CIE 9702

understand that all physical quantities consist of a numerical magnitude and a unit

make reasonable estimates of physical quantities included within the syllabus

recall the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K)

express derived units as products or quotients of the SI base units and use the derived units for quantities listed in this syllabus as appropriate

use SI base units to check the homogeneity of physical equations

recall and use the following prefixes and their symbols to indicate decimal submultiples 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)

understand and explain the effects of systematic errors (including zero errors) and random errors in measurements

understand the distinction between precision and accuracy

assess the uncertainty in a derived quantity by simple addition of absolute or percentage uncertainties

understand the difference between scalar and vector quantities and give examples of scalar and vector quantities included in the syllabus

add and subtract coplanar vectors

represent a vector as two perpendicular components

define and use distance, displacement, speed, velocity and acceleration

use graphical methods to represent distance, displacement, speed, velocity and acceleration

determine displacement from the area under a velocity–time graph

determine velocity using the gradient of a displacement–time graph

determine acceleration using the gradient of a velocity–time graph

derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line

solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance

describe an experiment to determine the acceleration of free fall using a falling object

describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

understand that mass is the property of an object that resists change in motion

recall F = ma and solve problems using it, understanding that acceleration and resultant force are always in the same direction

define and use linear momentum as the product of mass and velocity

define and use force as rate of change of momentum

state and apply each of Newton’s laws of motion

describe and use the concept of weight as the effect of a gravitational field on a mass and recall that the weight of an object is equal to the product of its mass and the acceleration of free fall

show a qualitative understanding of frictional forces and viscous/drag forces including air resistance (no treatment of the coefficients of friction and viscosity is required, and a simple model of drag force increasing as speed increases is sufficient)

describe and explain qualitatively the motion of objects in a uniform gravitational field with air resistance

understand that objects moving against a resistive force may reach a terminal (constant) velocity

state the principle of conservation of momentum

apply the principle of conservation of momentum to solve simple problems, including elastic and inelastic interactions between objects in both one and two dimensions (knowledge of the concept of coefficient of restitution is not required)

recall that, for an elastic collision, total kinetic energy is conserved and the relative speed of approach is equal to the relative speed of separation

understand that, while momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place

understand that the weight of an object may be taken as acting at a single point known as its centre of gravity

define and apply the moment of a force

understand that a couple is a pair of forces that acts to produce rotation only

define and apply the torque of a couple

state and apply the principle of moments

understand that, when there is no resultant force and no resultant torque, a system is in equilibrium

use a vector triangle to represent coplanar forces in equilibrium

define and use density

define and use pressure

derive, from the definitions of pressure and density, the equation for hydrostatic pressure ∆p = ρg∆ h

use the equation ∆p = ρg∆ h

understand that the upthrust acting on an object in a fluid is due to a difference in hydrostatic pressure

calculate the upthrust acting on an object in a fluid using the equation F = ρgV (Archimedes’ principle)

understand the concept of work, and recall and use work done = force × displacement in the direction of the force

recall and apply the principle of conservation of energy

recall and understand that the efficiency of a system is the ratio of useful energy output from the system to the total energy input

use the concept of efficiency to solve problems

define power as work done per unit time

solve problems using P = W / t

derive P = Fv and use it to solve problems

derive, using W = Fs, the formula ∆EP = mg∆ h for gravitational potential energy changes in a uniform gravitational field

recall and use the formula ∆EP = mg∆ h for gravitational potential energy changes in a uniform gravitational field 1

derive, using the equations of motion, the formula for kinetic energy EK = 2 mv2 1

recall and use EK = 2 mv2

understand that deformation is caused by tensile or compressive forces (forces and deformations will be assumed to be in one dimension only)

understand and use the terms load, extension, compression and limit of proportionality

recall and use Hooke’s law

recall and use the formula for the spring constant k = F / x

define and use the terms stress, strain and the Young modulus

describe an experiment to determine the Young modulus of a metal in the form of a wire

understand and use the terms elastic deformation, plastic deformation and elastic limit

understand that the area under the force–extension graph represents the work done

