LGCSE Physical Science (0181) cheat sheet

Variables: independent variable is changed deliberately; dependent variable is measured; control variables are kept constant to make the test fair.

A hypothesis is a testable prediction; a conclusion must be judged against the evidence collected, not against expectation.

Repeat readings and calculate a mean to reduce the effect of random error; random error scatters results about the true value.

Systematic error shifts all readings in one direction (e.g. zero error, mis-calibrated scale) and is not removed by averaging.

Precision = how closely repeats agree; accuracy = how close a reading is to the true value.

Uncertainty of a single scale reading is typically half the smallest division; for a difference of two readings, add the two uncertainties.

A valid experiment measures the intended quantity and controls other variables; a reliable one gives consistent results on repetition.

Tables: headings include quantity and unit (e.g. time / s); graphs: plot dependent against independent, draw line of best fit, describe trend and anomalies.

Scientific claims are accepted provisionally after peer review and replication; a single result is not proof.

Solid: particles closely packed in fixed positions, vibrate only. Liquid: close but irregular, slide past each other. Gas: far apart, random fast motion.

Changes of state (melting, boiling, condensing, freezing, subliming) are physical changes: particles rearrange but the substance is unchanged.

During melting or boiling, energy supplied breaks forces between particles, so temperature stays constant (flat portions of a heating curve).

Diffusion is net spreading of particles from high to low concentration; rate rises with temperature and is faster in gases than liquids.

Gas pressure arises from collisions of particles with container walls; heating raises pressure at constant volume because collisions are more frequent and forceful.

Filtration separates an insoluble solid from a liquid; evaporation or crystallisation recovers a dissolved solid.

Simple distillation separates a solvent from a solution; fractional distillation separates miscible liquids with different boiling points.

Chromatography separates dissolved substances by differing solubilities and attractions to the stationary phase; Rf = distance moved by spot / distance moved by solvent front.

Mixtures are separated by physical methods; compounds require chemical reactions to break bonds.

Atom: protons (charge +1, mass 1) and neutrons (0, mass 1) in the nucleus; electrons (charge −1, mass ≈1/1836) in shells.

Atomic number Z = protons = electrons in a neutral atom; mass number A = protons + neutrons; neutrons = A − Z.

Isotopes have the same Z but different A; relative atomic mass is the weighted mean of isotope masses by abundance.

Electron shells fill 2, 8, 8; the group number equals outer-shell electrons, the period number equals the number of occupied shells.

Ionic bonding: metal atoms lose electrons to form cations, non-metals gain electrons to form anions; electrostatic attraction gives a giant lattice with high melting point.

Covalent bonding: shared electron pairs between non-metals; simple molecules have weak intermolecular forces and low melting points.

Metallic bonding: positive ions in a sea of delocalised electrons - explains conduction and malleability.

Group 1 reactivity increases down the group (outer electron lost more easily); Group 7 reactivity decreases down the group.

Noble gases (Group 0) have full outer shells and are unreactive; transition metals form coloured compounds and variable oxidation states.

Conservation of mass: total mass of reactants equals total mass of products; balanced equations must have equal atoms of each element on both sides.

State symbols: (s) solid, (l) liquid, (g) gas, (aq) dissolved in water.

Moles n = m / M (mass in g, molar mass in g/mol); for gases at room temperature and pressure, 1 mol occupies about 24 dm³.

Concentration c = n / V, with V in dm³; 1 dm³ = 1000 cm³; c in mol/dm³ = mass concentration (g/dm³) / molar mass.

Percentage yield = (actual mass / theoretical mass) × 100; atom economy = (mass of desired product / total mass of reactants) × 100.

Reaction types: combination, decomposition, displacement (more reactive metal takes the place of a less reactive one), neutralisation, combustion, thermal decomposition.

Reacting-mass calculations: convert mass to moles, use the equation's mole ratio, convert back to mass.

Limiting reactant is the one used up first and determines the maximum product; the other is in excess.

Empirical formula from percentage composition: divide each percentage by the atomic mass, then divide by the smallest ratio.

Acid: proton (H⁺) donor; base: proton acceptor; alkali is a soluble base producing OH⁻ in water.

pH < 7 acidic, = 7 neutral, > 7 alkaline; pH 1 is strongly acidic, pH 14 strongly alkaline.

Neutralisation: acid + base → salt + water; acid + metal → salt + hydrogen; acid + carbonate → salt + water + carbon dioxide.

Salt name comes from the acid: hydrochloric → chloride, sulfuric → sulfate, nitric → nitrate, ethanoic → ethanoate.

Preparation: soluble salts by acid + excess insoluble base/carbonate, then filter and crystallise; insoluble salts by precipitation (mixing two solutions).

Strong acids ionise completely in water, weak acids only partially; this is why pH differs at the same concentration.

