PAT (Physics Admissions Test)

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

'Preparing for the PAT' video

Watch the recording of the 'Preparing for the PAT' session delivered at the June 2024 Open Day:

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.

In 2023 the PAT was hybrid - with online questions and a paper answer booklet; however, the older papers will still be of use when preparing. 

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. A set of model solutions for the 2010 paper is provided on the Physics website.   

• PAT paper 2023
• Admissions report 2023

• PAT paper 2022
• Admissions report 2022

• PAT paper 2021
• Admissions report 2021

• PAT paper 2020
• Admissions report 2020

• PAT paper 2019
• Admissions report 2019

• PAT paper 2018
• Admissions report 2018

• PAT paper 2017
• Admissions report 2017

• PAT paper 2016
• Admissions 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 June 2018 and still current)

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 θc when sinθc=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.

Websites and resources

Visit the Physics website for a list of other helpful resources and websites to help you to prepare for the PAT.