- Electric Fields
- Current of Electricity
- C. Circuits
- Electromagnetism
- Electromagnetic Induction
- Alternating Current

- Physical quantities and SI units
- Scalars and vectors
- Errors and uncertainties

- recall the following base quantities and their SI units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
- express derived units as products or quotients of the base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate
- use SI base units to check the homogeneity of physical equations
- show an understanding of and use the conventions for labelling graph axes and table columns as set out in the ASE publication
*Signs, Symbols and Systematics (The ASE Companion to 16–19 Science, 2000)* - use the following prefixes and their symbols to indicate decimal sub-multiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)
- make reasonable estimates of physical quantities included within the syllabus
- distinguish between scalar and vector quantities, and give examples of each
- add and subtract coplanar vectors
- represent a vector as two perpendicular components
- show an understanding of the distinction between systematic errors (including zero error) and random errors
- show an understanding of the distinction between precision and accuracy
- assess the uncertainty in a derived quantity by addition of actual, fractional, percentage uncertainties or by numerical substitution (a rigorous statistical treatment is not required).

- Rectilinear motion
- Non-linear motion

- define and use displacement, speed, velocity and acceleration
- use graphical methods to represent distance, displacement, speed, velocity and acceleration
- identify and use the physical quantities from the gradients of displacement-time graphs and areas under and gradients of velocity-time graphs, including cases of non-uniform acceleration
- derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line
- solve problems using equations which represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance
- describe qualitatively the motion of bodies falling in a uniform gravitational field with air resistance
- describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction.

- Newton’s laws of motion
- Linear momentum and its conservation

- state and apply each of Newton’s laws of motion
- show an understanding that mass is the property of a body which resists change in motion (inertia)
- describe and use the concept of weight as the effect of a gravitational field on a mass
- define and use linear momentum as the product of mass and velocity
- define and use impulse as the product of force and time of impact
- relate resultant force to the rate of change of momentum
- recall and solve problems using the relationship
*F = ma*, appreciating that resultant force and acceleration are always in the same direction - state the principle of conservation of momentum
- apply the principle of conservation of momentum to solve simple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required)
- show an understanding that, for a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation
- show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place.

- Types of force
- Centre of gravity
- Turning effects of forces
- Equilibrium of forces
- Upthrust

- recall and apply Hooke’s law (
*F = kx*, where*k*is the force constant) to new situations or to solve related problems - describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate
- show a qualitative understanding of normal contact forces, frictional forces and viscous forces including air resistance (no treatment of the coefficients of friction and viscosity is required)
- show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity
- define and apply the moment of a force and the torque of a couple
- show an understanding that a couple is a pair of forces which tends to produce rotation only
- apply the principle of moments to new situations or to solve related problems
- show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium
- use a vector triangle to represent forces in equilibrium
- derive, from the definitions of pressure and density, the equation
*p = ρgh* - solve problems using the equation
*p = ρgh* - show an understanding of the origin of the upthrust acting on a body in a fluid
- state that upthrust is equal to the weight of the fluid displaced by a submerged or floating object
- calculate the upthrust in terms of the weight of the displaced fluid
- recall and apply the principle that, for an object floating in equilibrium, the upthrust is equal to the weight of the object to new situations or to solve related problems.

- Work
- Energy conversion and conservation
- Efficiency
- Potential energy and kinetic energy
- Power

- show an understanding of the concept of work in terms of the product of a force and displacement in thedirection of the force
- calculate the work done in a number of situations including the work done by a gas which is expandingagainst a constant external pressure:
*W = pΔV* - give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation
- show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems
- derive, from the equations for uniformly accelerated motion in a straight line, the equation
*E*_{k}= ½mv^{2} - recall and use the equation
*E*_{k}= ½mv^{2} - distinguish between gravitational potential energy, electric potential energy and elastic potential energy
- deduce that the elastic potential energy in a deformed material is related to the area under the forceextensiongraph
- show an understanding of and use the relationship between force and potential energy in a uniform fieldto solve problems
- derive, from the definition of work done by a force, the equation
*E*for gravitational potentialenergy changes near the Earth’s surface_{p}= mgh - recall and use the equation
*E*for gravitational potential energy changes near the Earth’s surface_{p}= mgh - define power as work done per unit time and derive power as the product of a force and velocity in thedirection of the force.