Rate increases with higher concentration, higher temperature, larger surface area, and a catalyst; rate depends on frequency of successful collisions.

Higher temperature increases both collision frequency and the proportion of collisions with energy ≥ activation energy, so the effect is large.

A catalyst lowers activation energy by providing an alternative pathway and is not used up; enzymes are biological catalysts.

Speed = distance / time; velocity is speed in a stated direction; acceleration a = (v − u) / t.

Distance–time graph: gradient = speed. Velocity–time graph: gradient = acceleration, area under graph = distance travelled.

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

Newton's first law: no resultant force means constant velocity (or rest); second law: F = ma; third law: equal and opposite forces on two different bodies.

Weight W = mg (g ≈ 9.8 N/kg on Earth); mass is the amount of matter and is unchanged by location.

Friction and air resistance oppose motion; terminal velocity is reached when drag equals weight and acceleration becomes zero.

Moment of a force = force × perpendicular distance from pivot; for balance, total clockwise moments = total anticlockwise moments.

Pressure p = F / A; in a liquid p = ρgh; pressure increases with depth.

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

Energy is conserved: it is transferred between stores (kinetic, gravitational, elastic, thermal, chemical, nuclear) but never created or destroyed.

Work done W = Fd (force along the direction of motion), measured in joules.

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

Power P = work done / time = energy transferred / time; measured in watts (J/s).

Efficiency = useful output energy / total input energy × 100%; the rest is dissipated, usually as thermal energy.

Renewable resources: solar, wind, hydroelectric, tidal, wave, geothermal, biomass. Non-renewable: coal, oil, gas, nuclear fuel.

Renewables are replenished and produce no direct carbon dioxide; drawbacks include intermittency, low output per unit area and habitat or visual impact.

Fossil fuels are reliable and energy-dense but release carbon dioxide, a greenhouse gas linked to global warming.

Energy transfer by conduction, convection and radiation: conduction needs particles, convection needs a fluid, radiation (infrared) needs no medium.

Wave quantities: frequency f (Hz), wavelength λ (m), amplitude; wave speed v = fλ.

Transverse waves oscillate perpendicular to travel (light, water); longitudinal waves oscillate parallel (sound).

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

Refraction: light bends towards the normal entering a denser medium (slower) and away from the normal leaving it.

Refractive index n = c / v = sin i / sin r; for the critical angle, sin c = 1 / n; total internal reflection occurs above the critical angle.

Converging lens: parallel rays meet at the principal focus; power P = 1 / f (dioptres, f in metres); real images are inverted.

Sound needs a medium, travels faster in solids than gases, and cannot travel through a vacuum; higher frequency means higher pitch.

Law of reflection and ray diagrams: image in a plane mirror is virtual, same size, laterally inverted, as far behind as the object is in front.

Colour: white light disperses through a prism; filters transmit only their own colour and absorb the rest.

Current I = charge / time (Q = It), measured in amperes; conventional current flows positive to negative.

Voltage (potential difference) V = energy transferred / charge = W / Q, measured in volts.

Ohm's law V = IR for a conductor at constant temperature; resistance R = V / I in ohms.

Series: same current everywhere, voltages add, R_total = R₁ + R₂ + …; parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂ + ….

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

A filament lamp's resistance rises with temperature, so its V–I graph curves; a diode conducts in one direction only.

Charge carriers in metals are electrons; in electrolytes, ions move to the electrodes.

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

Electromagnetic induction: a changing magnetic field through a conductor induces a voltage; faster motion or more turns give a larger induced voltage.

Temperature measures average kinetic energy of particles; thermal energy transfers from hotter to colder bodies until thermal equilibrium.

Specific heat capacity: E = mcΔT, where c is the energy needed to raise 1 kg by 1 °C.

Specific latent heat: E = mL for a change of state at constant temperature; latent heat of vaporisation is larger than of fusion.

Thermal conduction in solids occurs by particle vibration and free-electron transfer; metals conduct well.

Convection is bulk movement of fluid caused by density differences; it cannot occur in solids.

Thermal radiation is infrared emission; dark, matt surfaces absorb and emit best, shiny light surfaces reflect.

Absolute temperature T (K) = θ (°C) + 273; gas pressure is proportional to absolute temperature at constant volume.

Boyle's law: pV = constant at constant temperature; p₁V₁ = p₂V₂.

Reducing heat loss uses insulation, trapped air, double glazing and reflective surfaces, all limiting conduction, convection or radiation.

Earth's structure: crust, mantle, outer core (liquid), inner core (solid); tectonic plate movement causes earthquakes, volcanoes and mountain building.

Rock cycle: igneous (cooled magma), sedimentary (compacted deposited layers), metamorphic (heat and pressure).

The Sun's energy comes from nuclear fusion of hydrogen into helium; it reaches Earth mainly by radiation.

