PAT (Physics Admissions Test)

Practice materials

Taking any type of test or exam can be stressful, but you can help build your confidence by doing a bit of preparation ahead of time. You may also do better in the real test if you've had a chance to practise some sample or past papers, and got used to the format and timings of the admissions test you have to take. Here are our top tips for preparing for the PAT:

1. Check the syllabus: we strongly recommend that you check the details and ensure that you have covered the relevant material. The material is aimed at A-level Maths and Physics plus knowledge of material covered at GCSE. However we cannot guarantee when the material will be covered in your school by the time of the test date. If this is the case, we recommend talking to your teacher about how best to tackle these subjects before the test. This may require you to do some independent study by reading through your textbook or looking at the online resources provided by your exam board.
2. Watch the PAT webinar on this page, which goes through some of the questions from the 2006 paper. 
3. Visit the Department of Physics Youtube channel, and watch their videos about admissions and preparing for the PAT. 
4. Review the sample papers for the PAT. This will help you to feel familiar with the test paper and know what to expect. 
5. Get practice doing some problem solving/hard physics questions that are not included in your A-level syllabus. It is advisable to do questions from a range of other sources, not just A-level type questions which can be more structured in nature than the PAT. There are some links below to other websites/material which you might find helpful.
6. Sit at least one past paper in test conditions. This is really important as it will help you get used to how much time to allocate to each question and keep within the two hour limit.

Don't worry if you find the past or specimen papers very difficult - they're supposed to be! All our tests are designed to stretch you further than you have been stretched before.

PAT webinar

Workbook questions

The PAT workbooks contain many questions of varying difficulty and subject matter, and the accompanying solutions manuals outline possible approaches to each question in detail. 

Workbook 1 ; Workbook 2

Solutions 1 ; Solutions 2

Past or specimen papers

As you may notice when going through past papers, the PAT has undergone various changes in the past few years.

In 2015, multiple-choice questions were removed, and longer 20 mark questions were replaced by shorter 10 mark questions. In 2017, multiple-choice questions were re-introduced and the physics and maths sections were mixed up.

The PAT now takes the same format as the past papers from 2018 onward; however, the older papers will still be of use when preparing. Please note that specified calculators are permitted.

We do not generally provide solutions to the past papers. When marking the PAT all suitable methods for solving the questions are allowed and we would not want you to feel only one specific way of solving the problem will gain you marks. Solutions to the 2009 paper can be found on the Physics website, together with a set of model solutions.    

• PAT paper 2022

• PAT paper 2020
  
  
• PAT paper 2019
• PAT report 2019

• PAT paper 2018
• PAT report 2018

• PAT paper 2017
• PAT report 2017

• PAT paper 2016
• PAT report 2016

• PAT paper 2015
• PAT report 2015

• PAT paper 2014
• PAT report 2014

• PAT paper 2013
• PAT report 2013

• PAT paper 2012
• PAT report 2012

• PAT paper 2011
• PAT report 2011

• PAT paper 2010
• PAT report 2010

• PAT paper 2009
• PAT report 2009

• PAT paper 2008
• PAT report 2008

• PAT paper 2007
• PAT report 2007

• PAT paper 2006
• PAT report 2006 

The University does not endorse, or allow use of, its tests that are protected by copyright for commercial use

PAT Syllabus 

Updated 6 June 2018

Please note that the formulae included in this syllabus do not represent an exhaustive list of formulae which may be used within the test. 

Syllabus for the Mathematics content

Elementary mathematics:

• Knowledge of elementary mathematics, in particular topics in arithmetic, geometry including coordinate geometry, and probability, will be assumed. Questions may require the manipulation of mathematical expressions in a physical context.