- Kinematics of uniform circular motion
- Centripetal acceleration
- Centripetal force

- express angular displacement in radians
- show an understanding of and use the concept of angular velocity to solve problems
- recall and use
*v = rω*to solve problems - describe qualitatively motion in a curved path due to a perpendicular force, and understand thecentripetal acceleration in the case of uniform motion in a circle
- recall and use centripetal acceleration
*a = rω*, and^{2}*a = v*to solve problems^{2}/r - recall and use centripetal force
*F = mrω*, and^{2}*F = mv*to solve problems.^{2}/r

- Gravitational field
- Gravitational force between point masses
- Gravitational field of a point mass
- Gravitational field near to the surface of the Earth
- Gravitational potential
- Circular orbits

- show an understanding of the concept of a gravitational field as an example of field of force and define the gravitational field strength at a point as the gravitational force exerted per unit mass placed at that point
- recognise the analogy between certain qualitative and quantitative aspects of gravitational and electric fields
- recall and use Newton’s law of gravitation in the form
*F =**Gm*_{1}*m*_{2}

_______

*r*^{2} - derive, from Newton’s law of gravitation and the definition of gravitational field strength,

the equation*g =*for the gravitational field strength of a point mass*G M*

_______

*r*^{2} - recall and apply the equation
*g =*for the gravitational field strength of a point mass to new situations or to solve related problems*G M*

_______

*r*^{2} - show an understanding that near the surface of the Earth g is approximately constant and equal to the acceleration of free fall
- define the gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to that point
- solve problems using the equation
*φ =*for the gravitational potential in the field of a point mass*G M*

_______

*r* - analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes
- show an understanding of geostationary orbits and their application.

- Thermal equilibrium
- Temperature scales
- Equation of state
- Kinetic theory of gases
- Kinetic energy of a molecule

- show an understanding that regions of equal temperature are in thermal equilibrium
- explain how empirical evidence leads to the gas laws and to the idea of an absolute scale of temperature(i.e. the thermodynamic scale that is independent of the property of any particular substance and has anabsolute zero)
- convert temperatures measured in kelvin to degrees Celsius:
*T / K = T / °C + 273.15* - recall and use the equation of state for an ideal gas expressed as
*pV = nRT*, where n is the amount ofgas in moles - state that one mole of any substance contains 6.02 × 10
^{23}particles and use the Avogadro number*N*= 6.02 × 10_{A}^{23}mol^{–1} - state the basic assumptions of the kinetic theory of gases
- explain how molecular movement causes the pressure exerted by a gas and hence derive the relationship
*pV =*, where N is the number of gas molecules (a simple model considering onedimensionalcollisions and then extending to three dimensions using^{1}/_{3}Nm<c^{2}><c^{1}/_{3}^{2}> = <c_{x}^{2}> is sufficient) - recall and apply the relationship that the mean kinetic energy of a molecule of an ideal gas isproportional to the thermodynamic temperature (i.e. ½ m<c
^{2}> =) to new situations or to solverelated problems.^{3}/_{2}kT

- Specific heat capacity and specific latent heat
- Internal energy
- First law of thermodynamics

- define and use the concepts of specific heat capacity and specific latent heat
- show an understanding that internal energy is determined by the state of the system and that it can beexpressed as the sum of a random distribution of kinetic and potential energies associated with themolecules of a system
- relate a rise in temperature of a body to an increase in its internal energy
- recall and use the first law of thermodynamics expressed in terms of the increase in internal energy, theheat supplied to the system and the work done on the system.