Solar System order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; planets orbit the Sun with gravity providing the centripetal force.

Gravity follows an inverse-square law: doubling distance reduces gravitational force to one quarter.

Seasons arise from the tilt of Earth's axis, not from distance from the Sun; day and night arise from rotation on the axis.

Moon phases arise from the changing angle between Earth, Moon and Sun; eclipses occur when the bodies are aligned.

The greenhouse effect: gases such as CO₂, CH₄ and water vapour absorb and re-emit infrared, warming the surface.

Human impacts include acid rain from sulfur dioxide and nitrogen oxides, and ozone depletion by CFCs.

Burning fuels is exothermic: chemical energy in bonds converts to thermal energy, which can drive turbines via steam.

Electrolysis uses electrical energy to drive a non-spontaneous reaction; electroplating and metal extraction are applications.

Batteries convert chemical energy to electrical energy; charging reverses the reaction and stores energy chemically.

Fuel cells combine hydrogen and oxygen to give water and electrical energy with no carbon dioxide at the point of use.

Exothermic reactions release energy (temperature rises); endothermic reactions absorb it (temperature falls).

Bond breaking requires energy; bond forming releases energy; the overall energy change depends on the balance.

Corrosion of iron needs oxygen and water; rusting is prevented by painting, greasing, galvanising or sacrificial protection with a more reactive metal.

Thermistors (resistance falls as temperature rises) and LDRs (resistance falls as light intensity rises) link physical properties to control circuits.

Recycling metals saves energy because extraction by reduction or electrolysis is energy-intensive.

Variables: independent variable is changed deliberately; dependent variable is measured; control variables are kept constant to make the test fair.

A hypothesis is a testable prediction; a conclusion must be judged against the evidence collected, not against expectation.

Repeat readings and calculate a mean to reduce the effect of random error; random error scatters results about the true value.

Systematic error shifts all readings in one direction (e.g. zero error, mis-calibrated scale) and is not removed by averaging.

Precision = how closely repeats agree; accuracy = how close a reading is to the true value.

Uncertainty of a single scale reading is typically half the smallest division; for a difference of two readings, add the two uncertainties.

A valid experiment measures the intended quantity and controls other variables; a reliable one gives consistent results on repetition.

Tables: headings include quantity and unit (e.g. time / s); graphs: plot dependent against independent, draw line of best fit, describe trend and anomalies.

Scientific claims are accepted provisionally after peer review and replication; a single result is not proof.

Solid: particles closely packed in fixed positions, vibrate only. Liquid: close but irregular, slide past each other. Gas: far apart, random fast motion.

Changes of state (melting, boiling, condensing, freezing, subliming) are physical changes: particles rearrange but the substance is unchanged.

During melting or boiling, energy supplied breaks forces between particles, so temperature stays constant (flat portions of a heating curve).

Diffusion is net spreading of particles from high to low concentration; rate rises with temperature and is faster in gases than liquids.

Gas pressure arises from collisions of particles with container walls; heating raises pressure at constant volume because collisions are more frequent and forceful.

Filtration separates an insoluble solid from a liquid; evaporation or crystallisation recovers a dissolved solid.

Simple distillation separates a solvent from a solution; fractional distillation separates miscible liquids with different boiling points.

Chromatography separates dissolved substances by differing solubilities and attractions to the stationary phase; Rf = distance moved by spot / distance moved by solvent front.

Mixtures are separated by physical methods; compounds require chemical reactions to break bonds.

Atom: protons (charge +1, mass 1) and neutrons (0, mass 1) in the nucleus; electrons (charge −1, mass ≈1/1836) in shells.

Atomic number Z = protons = electrons in a neutral atom; mass number A = protons + neutrons; neutrons = A − Z.

Isotopes have the same Z but different A; relative atomic mass is the weighted mean of isotope masses by abundance.

Electron shells fill 2, 8, 8; the group number equals outer-shell electrons, the period number equals the number of occupied shells.

Ionic bonding: metal atoms lose electrons to form cations, non-metals gain electrons to form anions; electrostatic attraction gives a giant lattice with high melting point.

Covalent bonding: shared electron pairs between non-metals; simple molecules have weak intermolecular forces and low melting points.

Metallic bonding: positive ions in a sea of delocalised electrons - explains conduction and malleability.

Group 1 reactivity increases down the group (outer electron lost more easily); Group 7 reactivity decreases down the group.

Noble gases (Group 0) have full outer shells and are unreactive; transition metals form coloured compounds and variable oxidation states.

Conservation of mass: total mass of reactants equals total mass of products; balanced equations must have equal atoms of each element on both sides.

State symbols: (s) solid, (l) liquid, (g) gas, (aq) dissolved in water.

Moles n = m / M (mass in g, molar mass in g/mol); for gases at room temperature and pressure, 1 mol occupies about 24 dm³.