Algebra:

• Knowledge of the properties of polynomials, including the solution of quadratics either using a formula or by factorising.
• Graph sketching including the use of differentiation to find stationary points.
• Transformations of variables.
• Solutions to inequalities.
• Elementary trigonometry including relationships between sine, cosine and tangent (sum and difference formulae will be stated if required).
• Properties of logarithms and exponentials and how to combine logarithms, e.g. log(a) + log(b) = log(ab) .
• Knowledge of the formulae for the sum of arithmetic and geometric progressions to n (or infinite) terms.
• Use of the binomial expansion for expressions such as (a+bx)ⁿ, using only positive integer values of n.

Calculus:

• Differentiation and integration of polynomials including fractional and negative powers.
• Differentiation to find the slope of a curve, and the location of maxima and minima.
• Integration as the reverse of differentiation and as finding the area under a curve.
• Simplifying integrals by symmetry arguments including use of the properties of even and odd functions (where an even function has f(x)= f(-x), an odd function has f(-x)= - f(x)).

Syllabus for the Physics content

Mechanics:

• Distance, velocity, speed, acceleration, and the relationships between them, eg velocity as the rate of change of distance with time, acceleration as rate of change of velocity with time. Understand the difference between vector quantities (eg velocity) and scalar quantities (eg speed). Knowledge and use of equations such as speed = distance / time, acceleration = change in velocity / time or the SUVAT equations.
• Interpretation of graphs, eg force-distance, distance-time, velocity-time graphs and what the gradient of a curve or area underneath a curve represents.
• Response of a system to multiple forces; Newton's laws of motion; know the difference between weight (= mg) and mass; vector addition of forces.
• Circular motion including equations for centripetal force (F=mω²r or F=mv²/r) and acceleration (a=v²/r or a=ω²r).
• The meaning of the terms friction, air resistance and terminal velocity and how they can be calculated.
• Levers (including taking moments about a point on an object), pulleys (including calculating the tension in a rope or the overall motion in a system of ropes and pulleys) and other simple machines combining levers, springs and pulleys.
• Springs, including knowledge of Hooke's law (Force = - kx) and stored potential energy ( = 1/2 kx² ).
• Kinetic energy (= 1/2 mv²) and gravitational potential energy (= mgh in a constant gravitational field) and their inter-conversion; what other forms of energy exist (eg thermal, sound).
• Conservation of energy and momentum (=mass x velocity); power ( = energy transfer/time) and work ( = force x distance moved in direction of force).

Waves and optics:

• An understanding of the terms longitudinal and transverse waves; and that waves transfer energy without net movement of matter.
• Be able to define the amplitude, frequency, period, wavelength and speed of a wave. Knowledge and use of formulae for the wave speed = wavelength x frequency and frequency = 1 / period (with units of hertz, Hz).
• Basic properties of the electromagnetic spectrum, eg identify and correctly order parts of the spectrum by wavelength or frequency (radio waves, microwaves, IR, visible light, UV, X rays and gamma rays) and the nature and properties of electromagnetic waves (transverse, travel at the speed of light in a vacuum).
• Description of reflection at plane mirrors, where the angle of incidence (the angle between the incident ray and the normal) = angle of reflection (angle between the reflected ray and the normal).
• Refraction, including the definition of refractive index (n) as the ratio of the speed of light in a vacuum to the speed of light in a material and Snell’s law n₁sinθ₁=n₂sinθ₂. Elementary properties of prisms and optical fibres including total internal reflection, where total internal reflection occurs at an angle θ_c when sinθ_c=n₂/n₁
• Qualitative understanding of how interference, diffraction and standing waves can occur.

Electricity and magnetism:

• Understanding of the terms current ( = charge / time), voltage (potential difference = energy / charge), charge, resistance ( = voltage / current) and links to energy and power (power = voltage x current, power = energy / time). Knowledge of transformers, including how the number of turns on the primary and secondary coils affect the voltage and current.
• Understanding circuit diagrams including batteries, wires, resistors, filament lamps, diodes, capacitors, light dependent resistors and thermistors. Knowledge of current, voltage and resistance rules for series and parallel circuits.
• Knowledge of the force between two point charges (Force= kQ₁Q₂/r²(where k is a constant)) and on a point charge in a constant electric field (Force = charge x electric field).
• Understanding that current is a flow of electrons; the photoelectric effect, where photoelectrons are emitted if they are given sufficient energy to overcome the work function of the material, and how to find the energy of accelerated electron beams ( energy = charge x potential difference).

