying your single mathematics course and thriving on it, then that’s fantastic – and there are lots of options open to you. See overleaf for examples of offers at some super universities with excellent maths departments, and great graduate prospects. Remember that a maths degree will make you singularly employable, so you don’t need to worry too much about issues of ‘caché’.
  5. It’s fun. 

Future Prospects. An article from the Telegraph says it all

Typical University offers
If you know your cosines from your differentials, the future looks rosy. As a mathematician, you are in a strong position to get a great job, whether in the banking sector, teaching, computing or many other related sectors that require analytical and numerical skills.
Kevin Goodman, group director of organisation and development at Babcock International Group, says: ''We value mathematics graduates because of their transferable skills: problem solving, logical thinking and the ability to understand technical information.”
“A growing number of students are choosing maths for a good reason – they are in demand in the job market,” says Bruce Woodcock, careers adviser for science, technology and mathematics at the University of Kent, which has seen its intake of maths and actuarial science undergraduates rise fourfold, from around 50 per year in 2010 to nearly 210 per year today. Financially it makes sense, too. “If students are investing £9,000 per year in tuition fees, they need that investment to pay. We see many graduates starting jobs at the higher end of the salary scale,” adds Woodcock.
The highest proportion of graduates from the University of Kent – 20 per cent – go into the finance sector, taking on roles in insurance, banking and risk management, but even more – 21pc – take a higher degree. “This can be an astute move, particularly if you want to go into statistics,” says Woodcock. By far the largest employer in this field is the Government Statistical Service (GSS), which employs 700 staff in more than 30 departments, but there is also a need for statisticians in the pharmaceuticals industry, medical schools, hospitals and in agricultural institutes. The GSS has an exceptional number of posts for Statistician Fast Streamers in 2014, in London and across the UK. The Fast Stream provides training for graduates who have the potential to become senior leaders in the Civil Service.
Teaching is also a popular choice for University of Kent graduates; incentivised by tax-free training bursaries, it attracts around 20pc. Another 10pc go into computing. “There’s a massive shortage of programmers and software engineers and salaries are very good. Computing is also an area that needs analytical skills, logic and numeracy,” says Woodcock.
Many mathematicians are also recruited into the defence industry and other science and engineering companies. Paul Barton, 30, studied maths and computer science at the University of York before entering the graduate scheme at BAE Systems’ Electronic Systems business in Rochester, Kent, where he worked on an innovative helmet for pilots of the Eurofighter Typhoon combat aircraft. Now a senior engineer with the leading aerospace, defence and security company, he says maths gave him an excellent grounding.
“It taught me how to tackle a range of issues in a logical way. Many of my peers at BAE Systems also have degrees in core STEM subjects, which form the basis of their professional skills.”
Barton, who gained Chartered engineer status in 2011 after five years’ experience and is now based at BAE Systems’ Advanced Technology Centre in Chelmsford, Essex, believes maths also helped him gain managerial skills. “I now have five research engineers in my team developing technology to improve computer security and detect malware in systems.”
Now, when he assesses candidates for year-long paid sandwich placements and summer placements at BAE Systems, he admits that he looks twice at maths students.

But what will I do afterwards?

Your degree will be in enormously high demand. According to a recent government survey, only behind teachers and doctors [see below, find the whole text: SFR60/2016]. Jobs for mathematicians are really varied – from engineering to consultancy, and what you do will depend on what type of mathematics you have chosen to specialise in. 
​And it’s lovely work – the best in the world, according to the Wall Street Journal...
​These are all for mathematics but will be similar (or lower) for mathematically-based courses.
University of Bristol
The usual entry requirements are: A*A*A including A* in Mathematics, plus at least one of Physics, Chemistry, Biology, Economics or Computer Science.
University of Reading
At the University of Reading we require candidates to have achieved at least a grade A at A level Mathematics. Our typical offer for our BSc Mathematics course is in the range AAB-ABB.  If you are studying Further Mathematics at AS level we will make an alternative offer of ABC with a grade A in A level in Mathematics and a grade A in AS level Further Mathematics.
University of Bath
A* in A-level Mathematics with A's in each module, grades A* and A in two further A- level subjects plus at least 2/Merit in one STEP/AEA paper. A second scientific or quantitative subject, preferably physics.
Loughborough University
AAA - AAB, including Mathematics at grade A. Applicants with any of the following will usually be given the lower offer (AAB): Further Mathematics, Physics, Chemistry, Computing or Economics; Further Mathematics AS-Level at grade A; AEA or STEP in Maths.
University of York
AAA in three A levels, including Mathematics. We will offer you an interview if you present with a strong school performance and application form. Although the interview is not part of your offer and you do not need to attend, if you do, your offer could be reduced by one A Level grade or equivalent.
Leeds University
For applicants taking A-levels, we require at least Grade A in A-level Mathematics. Note that Leeds runs a taster course – speak to MSC if you are interested in this!
Lancaster University
Our minimum requirement for A Level applicants is that you should be studying at least three A Levels including A Level Mathematics. For the majority of our degrees, our offer will usually be as follows. Firstly, we require grade A or higher in A Level Mathematics. Secondly, we require that your grades from your best 3 A Levels satisfy the following condition: best 3 A Levels (with at least Grade 3 in STEP) at AAB.