determine the elastic potential energy of a material deformed within its limit of proportionality from the area under the force–extension graph 1 1

recall and use EP = 2 Fx = 2 kx2 for a material deformed within its limit of proportionality

describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks

understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelength and speed

understand the use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

derive, using the definitions of speed, frequency and wavelength, the wave equation v = f λ

recall and use v = f λ

understand that energy is transferred by a progressive wave

recall and use intensity = power/area and intensity ∝ (amplitude)2 for a progressive wave

compare transverse and longitudinal waves

analyse and interpret graphical representations of transverse and longitudinal waves

understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency (understanding of the Doppler effect for a stationary source and a moving observer is not required)

use the expression fο = f sv / (v ± vs) for the observed frequency when a source of sound waves moves relative to a stationary observer

state that all electromagnetic waves are transverse waves that travel with the same speed c in free space

recall the approximate range of wavelengths in free space of the principal regions of the electromagnetic spectrum from radio waves to γ-rays

recall that wavelengths in the range 400–700 nm in free space are visible to the human eye

understand that polarisation is a phenomenon associated with transverse waves

recall and use Malus’s law (I = I0 cos2θ ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters (calculation of the effect of a polarising filter on the intensity of an unpolarised wave is not required)

explain and use the principle of superposition

show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns (it will be assumed that end corrections are negligible; knowledge of the concept of end corrections is not required)

explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes

understand how wavelength may be determined from the positions of nodes or antinodes of a stationary wave

explain the meaning of the term diffraction

show an understanding of experiments that demonstrate diffraction including the qualitative effect of the gap width relative to the wavelength of the wave; for example diffraction of water waves in a ripple tank

understand the terms interference and coherence

show an understanding of experiments that demonstrate two-source interference using water waves in a ripple tank, sound, light and microwaves

understand the conditions required if two-source interference fringes are to be observed

recall and use λ = ax / D for double-slit interference using light

recall and use d sin θ = nλ

describe the use of a diffraction grating to determine the wavelength of light (the structure and use of the spectrometer are not included)

understand that an electric current is a flow of charge carriers

understand that the charge on charge carriers is quantised

recall and use Q = It

use, for a current-carrying conductor, the expression I = Anvq, where n is the number density of charge carriers

define the potential difference across a component as the energy transferred per unit charge

recall and use V = W / Q

recall and use P = VI, P = I 2R and P = V 2 / R

define resistance

recall and use V = IR

sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp

explain that the resistance of a filament lamp increases as current increases because its temperature increases

state Ohm’s law

recall and use R = ρL / A

understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases

understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)

recall and use the circuit symbols shown in section 6 of this syllabus

draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus

define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit

distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations

understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference

recall Kirchhoff’s first law and understand that it is a consequence of conservation of charge

recall Kirchhoff’s second law and understand that it is a consequence of conservation of energy

derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in series

use the formula for the combined resistance of two or more resistors in series

derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in parallel

use the formula for the combined resistance of two or more resistors in parallel

use Kirchhoff’s laws to solve simple circuit problems

understand the principle of a potential divider circuit

recall and use the principle of the potentiometer as a means of comparing potential differences

understand the use of a galvanometer in null methods

explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and light intensity

infer from the results of the α-particle scattering experiment the existence and small size of the nucleus

describe a simple model for the nuclear atom to include protons, neutrons and orbital electrons

distinguish between nucleon number and proton number

understand that isotopes are forms of the same element with different numbers of neutrons in their nuclei

understand and use the notation AZ X for the representation of nuclides

understand that nucleon number and charge are conserved in nuclear processes

describe the composition, mass and charge of α-, β- and γ-radiations (both β – (electrons) and β+ (positrons) are included)

understand that an antiparticle has the same mass but opposite charge to the corresponding particle, and that a positron is the antiparticle of an electron

state that (electron) antineutrinos are produced during β – decay and (electron) neutrinos are produced during β+ decay

understand that α-particles have discrete energies but that β-particles have a continuous range of energies because (anti)neutrinos are emitted in β-decay

represent α- and β-decay by a radioactive decay equation of the form 238 92 U " 234 90 Th + 24 α

