SAT / ACT Prep Online Guides and Tips

1.1

• Fundamental and derived SI units
• Scientific notation and metric multipliers
• Significant figures
• Orders of magnitude
• Estimation

1.2

• Random and systematic errors
• Absolute, fractional and percentage uncertainties
• Error bars
• Uncertainty of gradient and intercepts

• Vector and scalar quantities
• Combination and resolution of vectors

2.1

• Distance and displacement
• Speed and velocity
• Acceleration
• Graphs describing motion
• Equations of motion for uniform acceleration
• Projectile motion
• Fluid resistance and terminal speed

2.2

• Objects as point particles
• Free-body diagrams
• Translational equilibrium
• Newton’s laws of motion
• Solid friction

2.3

• Kinetic energy
• Gravitational potential energy
• Elastic potential energy
• Work done as energy transfer
• Power as rate of energy transfer
• Principle of conservation of energy
• Efficiency

• Newton’s second law expressed in terms of rate of change of momentum
• Impulse and force–time graphs
• Conservation of linear momentum
• Elastic collisions, inelastic collisions and explosions

3.1

• Molecular theory of solids, liquids and gases
• Temperature and absolute temperature
• Internal energy
• Specific heat capacity
• Phase change
• Specific latent heat

3.2

• Pressure
• Equation of state for an ideal gas
• Kinetic model of an ideal gas
• Mole, molar mass and the Avogadro constant
• Differences between real and ideal gases

4.1

• Simple harmonic oscillations
• Time period, frequency, amplitude, displacement and phase difference
• Conditions for simple harmonic motion

4.2

• Travelling waves
• Wavelength, frequency, period and wave speed
• Transverse and longitudinal waves
• The nature of electromagnetic waves
• The nature of sound waves

4.3

• Wavefronts and rays
• Amplitude and intensity
• Superposition
• Polarization

• Reflection and refraction
• Snell’s law, critical angle and total internal reflection
• Diffraction through a single-slit and around objects
• Interference patterns
• Double-slit interference
• Path difference

• The nature of standing waves
• Boundary conditions
• Nodes and antinodes

5.1

• Charge
• Electric field
• Coulomb’s law
• Electric current
• Direct current (dc)
• Potential difference

5.2

• Circuit diagrams
• Kirchhoff’s circuit laws
• Heating effect of current and its consequences
• Resistance expressed as R = V/I
• Ohm’s law
• Resistivity
• Power dissipation

5.3

• Cells
• Internal resistance
• Secondary cells
• Terminal potential difference
• Electromotive force (emf)

• Magnetic fields
• Magnetic force

6.1

• Period, frequency, angular displacement and angular velocity
• Centripetal force
• Centripetal acceleration

6.2

• Newton’s law of gravitation
• Gravitational field strength

7.1

• Discrete energy and discrete energy levels
• Transitions between energy levels
• Radioactive decay
• Fundamental forces and their properties
• Alpha particles, beta particles and gamma rays
• Half-life
• Absorption characteristics of decay particles
• Isotopes
• Background radiation

7.2

• The unified atomic mass unit
• Mass defect and nuclear binding energy
• Nuclear fission and nuclear fusion

7.3

• Quarks, leptons and their antiparticles
• Hadrons, baryons and mesons
• The conservation laws of charge, baryon number, lepton number and strangeness
• The nature and range of the strong nuclear force, weak nuclear force and electromagnetic force
• Exchange particles
• Feynman diagrams
• Confinement
• The Higgs boson

8.1

• Specific energy and energy density of fuel sources
• Sankey diagrams
• Primary energy sources
• Electricity as a secondary and versatile form of energy
• Renewable and non-renewable energy sources

8.2

• Conduction, convection and thermal radiation
• Black-body radiation
• Albedo and emissivity
• The solar constant
• The greenhouse effect
• Energy balance in the Earth surface–atmosphere system

9.1

• The defining equation of SHM
• Energy changes

9.2

• The nature of single-slit diffraction

9.3

• Young’s double-slit experiment
• Modulation of two-slit interference pattern by one-slit diffraction effect
• Multiple slit and diffraction grating interference patterns
• Thin film interference

• The size of a diffracting aperture
• The resolution of simple monochromatic two-source systems

• The Doppler effect for sound waves and light waves

10.1

• Gravitational fields
• Electrostatic fields
• Electric potential and gravitational potential
• Field lines
• Equipotential surfaces

10.2

• Potential and potential energy
• Potential gradient
• Potential difference
• Escape speed
• Orbital motion, orbital speed and orbital energy
• Forces and inverse-square law behaviour

