Prepare for University - Mathematical Physics

Age 16 to 18
Challenge Level

Here we collect 10 essential physics problems to get you thinking before you embark on your degree. We recommend that you try them over the summer before starting university and give an explanation of why they will be useful to you.

These problems will give you a good mathematical grounding in the topics likely to arise in your degree course.

Remember, these problems are designed to make you think and there is not necessarily a 'right' answer. Approach them in a thoughtful way; it is hoped that they are both interesting and stimulating. What questions do they raise in you mind? Where do these questions lead you? Take them to a level that feels comfortable for you.

Finally, once you have done the problems, study the solutions. These will give you additional insights into the problems and the underlying mathematics and science.


Big and small numbers in physics This problem will refine your skills at estimation, approximation and the basic equations of physics. There are several parts for you to come back to.
Model solutions The basic modelling assumptions made in physics at school will be challenged at university. This problem allows you to start to think about these issues and how various factors alter the solution to a problem.
Escape from planet earth Get deeper into Newton's laws of gravity by exploring escape velocities from planets large and small.
The Ultra Particle This fascinating problem will draw together various strands of basic physics.
Universal time, length, mass Dimensional analysis and units play an important role in advanced physics. Find out how the universe prefers to measure various quantities.
Hold still please This problem will help you to develop skill and intuition with forces, vectors and static electricity.
Ideal gases This problem will get you thinking about the kinetic assumptions underlying ideal gasses. It draws together many different types of calculation, many involving non-standard estimations. This gives good training in the sorts of open-thinking required at university.
Cobalt decay Numerical calculations involving clear thinking are a feature of advanced physics. Develop these skills by investigating the effects of the half-lives of the isotopes of cobalt on the mass of a mystery lump of the element.
The not-so-simple Pendulum In physics you will take differential equations to a new level. See how simple equations can be made somewhat more involved by relaxing the modelling assumptions.
Earth Orbit This mathematically involved problem will allow you to concentrate your mathematical skills whilst following in the steps of Newton and finding the path that the earth follows around the sun.

A key topic at university is electromagnetism. You can find out more about this area of physics by working through our article. More than just a very useful read, it is interspersed with small problems to provide maximum learning impact. So, get a paper and pencil and click here to get started.