# PAT syllabus

** Syllabus revised 24 February 2014 **

### Syllabus for the Mathematics for Physics of the aptitude test

*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.

*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*.

### Syllabus for the Physics of the aptitude test

*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 optical fibres including total internal reflection. Elementary understanding of interference and diffraction.

*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; electromagnets, motors and generators. Current as a flow of electrons; thermionic emission and energy of accelerated electron beams.

*Natural world:* atomic structure. 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.

*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.

*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

No calculators or tables may be used. Candidates may be expected to perform standard arithmetical operations by hand, including multiplication and division, simple powers and roots, and the manipulation of fractions. Numeric answers should be calculated to 2 significant figures unless indicated otherwise. Knowledge of the values of sin, cos and tan for angles of 0, 30, 45, 60 and 90 degrees (and angles offset from these by multiples of 90 degrees) may be assumed.