- Simple harmonic motion
- Energy in simple harmonic motion
- Damped and forced oscillations, resonance

- describe simple examples of free oscillations
- investigate the motion of an oscillator using experimental and graphical methods
- show an understanding of and use the terms amplitude, period, frequency, angular frequency andphase difference and express the period in terms of both frequency and angular frequency
- recall and use the equation
*a*= -*ω*as the defining equation of simple harmonic motion^{2}x - recognise and use
*x*=*x*_{0}sin*ω t*as a solution to the equation*a*= -*ω*^{2}x - recognise and use the equations
*v = v*_{0}cos*ω t*and*v = ±ω*√(*x*)^{2}_{o}- x^{2} - describe, with graphical illustrations, the changes in displacement, velocity and acceleration duringsimple harmonic motion
- describe the interchange between kinetic and potential energy during simple harmonic motion
- describe practical examples of damped oscillations with particular reference to the effects of the degreeof damping and to the importance of critical damping in applications such as a car suspension system
- describe practical examples of forced oscillations and resonance
- describe graphically how the amplitude of a forced oscillation changes with driving frequency near to thenatural frequency of the system, and understand qualitatively the factors which determine the frequencyresponse and sharpness of the resonance
- show an appreciation that there are some circumstances in which resonance is useful, and othercircumstances in which resonance should be avoided.

- Progressive waves
- Transverse and longitudinal waves
- Polarisation
- Determination of frequency and wavelength of sound waves

- show an understanding of and use the terms displacement, amplitude, period, frequency, phasedifference, wavelength and speed
- deduce, from the definitions of speed, frequency and wavelength, the equation
*v = fλ* - recall and use the equation
*v = fλ* - show an understanding that energy is transferred due to a progressive wave
- recall and use the relationship,
*intensity ∝ (amplitude)*^{2} - show an understanding of and apply the concept that a wave from a point source and travelling withoutloss of energy obeys an inverse square law to solve problems
- analyse and interpret graphical representations of transverse and longitudinal waves
- show an understanding that polarisation is a phenomenon associated with transverse waves
- recall and use Malus’ law
*(intensity ∝ cos*to calculate the amplitude and intensity of a plane polarised electromagnetic wave after transmission through a polarising filter^{2}θ) - determine the frequency of sound using a calibrated oscilloscope
- determine the wavelength of sound using stationary waves.

- Principle of superposition
- Stationary waves
- Diffraction
- Two-source interference
- Single slit and multiple slit diffraction

- explain and use the principle of superposition in simple applications
- show an understanding of the terms interference, coherence, phase difference and path difference
- show an understanding of experiments which demonstrate stationary waves using microwaves,stretched strings and air columns
- explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes
- explain the meaning of the term diffraction
- show an understanding of experiments which demonstrate diffraction including the diffraction of waterwaves in a ripple tank with both a wide gap and a narrow gap
- show an understanding of experiments which demonstrate two-source interference using water waves,sound waves, light and microwaves
- show an understanding of the conditions required for two-source interference fringes to be observed
- recall and solve problems using the equation
*λ = ax / D*for double-slit interference using light - recall and use the equation
*sinθ = λ / b*to locate the position of the first minima for single slit diffraction - recall and use the Rayleigh criterion
*θ ≈ λ / b*for the resolving power of a single aperture - recall and use the equation
*dsinθ = nλ*to locate the positions of the principal maxima produced by adiffraction grating - describe the use of a diffraction grating to determine the wavelength of light (the structure and use of aspectrometer are not required).

- Concept of an electric field
- Electric force between point charges
- Electric field of a point charge
- Uniform electric fields
- Electric potential

- show an understanding of the concept of an electric field as an example of a field of force and defineelectric field strength at a point as the electric force exerted per unit positive charge placed at that point
- represent an electric field by means of field lines
- recognise the analogy between certain qualitative and quantitative aspects of electric field andgravitational field
- recall and use Coulomb\'s law in the form
*F = Q*for the electric force between two pointcharges in free space or air_{1}Q_{2}/ 4πε_{0}r^{2} - recall and use
*E = Q / 4πε*for the electric field strength of a point charge in free space or air_{0}r^{2} - calculate the electric field strength of the uniform field between charged parallel plates in terms of thepotential difference and plate separation
- calculate the forces on charges in uniform electric fields
- describe the effect of a uniform electric field on the motion of charged particles
- define the electric potential at a point as the work done per unit positive charge in bringing a small testcharge from infinity to that point
- state that the field strength of the electric field at a point is numerically equal to the potential gradient atthat point
- use the equation
*V = Q / 4πε*for the electric potential in the field of a point charge, in free space or air._{0}r

