BGCSE Physics (0571) cheat sheet

SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).

Prefixes: nano 10^-9, micro 10^-6, milli 10^-3, centi 10^-2, kilo 10^3, mega 10^6, giga 10^9.

Derived-unit checks: force = kg·m·s^-2 (N); energy = kg·m^2·s^-2 (J); power = kg·m^2·s^-3 (W); pressure = kg·m^-1·s^-2 (Pa).

Precision is set by the smallest scale division; a ruler with 1 mm divisions is read to ±0.5 mm.

Percentage error = (measured value − accepted value) ÷ accepted value × 100%; report sign and magnitude.

Density ρ = m/V; a body floats in a fluid when its density is less than the fluid's density.

Variables: independent variable is deliberately changed; dependent variable is measured; all others are controlled.

A hypothesis is a testable prediction; a theory is a well-tested explanation supported by repeated evidence.

Newton's second law: resultant force F = ma; weight W = mg with g ≈ 9.8 N/kg near Earth's surface.

Uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.

Average speed = total distance ÷ total time; velocity is speed in a stated direction.

Momentum p = mv; in a closed system total momentum before a collision equals total momentum after.

Work done W = Fs (force along displacement); power P = W/t = Fv for constant speed.

Kinetic energy KE = ½mv²; gravitational potential energy ΔGPE = mgΔh.

Principle of moments: for equilibrium about a pivot, sum of clockwise moments = sum of anticlockwise moments.

Pressure P = F/A; in a liquid P = ρgh, so pressure depends only on depth and density.

Hooke's law: extension is proportional to applied force up to the limit of proportionality (F = kx).

Temperature is a measure of the average kinetic energy of particles; heat is energy transferred due to a temperature difference.

Specific heat capacity: E = mcΔθ, where c is energy per kilogram per kelvin.

Specific latent heat: E = mL; latent heat of fusion applies at melting point, vaporisation at boiling point.

Thermal energy moves by conduction (solids, particle collisions), convection (fluids, density currents) and radiation (infrared, needs no medium).

Dark, matt surfaces are good absorbers and emitters of infrared; shiny, light surfaces are poor emitters and good reflectors.

Gas laws for a fixed mass: P₁V₁/T₁ = P₂V₂/T₂ with T in kelvin (K = °C + 273).

Boyle's law: at constant temperature, pressure is inversely proportional to volume.

At a change of state the temperature stays constant because energy changes the potential energy of particles, not their kinetic energy.

Wave equation: speed v = frequency f × wavelength λ; frequency is set by the source, speed by the medium.

Transverse waves oscillate perpendicular to energy transfer (light); longitudinal waves oscillate parallel (sound).

Reflection: angle of incidence = angle of reflection, both measured from the normal.

Refraction: light bends toward the normal entering a denser medium; Snell's law n = sin i ÷ sin r.

Total internal reflection occurs when light travels from denser to less dense medium and the angle of incidence exceeds the critical angle.

Sound needs a material medium; it travels fastest in solids, slowest in gases, and cannot cross a vacuum.

Frequency determines pitch; amplitude determines loudness; the audible range for humans is about 20 Hz to 20 kHz.

Converging lenses focus parallel rays at the principal focus; a real image is inverted and can be projected on a screen.

Current I = Q/t (ampere = coulomb per second); conventional current flows from positive to negative terminal.

Ohm's law: V = IR, valid for a conductor at constant temperature.

Series circuit: same current in every component; total resistance R = R₁ + R₂ + …; voltages add.

Parallel circuit: same voltage across each branch; total resistance is less than the smallest branch resistance.

Electrical power P = VI = I²R = V²/R; energy transferred E = Pt.

Charge on one electron ≈ 1.6 × 10^-19 C; charge is conserved and quantised.

Magnetic field lines run from north to south outside a magnet; a current-carrying wire in a magnetic field experiences a force.

Electromagnetic induction: a changing magnetic field through a conductor induces an emf; faster change gives larger emf.

Fuse ratings are chosen just above the normal operating current to protect against overheating.

Kinetic particle model: solids vibrate in fixed positions, liquids slide past each other, gases move randomly at high speed.

Brownian motion of smoke particles in air gives evidence for randomly moving invisible molecules.

Density differences explain floating, sinking, convection and diffusion rates.

Atom: protons (+1) and neutrons (0) in the nucleus, electrons (−1) in shells; proton number fixes the element.

Isotopes have the same proton number but different neutron numbers; nucleon number = protons + neutrons.

Radioactive decay is random: alpha (⁴₂He), beta (electron) and gamma (electromagnetic) emissions differ in charge and penetrating power.

Half-life is the time for half the unstable nuclei in a sample to decay; activity halves each half-life.

Nuclear fission splits a heavy nucleus; fusion joins light nuclei and powers stars.

Earth orbits the Sun once in about 365.25 days; the Moon orbits Earth in about 27.3 days.

Day and night arise from Earth's rotation on its axis (about 24 hours); seasons arise from the tilt of the axis, not distance from the Sun.

Gravitational force between masses: F = Gm₁m₂/r²; it provides the centripetal force keeping planets in orbit.

Weight differs on other planets because g differs; mass is unchanged.

Solar system order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

The Moon causes tides; the Sun and Moon align at spring tides and are at right angles at neap tides.

The Universe is expanding: distant galaxies show redshift, and Hubble's law links recession speed to distance.

Stars form from collapsing gas clouds; the Sun's energy comes from nuclear fusion of hydrogen into helium.

Repeat readings and average them to reduce random error; use the same instrument to keep systematic error consistent.

Zero a balance or ammeter before use; check for a zero error and subtract it from readings.

Measure time over many oscillations and divide by the count to reduce timing error.

Choose an instrument whose smallest division is appropriate: vernier callipers for diameters, metre rule for lengths, stopwatch for periods.

Plot the independent variable on the x-axis and the dependent variable on the y-axis; label axes with quantity and unit.

A straight-line graph through the origin shows direct proportionality; gradient equals the constant of proportionality.

Anomalous points are identified and excluded; a line of best fit balances points above and below it.

Safety: use a sand tray under a falling mass, switch off circuits before rewiring, and handle hot objects with tongs.