Sample courses at Leeds

Sample Courses (Leeds)
Mathematics BSc
In your first year, you’ll gain a solid grounding in the major branches of mathematics, including calculus, algebra, statistics and mechanics. Having been able to establish the areas that most interest you in your first year, we give you a huge amount of choice in the years that follow. Modules are available in topics as diverse as fluid dynamics, environmental statistics, coding theory, and groups and symmetry. You can specialise in a particular area of mathematics according to your interests or aspirations. Or, you can retain a broad set of interests and explore several different areas.
This course offers you the opportunity to spend a year working in industry or studying at a university abroad, both of which provide valuable experience and help your personal development. Both of these schemes add an additional year to your course, taking the total course length to 4 years.
Related Course
Actuarial Mathematics BSc
The most interesting degree that no-one has ever heard of
Actuaries use mathematical, statistical, financial and economic theory to solve real business problems, typically involving risk, uncertainty and the financial impact of undesirable events. There is an increasing demand for actuaries in both the private and public sectors, working within a variety of areas such as banking, investment management, consultancy, manufacturing, transport, insurance and pensions.
On this course, you’ll be taught jointly by the School of Mathematics and Leeds University Business School, exploring key topics in mathematics, finance, economics and accounting. You’ll be intellectually stimulated whilst preparing for a potential career that is highly financially-rewarding.
This programme covers most of the content of The Actuarial Profession’s (Institute/Faculty of Actuaries) core technical subjects CT 1-8. On graduation, you will be able to apply for exemptions from some of The Actuarial Profession’s exams.
Related Course
Data Science MSc
The Data Science and Analytics MSc is a highly flexible course which includes analysing structured and unstructured data, analysing large datasets and critically evaluating results in context, through a combination of compulsory and optional modules. By choosing appropriate modules you can follow specific pathways, in business management, healthcare or geographic information systems.
The course combines expertise from the Schools of Computing, Geography and Mathematics with that of Leeds University Business School and the Yorkshire Centre for Health Informatics. This collaboration allows you to benefit from a range of data science perspectives and applications, supporting you to tailor your learning to your career ambitions.
 
See the website for other related courses such as Mathematics with Finance or Operational Systems.

Which test should I take?

How can I prepare for interview?
Many universities require students to sit an extra maths test on top of their A-levels. The STEP paper is taken at the end of year 13, and is required by Cambridge and Warwick, and is optional for other universities such as Bath and UCL. For these, the A-level requirements are lower if candidates achieve a high grade in STEP.
The MAT is sat in the first term of year 13, and is required by Oxford and Imperial.
One of the benefits of the MAT is that it is over early, and so any offers received are more certain. However, there are three STEP papers, which means that there are more chances, and there is often more flexibility with offers.
Links to STEP and MAT questions are provided at the top of the page. It is worth giving STEP questions a go whichever exam you choose, because they are recommended by Oxford as useful practise to help with the MAT, and there is a huge bank of questions available across all topics.



Doing the TSA for economics, Natural Sciences, or Law? Find past papers here.
You can read reports from ONLs about what happened in their interviews at Oxford or Cambridge to know what to expect.
You can also watch some mock interviews below.
Recommended reading material can be found here, but don't go mad over quantity. Instead, make sure you know any reading you put in your personal statement really well, and it may help you to take brief notes about the books that you can skim through beforehand to refresh your memory and calm yourself down.

Cambridge has issued a workbook of useful material to cover before starting their undergraduate course, which could be worth looking for more practise problems.

Engineering Interview Questions

Check out this website of problems which allows you to chart your progress!
Recommended by you, the "I want to study engineering" website, with a collection of problems.  
First year lecture notes from the University of Oxford which can make useful reading - interviewers often invent questions from these! (to be uploaded).
1. A cubic block is submerged in water inside a tank. What is the normal reaction on the block by the tank if the depth of water is H and the height of the block is A? What is the pressure on the top surface of the block?
2. You have a boat floating in water. Draw a graph of minimum force required to lift the boat against the displacement from the equilibrium position. 
3. You have as many 50µF capacitors as you like but they only withstand 100V. Make a capacitor of 100 µF which withstands 230V.
4. A magnet is glued to the ceiling with a N pole facing down. A second magnet, with the S pole up, is moved sufficiently close to the top magnet that the force of electromagnetic attraction is equal to the weight of the magnet. Will the second magnet be in a stable equilibrium?
5. A cyclist of mass m rides up the loop of radius r. The gravitational acceleration is g. What minimum initial speed is required for the cyclist to complete the loop?
6. A suitcase with a long handle is held on a smooth ground by a man’s hand such that it is at equilibrium. The suitcase is at an angle to the vertical. What is the direction of the force on the man’s hand?
7. A tank is filled with water to the height H. A small hole is made in the side of the tank at the height L from the bottom. Find the distance S from the tank at which the water jet from the hole hits the ground. What is the optimal value of L which maximises the distance S?
8. Why do bicycles have gears? 
9. In projectile motion, prove that the angle for maximum range is 45˚.
10. The swings have one end attached to the ground with a spring. The second end has a mass attached to it. Prove that small displacements of the mass from the equilibrium result in simple harmonic motion.
11. Estimate the number of air molecules in a box. How does the pressure inside the box change when a certain number of new air molecules are added?
12. A circular wheel is moving up a step. What are the forces acting on the wheel?
13. A fridge is placed in the middle of the room. Sketch the temperature graph against time when the fridge door is opened and then closed after a certain time.
14. Explain how the spirit level works.
15. Would the Arctic ice melting raise the sea levels?
16. Two spheres of mass M each are at a distance 2A from each other. The third mass, m, is placed at a distance x from the mid-point between the first two masses at equal distances to them. Estimate the gravitational force on the mass m when (i) x>>A and (ii) x<
17. What are the forces acting on a floating block of ice as it melts? 
18. Describe the experiments that prove the wave/particle nature of light.
19. What energy is required to launch a geostationary satellite?
20. A block of metal is thrown into water from the boat. What happens to the water level? What about a block of wood?
21. Draw the graph of displacement, velocity and acceleration for a rocket.