Natural world:

• Atomic structure; that atoms consist of protons, neutrons and electrons, definition of the atomic number, Bohr model of the atom.
• Basic knowledge of bodies in our Solar System, including planets, moons, comets and asteroids. (Name and relative positions of the planets should be known but detailed knowledge of their physical parameters is not required).
• Know what is meant by the phrases ‘phases of the moon’ and ‘eclipses’ and how the position of the observer on the Earth affects their view of these events.
• Knowledge of circular orbits under gravity including orbital speed, radius, period, centripetal acceleration, and gravitational centripetal force. This may include equating the force between two masses due to gravity (F=GM₁M₂/r²) to centripetal force of a smaller body orbiting a larger body (F=mω²r or F=mv²/r) and use of centripetal acceleration (a=v²/r or a=ω²r).
• Understanding of the terms satellites; geostationary and polar orbits.

Problem solving:

• Problems may be set which require problem solving based on information provided rather than knowledge about a topic.

If there are parts of the syllabus you haven’t yet covered in school, we recommend talking to your teacher about how best to tackle these topics before the test date. This may require you to do some independent study by reading through your textbook or looking at the online resources provided by your exam board. You can then test yourself using the further resources outlined on this page and picking relevant questions.

Calculators and tables

Non-graphical calculators may be used but no tables or lists of formulae are allowed. Candidates may be expected to perform standard arithmetical operations by hand, including simple powers and roots, and the manipulation of fractions. Numeric answers should be calculated to 2 significant figures unless indicated otherwise. Specifications for Calculators used in the PAT.

Websites and resources

Isaac Physics

This website contains lots of Maths and Physics problem solving questions.

We suggest you either look through the A- level book suggested here and try a few questions on topics you find tricky or select your own questions (Visit the Isaac Physics website, select ‘Problem solving’ and click on 'Physics' or 'Maths' and the level of question you want.)

Questions at the same level as the PAT tend to be around level 4-5. Remember to register/log in so the website records your progress. Their website also contains lots of questions which are suitable as university entrance preparation (eg for interviews).

British Physics Olympiad

This website contains lots of past papers and solutions of problem solving type questions.

Next time

This website contains some fun questions designed to make you think about physical concepts. They are often multiple choice or yes/no questions, and there is usually not much maths involved. 

Questions are grouped into topics, and each question has a title that is a link to a PDF that includes the question on one page and the solution on a second. Some of the questions are probably more relevant for interview questions than the PAT as they might not contain the level of maths required in the PAT but it can be useful for checking your understanding of general concepts.

I want to study Engineering.org

This website is a useful for all applicants not just those applying to engineering. On the first page there is a choice of level of question; you should be looking at the 'mathematics and physics questions at the level of university engineering admissions interviews' for preparation for the PAT or university interview practice.

This section then has an index of problems, divided into smaller groups of about 10-20 questions by topic. Each question has a multiple choice answer, plus hints for a solution strategy and summaries of relevant bits of theory.

There is also a (usually concise and mathematical) solution, plus little videos to help with understanding.

You might need a paper and pen to work out some of the problems and some of the material is beyond the PAT syllabus – you should double check if you are in doubt.

Brilliant.org

This website has some resources to test your mathematical and physics knowledge. Questions are usually answered via multiple choice and one of the nice aspects of this website is that you can see how many other people have got the question right or wrong.

The ‘Problems of the week’ on the home page are always free but quite a large part of the website requires a subscription to get full access.

Try the ‘Practice’ section of the website for some free questions on maths, electricity and magnetism and classical mechanics.