11.1

• Electromotive force (emf)
• Magnetic flux and magnetic flux linkage
• Faraday’s law of induction
• Lenz’s law

11.2

• Alternating current (ac) generators
• Average power and root mean square (rms) values of current and voltage
• Transformers
• Diode bridges
• Half-wave and full-wave rectification

11.3

• Capacitance
• Dielectric materials
• Capacitors in series and parallel
• Resistor-capacitor (RC) series circuits
• Time constant

12.1

• Photons
• The photoelectric effect
• Matter waves
• Pair production and pair annihilation
• Quantization of angular momentum in the Bohr model for hydrogen
• The wave function
• The uncertainty principle for energy and time and position and momentum
• Tunnelling, potential barrier and factors affecting tunnelling probability

12.2

• Rutherford scattering and nuclear radius
• Nuclear energy levels
• The neutrino
• The law of radioactive decay and the decay constant

A.1

• Reference frames
• Galilean relativity and Newton’s postulates concerning time and space
• Maxwell and the constancy of the speed of light
• Forces on a charge or current

A.2

• The two postulates of special relativity
• Clock synchronization
• The Lorentz transformations
• Velocity addition
• Invariant quantities (spacetime interval, proper time, proper length and rest mass)
• Time dilation
• Length contraction
• The muon decay experiment

• Spacetime diagrams
• Worldlines
• The twin paradox

A.4

• Total energy and rest energy
• Relativistic momentum
• Particle acceleration
• Electric charge as an invariant quantity
• Photons
• MeV c^–2 as the unit of mass and MeV c^–1 as the unit of momentum

A.5

• The equivalence principle
• The bending of light
• Gravitational redshift and the Pound–Rebka–Snider experiment
• Schwarzschild black holes
• Event horizons
• Time dilation near a black hole
• Applications of general relativity to the universe as a whole

B.1

• Torque
• Moment of inertia
• Rotational and translational equilibrium
• Angular acceleration
• Equations of rotational motion for uniform angular acceleration
• Newton’s second law applied to angular motion
• Conservation of angular momentum

B.2

• The first law of thermodynamics
• The second law of thermodynamics
• Entropy
• Cyclic processes and pV diagrams
• Isovolumetric, isobaric, isothermal and adiabatic processes
• Carnot cycle
• Thermal efficiency

B.3

• Density and pressure
• Buoyancy and Archimedes’ principle
• Pascal’s principle
• Hydrostatic equilibrium
• The ideal fluid
• Streamlines
• The continuity equation
• The Bernoulli equation and the Bernoulli effect
• Stokes’ law and viscosity
• Laminar and turbulent flow and the Reynolds number

B.4

• Natural frequency of vibration
• Q factor and damping
• Periodic stimulus and the driving frequency
• Resonance

C.1

• Thin lenses
• Converging and diverging lenses
• Converging and diverging mirrors
• Ray diagrams
• Real and virtual images
• Linear and angular magnification
• Spherical and chromatic aberrations

C.2

• Optical compound microscopes
• Simple optical astronomical refracting telescopes
• Simple optical astronomical reflecting telescopes
• Single-dish radio telescopes
• Radio interferometry telescopes
• Satellite-borne telescopes

C.3

• Structure of optic fibres
• Step-index fibres and graded-index fibres
• Total internal reflection and critical angle
• Waveguide and material dispersion in optic fibres
• Attenuation and the decibel (dB) scale

C.4

• Detection and recording of X-ray images in medical contexts
• Generation and detection of ultrasound in medical contexts
• Medical imaging techniques (magnetic resonance imaging) involving nuclear magnetic resonance (NMR)

D.1

• Objects in the universe
• The nature of stars
• Astronomical distances
• Stellar parallax and its limitations
• Luminosity and apparent brightness

D.2

• Stellar spectra
• Hertzsprung–Russell (HR) diagram
• Mass–luminosity relation for main sequence stars
• Cepheid variables
• Stellar evolution on HR diagrams
• Red giants, white dwarfs, neutron stars and black holes
• Chandrasekhar and Oppenheimer–Volkoff limits

• The Big Bang model
• Cosmic microwave background (CMB) radiation
• Hubble’s law
• The accelerating universe and redshift (z)
• The cosmic scale factor (R)

D.4

• The Jeans criterion
• Nuclear fusion
• Nucleosynthesis off the main sequence
• Type Ia and II supernovae

D.5

• The cosmological principle
• Rotation curves and the mass of galaxies
• Dark matter
• Fluctuations in the CMB
• The cosmological origin of redshift
• Critical density
• Dark energy