- Electric current
- Potential difference
- Resistance and resistivity
- Electromotive force

- show an understanding that electric current is the rate of flow of charge
- derive and use the equation
*I = nAvq*for a current-carrying conductor, where n is the number density ofcharge carriers and v is the drift velocity - recall and solve problems using the equation
*Q = It* - recall and solve problems using the equation
*V = W / Q* - recall and solve problems using the equations
*P = VI, P = I*and^{2}R*P = V*^{2}/ R - recall and solve problems using the equation
*V = IR* - sketch and explain the
*I–V*characteristics of various electrical components such as an ohmic resistor, asemiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor - sketch the resistance-temperature characteristic of an NTC thermistor
- recall and solve problems using the equation
*R =ρl / A* - distinguish between electromotive force (e.m.f.) and potential difference (p.d.) using energyconsiderations
- show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminalpotential difference and output power.

- Circuit symbols and diagrams
- Series and parallel arrangements
- Potential divider
- Balanced potentials

- recall and use appropriate circuit symbols as set out in the ASE publication
*Signs, Symbols andSystematics (The ASE Companion to 16–19 Science, 2000)* - draw and interpret circuit diagrams containing sources, switches, resistors, ammeters, voltmeters,and/or any other type of component referred to in the syllabus
- solve problems using the formula for the combined resistance of two or more resistors in series
- solve problems using the formula for the combined resistance of two or more resistors in parallel
- solve problems involving series and parallel circuits for one source of e.m.f.
- show an understanding of the use of a potential divider circuit as a source of variable p.d.
- explain the use of thermistors and light-dependent resistors in potential divider circuits to provide apotential difference which is dependent on temperature and illumination respectively
- recall and solve problems by using the principle of the potentiometer as a means of comparing potentialdifferences.

- Concept of a magnetic field
- Magnetic fields due to currents
- Force on a current-carrying conductor
- Force between current-carrying conductors
- Force on a moving charge

- show an understanding that a magnetic field is an example of a field of force produced either by currentcarryingconductors or by permanent magnets
- sketch flux patterns due to currents in a long straight wire, a flat circular coil and a long solenoid
- use
*B = μ*and_{0}I / 2πd, B = μ_{0}NI / 2r*B = μ*for the flux densities of the fields due to currents in a longstraight wire, a flat circular coil and a long solenoid respectively_{0}nI - show an understanding that the magnetic field due to a solenoid may be influenced by the presence of aferrous core
- show an understanding that a current-carrying conductor placed in a magnetic field might experience aforce
- recall and solve problems using the equation
*F = BIl sinθ*, with directions as interpreted by Fleming’sleft-hand rule - define magnetic flux density and the tesla
- show an understanding of how the force on a current-carrying conductor can be used to measure theflux density of a magnetic field using a current balance
- explain the forces between current-carrying conductors and predict the direction of the forces
- predict the direction of the force on a charge moving in a magnetic field
- recall and solve problems using the equation
*F = BQvsinθ* - describe and analyse deflections of beams of charged particles by uniform electric and uniformmagnetic fields
- explain how electric and magnetic fields can be used in velocity selection for charged particles.

- Magnetic flux
- Laws of electromagnetic induction

- define magnetic flux and the weber
- recall and solve problems using
*Φ = BA* - define magnetic flux linkage
- infer from appropriate experiments on electromagnetic induction:
- that a changing magnetic flux can induce an e.m.f.
- that the direction of the induced e.m.f. opposes the change producing it
- the factors affecting the magnitude of the induced e.m.f.

- recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law
- explain simple applications of electromagnetic induction.