use the unified atomic mass unit (u) as a unit of mass

understand that a quark is a fundamental particle and that there are six flavours (types) of quark: up, down, strange, charm, top and bottom

recall and use the charge of each flavour of quark and understand that its respective antiquark has the opposite charge (no knowledge of any other properties of quarks is required)

recall that protons and neutrons are not fundamental particles and describe protons and neutrons in terms of their quark composition

understand that a hadron may be either a baryon (consisting of three quarks) or a meson (consisting of one quark and one antiquark)

describe the changes to quark composition that take place during β – and β+ decay

recall that electrons and neutrinos are fundamental particles called leptons

define the radian and express angular displacement in radians

understand and use the concept of angular speed

recall and use ω = 2π / T and v = rω

understand that a force of constant magnitude that is always perpendicular to the direction of motion causes centripetal acceleration

understand that centripetal acceleration causes circular motion with a constant angular speed

recall and use a = rω2 and a = v2 / r

recall and use F = mrω2 and F = mv2 / r

understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass

represent a gravitational field by means of field lines

understand that, for a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre

recall and use Newton’s law of gravitation F = Gm1m2 / r2 for the force between two point masses

analyse circular orbits in gravitational fields by relating the gravitational force to the centripetal acceleration it causes

understand that a satellite in a geostationary orbit remains at the same point above the Earth’s surface, with an orbital period of 24 hours, orbiting from west to east, directly above the Equator

derive, from Newton’s law of gravitation and the definition of gravitational field, the equation g = GM / r 2 for the gravitational field strength due to a point mass

recall and use g = GM / r 2

understand why g is approximately constant for small changes in height near the Earth’s surface

define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point

use ϕ = –GM / r for the gravitational potential in the field due to a point mass

understand how the concept of gravitational potential leads to the gravitational potential energy of two point masses and use EP = –GMm / r

understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature

understand that regions of equal temperature are in thermal equilibrium

understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties, including the density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple

understand that the scale of thermodynamic temperature does not depend on the property of any particular substance

convert temperatures between kelvin and degrees Celsius and recall that T / K = θ / °C + 273.15

understand that the lowest possible temperature is zero kelvin on the thermodynamic temperature scale and that this is known as absolute zero

define and use specific heat capacity

define and use specific latent heat and distinguish between specific latent heat of fusion and specific latent heat of vaporisation

understand that amount of substance is an SI base quantity with the base unit mol

use molar quantities where one mole of any substance is the amount containing a number of particles of that substance equal to the Avogadro constant NA

understand that a gas obeying pV ∝ T, where T is the thermodynamic temperature, is known as an ideal gas

recall and use the equation of state for an ideal gas expressed as pV = nRT, where n = amount of substance (number of moles) and as pV = NkT, where N = number of molecules

recall that the Boltzmann constant k is given by k = R / NA

state the basic assumptions of the kinetic theory of gases

explain how molecular movement causes the pressure exerted by a gas and derive and use the 1 1

understand that the root-mean-square speed cr.m.s. is given by <c 2 > 1

compare pV = 3 Nm<c2> with pV = NkT to deduce that the average translational kinetic energy of a 3

understand that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system

relate a rise in temperature of an object to an increase in its internal energy

recall and use W = p∆V for the work done when the volume of a gas changes at constant pressure and understand the difference between the work done by the gas and the work done on the gas

recall and use the first law of thermodynamics ∆U = q + W expressed in terms of the increase in internal energy, the heating of the system (energy transferred to the system by heating) and the work done on the system

understand and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations, and express the period in terms of both frequency and angular frequency

understand that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction

use a = – ω2 x and recall and use, as a solution to this equation, x = x0 sin ωt

use the equations v = v0 cos ωt and v = ± ω (x02 − x 2)

analyse and interpret graphical representations of the variations of displacement, velocity and acceleration for simple harmonic motion

describe the interchange between kinetic and potential energy during simple harmonic motion 1

recall and use E = 2 mω2 x02 for the total energy of a system undergoing simple harmonic motion

