The PAT syllabus comes with the health warning “revised 24 February 2014” at the top. You should be aware of the changes to the syllabus when you are going through the past paper, so that you don’t spend too much time looking at things that aren’t going to get asked in the actual test.

Using the wayback engine it is possible to compare the current syllabus with the old one, to see exactly what has changed. In summary: the Maths syllabus hasn’t changed at all; the Physics syllabus has been slimmed down and made more mathematical. Areas with relatively increased emphasis, and where you can expect more questions in future, are

**Mechanics**. The mechanics paragraph itself hasn’t changed much apart from the addition of conservation of momentum (which was always implicitly there anyway). But if you look at the ‘natural world’ paragraph, you can see that it is now dominated by the sentence about circular orbits, which is just applied mechanics.**Waves and optics**. All the phrases ‘mathematical treatment not required’ have been removed. This means that there will be more mathematical questions dealing with refractive indices, total internal reflection, and presumably the ‘colour splitting’ effects that result from changes of refractive index with frequency.**Electricity and magnetism**. The phrase ‘mathematical treatment not required’ has been removed from the section about electrostatic and magnetic forces. I assume this means that you will need to be able to deal mathematically with the effect of electric and magnetic fields on a moving charge, which is another way of bringing in mechanics into the questions.

These three topics take up the whole syllabus apart from ‘problem solving’, and the rest of the ‘natural world’ topic (atomic structure; structure of the solar system; phases of the moon and eclipses; satellites; geostationary and polar orbits).

Areas that have been removed are:

- Everything to do with nuclear physics and radioactive decay.
- Everything to do with thermal properties of matter (e.g. gas laws, heat capacity, expansion).

If you want the full details, below we have the 2015 syllabus with the additions since 2012 in **bold** and the deleted sections since 2012 in ~~strikethrough~~.

### Syllabus for Part A of the aptitude test (mathematics for physics)

*Elementary mathematics:* knowledge of elementary mathematics, in particular topics in arithmetic, geometry including coordinate geometry, and probability, will be assumed.

*Algebra:* properties of polynomials, including the solution of quadratics. Graph sketching and transformations of variables. Inequalities and their solution. Elementary trigonometry including relationships between sin, cos and tan (sum and difference formulae will be stated if required). Properties of logarithms and exponentials. Arithmetic and geometric progressions and the binomial expansion.

*Calculus:* differentiation and integration of polynomials including fractional and negative powers. Differentiation as finding the slope of a curve, and the location of maxima, minima and points of inflection. Integration as the reverse of differentiation and as finding the area under a curve. Simplifying integrals by symmetry arguments.

*Physics:* knowledge of elementary physics will be assumed. Questions may require the manipulation of mathematical expressions in a physical context.

### Syllabus for Part B of the aptitude test (physics)

*Mechanics*: distance, velocity, speed, acceleration, and the relationships between them. Interpretation of graphs. Response to forces; Newton’s laws of motion; weight and mass; addition of forces; circular motion. Friction, air resistance, and terminal velocity. Levers, pulleys and other elementary machines. Springs and Hooke’s law. Kinetic and potential energy and their inter-conversion; other forms of energy; conservation of energy **and momentum**; power and work.

*Waves and optics*: longitudinal and transverse waves; amplitude, frequency, period, wavelength and speed, and the relationships between them. Basic properties of the electromagnetic spectrum. Reflection at plane mirrors. Refraction and elementary properties of prisms and lenses including total internal reflection ~~(mathematical treatment not required)~~. Elementary understanding of interference and diffraction ~~(mathematical treatment not required)~~.

*Electricity and magnetism*: current, voltage (potential difference), charge, resistance; relationships between them and links to energy and power. Elementary circuits including batteries, wires, resistors, filament lamps, diodes, capacitors, light dependent resistors and thermistors; series and parallel circuits. Elementary electrostatic forces and magnetism ~~(mathematical treatment not required). Links between electricity and magnetism~~; electromagnets, motors, generators ~~and transformers~~. Current as a flow of electrons; thermionic emission and energy of accelerated electron beams.

*Natural world*: atomic ~~and nuclear~~ structure; ~~properties of alpha, beta and gamma radiation; half lives. Nuclear fission.~~ Structure of the solar system. Phases of the moon and eclipses. Elementary treatment of circular orbits under gravity including orbital speed, radius, period, centripetal acceleration, and gravitational centripetal force. Satellites; geostationary and polar orbits. ~~Elementary properties of solids, liquids and gases including responses to pressure and temperature.~~

*Mathematics:* knowledge of elementary mathematics will be assumed. Questions may require the manipulation of mathematical expressions in a physical context.

*Problem solving:* problems may be set which require problem solving based on information provided rather than knowledge about a topic.

According to you, what’s the best method to find tangents from a point to a circle? This is assuming only the equation of the circle and the point itself are known. Could you use calculus here or what?

I tend to like using geometric methods because they sometimes work out very cleanly, but if you want a completely general method you should construct two equations (one for the circle, and one for a line going through the point) and combine them to generate a single quadratic equation. Then you can find the conditions for the discriminant of the quadratic to be zero, and substitute the values back in to the line equation.

For example, the equation of a line going through a known point

(X,Y)is(y-Y) = m(x-X), where m is the unknown gradient. The equation of a circle centred at a known point(A,B), with a known radius R is(x-A)² + (y-B)² = R². From the line equation you can see thaty-B = m(x-X) + Y – B, so therefore(x-A)² + (m(x-X) + Y – B)² = R². Rearrange this to the form ofax² + bx + c = 0, and find the conditions whenb² – 4ac = 0. This will give you another quadratic equation which you can solve form. Substitute each value ofmback into the line equation, and you will get the equations of the two lines that meet the circle at a tangent. Notice that if your point is inside the circle, you’ll get no solutions for m in the second quadratic, if the point is on the circle you’ll get one, and if the point is outside the circle you’ll get two.Hi, do you think diffraction equations will be required? (For single and double slits and diffraction grating?)

I don’t really know, but to be honest I don’t know those equations off the top of my head.

It’s best really to focus on problem solving rather than remembering equations. You should understand what diffraction is and how interference works, and given that knowledge you should be able to derive any results that you need relating to slit systems.

hi will we be expected to know the equations of magnetic and electric fields from A2

I don’t think so — I can’t recall these topics ever having come up so I wouldn’t worry.

thankyou

Hi, do you think any knowledge on stationary waves is necessary? Also thank you very much for this website, I have found it extremely useful in preparing for the PAT!

I don’t think you need to understand anything in particular about stationary waves. I guess it’s useful to know that the wavelengths of possible stationary waves are determined by the length of the string (or tube), but I think you’ll probably be able to work out anything like that from first principles in the test.

Hey, hi I am gonna give the PAT for Eng Sci. this year! How should I practice?

You’ve made the right start by reading this page to see what it is you need to know.

Apart from that it’s hard to say. I can’t do much more that to suggest you read the comment/reply below and the comment/reply at https://oxfordpat.wordpress.com/oxford-pat-2011-questions-9-and-10/comment-page-1/#comment-423

Do you have any idea about other resources I can use to practice? At the moment all I have is the past papers and some British Olympiad questions!

I think that if you do all those then you will probably have done enough practice. If you feel you need to do some more revision on specific subjects then try using A2 physics questions about the relevant topic. Just search for ‘physics A2 past papers’, but only bother if you feel you need to improve your understanding of some topics.