- Characteristics of alternating currents
- The transformer
- Rectification with a diode

- show an understanding of and use the terms period, frequency, peak value and root-mean-square(r.m.s.) value as applied to an alternating current or voltage
- deduce that the mean power in a resistive load is half the maximum (peak) power for a sinusoidalalternating current
- represent an alternating current or an alternating voltage by an equation of the form
*x = x*sin_{0}*ωt* - distinguish between r.m.s. and peak values and recall and solve problems using the relationship
*I*for the sinusoidal case_{rms}= I_{o}/ √2 - show an understanding of the principle of operation of a simple iron-core transformer and recall andsolve problems using
*N*for an ideal transformer_{s}/ N_{p}= V_{s}/ V_{p}= I_{p}/ I_{s} - explain the use of a single diode for the half-wave rectification of an alternating current.

- Energy of a photon
- The photoelectric effect
- Wave-particle duality
- Energy levels in atoms
- Line spectra
- X-ray spectra
- The uncertainty principle

- show an appreciation of the particulate nature of electromagnetic radiation
- recall and use the equation
*E = hf* - show an understanding that the photoelectric effect provides evidence for the particulate nature ofelectromagnetic radiation while phenomena such as interference and diffraction provide evidence forthe wave nature
- recall the significance of threshold frequency
- recall and use the equation
*½ mv*, where_{max}^{2}= eV_{s}*V*is the stopping potential_{s} - explain photoelectric phenomena in terms of photon energy and work function energy
- explain why the stopping potential is independent of intensity whereas the photoelectric current isproportional to intensity at constant frequency
- recall, use and explain the significance of the equation
*hf = Φ + ½ mv*_{max}^{2} - describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature ofparticles
- recall and use the relation for the de Broglie wavelength
*λ = h / p* - show an understanding of the existence of discrete electronic energy levels in isolated atoms(e.g. atomic hydrogen) and deduce how this leads to the observation of spectral lines
- distinguish between emission and absorption line spectra
- recall and solve problems using the relation
*hf = E*_{2}– E_{1} - explain the origins of the features of a typical X-ray spectrum
- show an understanding of and apply
*ΔpΔx ≳ h*as a form of the Heisenberg position-momentum uncertainty principle to new situations or to solve related problems.

- The nucleus
- Isotopes
- Nuclear processes
- Mass defect and nuclear binding energy
- Radioactive decay
- Biological effects of radiation

- infer from the results of the Rutherford α-particle scattering experiment the existence and small size ofthe atomic nucleus
- distinguish between nucleon number (mass number) and proton number (atomic number)
- show an understanding that an element can exist in various isotopic forms each with a different numberof neutrons in the nucleus
- use the usual notation for the representation of nuclides and represent simple nuclear reactions bynuclear equations of the form
^{14}_{7}N +^{4}_{2}He →^{17}_{8}O +^{1}_{1}H - state and apply to problem solving the concept that nucleon number, charge and mass-energy are allconserved in nuclear processes.
- show an understanding of the concept of mass defect
- recall and apply the equivalence relationship between energy and mass as represented by
*E = mc*to solve problems^{2} - show an understanding of the concept of nuclear binding energy and its relation to mass defect
- sketch the variation of binding energy per nucleon with nucleon number
- explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission
- show an understanding of the spontaneous and random nature of nuclear decay
- infer the random nature of radioactive decay from the fluctuations in count rate
- show an understanding of the origin and significance of background radiation
- show an understanding of the nature of α, β and γ radiations (knowledge of positron emission is notrequired)
- show an understanding of how the conservation laws for energy and momentum in β decay were usedto predict the existence of the neutrino (knowledge of antineutrino and antiparticles is not required)
- define the terms activity and decay constant and recall and solve problems using the equation
*A = λN* - infer and sketch the exponential nature of radioactive decay and solve problems using the relationship
*x = x*_{0}exp(*-λt*) where*x*could represent activity, number of undecayed particles and received count rate - define half-life
- solve problems using the relation
*λ*=ln 2

_______

*t*_{½} - discuss qualitatively the effects, both direct and indirect, of ionising radiation on living tissues and cells.

® THE PHYSICS CAFÉ and THE MATHS CAFÉ are the Registered Trademark (TM No. 40201519273W) of ThePhysicsCafe.com and www.pmc.sg