## Syllabus 6 June 2018

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

### Syllabus for the mathematics content of Physics Aptitude Test

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 of Physics Aptitude Test

Mechanics:

- Distance, velocity, speed, acceleration, and the relationships between them, e.g. 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 (e.g. velocity) and scalar quantities (e.g. speed). Knowledge and use of equations such as speed = distance / time, acceleration = change in velocity / time or the SUVAT equations.
- Interpretation of graphs, e.g. 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=mω
^{2}r or F=mv^{2}/r) and acceleration (a=v^{2}/r or a=ω^{2}r). - 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 kx
^{2}). - Kinetic energy (= 1/2 mv
^{2}) and gravitational potential energy (= mgh in a constant gravitational field) and their inter-conversion; what other forms of energy exist (e.g. 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, e.g. 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 n
_{1}sinθ_{1}=n_{2}sinθ_{2}. Elementary properties of prisms and optical fibres including total internal reflection, where total internal reflection occurs at an angle θ_{c}when sinθ_{c}=n_{2}/n_{1} - 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= kQ1Q
_{2}/r^{2}(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=GM
_{1}M_{2}/r^{2}) to centripetal force of a smaller body orbiting a larger body (F=mω^{2}r or F=mv^{2}/r) and use of centripetal acceleration (a=v^{2}/r or a=ω^{2}r). - 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 which you think won't be covered at school by the time of the PAT, we expect you to work on them by yourself. Your teachers might be able to advise you.

### 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.