understand that a resistive force acting on an oscillating system causes damping

understand and use the terms light, critical and heavy damping and sketch displacement–time graphs illustrating these types of damping

understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency

understand that an electric field is an example of a field of force and define electric field as force per unit positive charge

recall and use F = qE for the force on a charge in an electric field

represent an electric field by means of field lines

recall and use E = ∆V / ∆d to calculate the field strength of the uniform field between charged parallel plates

describe the effect of a uniform electric field on the motion of charged particles

understand that, for a point outside a spherical conductor, the charge on the sphere may be considered to be a point charge at its centre

recall and use Coulomb’s law F = Q1Q2 / (4πε 0 r 2) for the force between two point charges in free space

recall and use E = Q / (4πε 0 r 2) for the electric field strength due to a point charge in free space

define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to the point

recall and use the fact that the electric field at a point is equal to the negative of potential gradient at that point

use V = Q / (4πε 0 r) for the electric potential in the field due to a point charge

understand how the concept of electric potential leads to the electric potential energy of two point charges and use EP = Qq / (4πε 0 r)

define capacitance, as applied to both isolated spherical conductors and to parallel plate capacitors

recall and use C = Q / V

derive, using C = Q / V, formulas for the combined capacitance of capacitors in series and in parallel

use the capacitance formulas for capacitors in series and in parallel

determine the electric potential energy stored in a capacitor from the area under the potential–charge graph 1 1

recall and use W = 2 QV = 2 CV 2

analyse graphs of the variation with time of potential difference, charge and current for a capacitor discharging through a resistor

recall and use τ = RC for the time constant for a capacitor discharging through a resistor

use equations of the form x = x0 e –(t / RC) where x could represent current, charge or potential difference for a capacitor discharging through a resistor

understand that a magnetic field is an example of a field of force produced either by moving charges or by permanent magnets

represent a magnetic field by field lines

understand that a force might act on a current-carrying conductor placed in a magnetic field

recall and use the equation F = BIL sin θ, with directions as interpreted by Fleming’s left-hand rule

define magnetic flux density as the force acting per unit current per unit length on a wire placed at right‑angles to the magnetic field

determine the direction of the force on a charge moving in a magnetic field

recall and use F = BQv sin θ

understand the origin of the Hall voltage and derive and use the expression VH = BI / (ntq), where t = thickness

understand the use of a Hall probe to measure magnetic flux density

describe the motion of a charged particle moving in a uniform magnetic field perpendicular to the direction of motion of the particle

explain how electric and magnetic fields can be used in velocity selection

sketch magnetic field patterns due to the currents in a long straight wire, a flat circular coil and a long solenoid

understand that the magnetic field due to the current in a solenoid is increased by a ferrous core

explain the origin of the forces between current-carrying conductors and determine the direction of the forces

define magnetic flux as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

recall and use Φ = BA

understand and use the concept of magnetic flux linkage

understand and explain experiments that demonstrate: • that a changing magnetic flux can induce an e.m.f. in a circuit • that the induced e.m.f. is in such a direction as to oppose the change producing it • the factors affecting the magnitude of the induced e.m.f.

recall and use Faraday’s and Lenz’s laws of electromagnetic induction

understand and use the terms period, frequency and peak value as applied to an alternating current or voltage

use equations of the form x = x0 sin ωt representing a sinusoidally alternating current or voltage

recall and use the fact that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current

distinguish between root-mean-square (r.m.s.) and peak values and recall and use I r.m.s. = I0 / 2 and Vr.m.s. = V0 / 2 for a sinusoidal alternating current

distinguish graphically between half-wave and full-wave rectification

explain the use of a single diode for the half-wave rectification of an alternating current

explain the use of four diodes (bridge rectifier) for the full-wave rectification of an alternating current

analyse the effect of a single capacitor in smoothing, including the effect of the values of capacitance and the load resistance

understand that electromagnetic radiation has a particulate nature

understand that a photon is a quantum of electromagnetic energy

recall and use E = hf

use the electronvolt (eV) as a unit of energy

understand that a photon has momentum and that the momentum is given by p = E / c

understand that photoelectrons may be emitted from a metal surface when it is illuminated by electromagnetic radiation

understand and use the terms threshold frequency and threshold wavelength

explain photoelectric emission in terms of photon energy and work function energy 1

recall and use hf = Φ + 2 mvmax2

explain why the maximum kinetic energy of photoelectrons is independent of intensity, whereas the photoelectric current is proportional to intensity

understand that the photoelectric effect provides evidence for a particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence for a wave nature

describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature of particles

understand the de Broglie wavelength as the wavelength associated with a moving particle

recall and use λ = h / p

understand that there are discrete electron energy levels in isolated atoms (e.g. atomic hydrogen)

understand the appearance and formation of emission and absorption line spectra

recall and use hf = E1 – E2

understand the equivalence between energy and mass as represented by E = mc2 and recall and use this equation

represent simple nuclear reactions by nuclear equations of the form 147 N + 24 He " 178 O + 11 H

define and use the terms mass defect and binding energy

sketch the variation of binding energy per nucleon with nucleon number

explain what is meant by nuclear fusion and nuclear fission

explain the relevance of binding energy per nucleon to nuclear reactions, including nuclear fusion and nuclear fission

calculate the energy released in nuclear reactions using E = c2∆ m

understand that fluctuations in count rate provide evidence for the random nature of radioactive decay

understand that radioactive decay is both spontaneous and random

define activity and decay constant, and recall and use A = λN

define half-life

use λ = 0.693 / t 1 2

understand the exponential nature of radioactive decay, and sketch and use the relationship x = x0e –λt, where x could represent activity, number of undecayed nuclei or received count rate

understand that a piezo-electric crystal changes shape when a p.d. is applied across it and that the crystal generates an e.m.f. when its shape changes

understand how ultrasound waves are generated and detected by a piezoelectric transducer

understand how the reflection of pulses of ultrasound at boundaries between tissues can be used to obtain diagnostic information about internal structures

define the specific acoustic impedance of a medium as Z = ρc, where c is the speed of sound in the medium

use IR / I0 = (Z1 – Z2)2 / (Z1 + Z2)2 for the intensity reflection coefficient of a boundary between two media

recall and use I = I0e –µx for the attenuation of ultrasound in matter

explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum wavelength of X-rays produced from the accelerating p.d.

understand the use of X-rays in imaging internal body structures, including an understanding of the term contrast in X-ray imaging

recall and use I = I0e –µx for the attenuation of X-rays in matter

understand that computed tomography (CT) scanning produces a 3D image of an internal structure by first combining multiple X-ray images taken in the same section from different angles to obtain a 2D image of the section, then repeating this process along an axis and combining 2D images of multiple sections

understand that a tracer is a substance containing radioactive nuclei that can be introduced into the body and is then absorbed by the tissue being studied

recall that a tracer that decays by β+ decay is used in positron emission tomography (PET scanning)

understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process

explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions

calculate the energy of the gamma-ray photons emitted during the annihilation of an electron-positron pair

understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons

understand the term luminosity as the total power of radiation emitted by a star

recall and use the inverse square law for radiant flux intensity F in terms of the luminosity L of the source F = L / (4πd 2)

understand that an object of known luminosity is called a standard candle

understand the use of standard candles to determine distances to galaxies

recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the peak surface temperature of a star

use the Stefan–Boltzmann law L = 4πσr 2 T 4

use Wien’s displacement law and the Stefan–Boltzmann law to estimate the radius of a star

understand that the lines in the emission and absorption spectra from distant objects show an increase in wavelength from their known values

use ∆λ / λ . ∆f / f . v / c for the redshift of electromagnetic radiation from a source moving relative to an observer

explain why redshift leads to the idea that the universe is expanding

recall and use Hubble’s law v . H0 d and explain how this leads to the Big Bang theory (candidates will only be required to use SI units) Faculty feedback: ‘Understanding how and why our climate is changing and providing the knowledge and skills to explore the challenges plays a key role in every student’s education.’ Feedback from: Dr Amy Munro-Faure, Head of Education and Student Engagement of Cambridge Zero