Concentration c = n / V, with V in dm³; 1 dm³ = 1000 cm³; c in mol/dm³ = mass concentration (g/dm³) / molar mass.

Percentage yield = (actual mass / theoretical mass) × 100; atom economy = (mass of desired product / total mass of reactants) × 100.

Reaction types: combination, decomposition, displacement (more reactive metal takes the place of a less reactive one), neutralisation, combustion, thermal decomposition.

Reacting-mass calculations: convert mass to moles, use the equation's mole ratio, convert back to mass.

Limiting reactant is the one used up first and determines the maximum product; the other is in excess.

Empirical formula from percentage composition: divide each percentage by the atomic mass, then divide by the smallest ratio.

Acid: proton (H⁺) donor; base: proton acceptor; alkali is a soluble base producing OH⁻ in water.

pH < 7 acidic, = 7 neutral, > 7 alkaline; pH 1 is strongly acidic, pH 14 strongly alkaline.

Neutralisation: acid + base → salt + water; acid + metal → salt + hydrogen; acid + carbonate → salt + water + carbon dioxide.

Salt name comes from the acid: hydrochloric → chloride, sulfuric → sulfate, nitric → nitrate, ethanoic → ethanoate.

Preparation: soluble salts by acid + excess insoluble base/carbonate, then filter and crystallise; insoluble salts by precipitation (mixing two solutions).

Strong acids ionise completely in water, weak acids only partially; this is why pH differs at the same concentration.

Rate increases with higher concentration, higher temperature, larger surface area, and a catalyst; rate depends on frequency of successful collisions.

Higher temperature increases both collision frequency and the proportion of collisions with energy ≥ activation energy, so the effect is large.

A catalyst lowers activation energy by providing an alternative pathway and is not used up; enzymes are biological catalysts.

Speed = distance / time; velocity is speed in a stated direction; acceleration a = (v − u) / t.

Distance–time graph: gradient = speed. Velocity–time graph: gradient = acceleration, area under graph = distance travelled.

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

Newton's first law: no resultant force means constant velocity (or rest); second law: F = ma; third law: equal and opposite forces on two different bodies.

Weight W = mg (g ≈ 9.8 N/kg on Earth); mass is the amount of matter and is unchanged by location.

Friction and air resistance oppose motion; terminal velocity is reached when drag equals weight and acceleration becomes zero.

Moment of a force = force × perpendicular distance from pivot; for balance, total clockwise moments = total anticlockwise moments.

Pressure p = F / A; in a liquid p = ρgh; pressure increases with depth.

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

Energy is conserved: it is transferred between stores (kinetic, gravitational, elastic, thermal, chemical, nuclear) but never created or destroyed.

Work done W = Fd (force along the direction of motion), measured in joules.

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

Power P = work done / time = energy transferred / time; measured in watts (J/s).

Efficiency = useful output energy / total input energy × 100%; the rest is dissipated, usually as thermal energy.

Renewable resources: solar, wind, hydroelectric, tidal, wave, geothermal, biomass. Non-renewable: coal, oil, gas, nuclear fuel.

Renewables are replenished and produce no direct carbon dioxide; drawbacks include intermittency, low output per unit area and habitat or visual impact.

Fossil fuels are reliable and energy-dense but release carbon dioxide, a greenhouse gas linked to global warming.

Energy transfer by conduction, convection and radiation: conduction needs particles, convection needs a fluid, radiation (infrared) needs no medium.

Wave quantities: frequency f (Hz), wavelength λ (m), amplitude; wave speed v = fλ.

Transverse waves oscillate perpendicular to travel (light, water); longitudinal waves oscillate parallel (sound).

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

Refraction: light bends towards the normal entering a denser medium (slower) and away from the normal leaving it.

Refractive index n = c / v = sin i / sin r; for the critical angle, sin c = 1 / n; total internal reflection occurs above the critical angle.

Converging lens: parallel rays meet at the principal focus; power P = 1 / f (dioptres, f in metres); real images are inverted.

Sound needs a medium, travels faster in solids than gases, and cannot travel through a vacuum; higher frequency means higher pitch.

Law of reflection and ray diagrams: image in a plane mirror is virtual, same size, laterally inverted, as far behind as the object is in front.

Colour: white light disperses through a prism; filters transmit only their own colour and absorb the rest.

Current I = charge / time (Q = It), measured in amperes; conventional current flows positive to negative.

Voltage (potential difference) V = energy transferred / charge = W / Q, measured in volts.

Ohm's law V = IR for a conductor at constant temperature; resistance R = V / I in ohms.

Series: same current everywhere, voltages add, R_total = R₁ + R₂ + …; parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂ + ….

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

A filament lamp's resistance rises with temperature, so its V–I graph curves; a diode conducts in one direction only.

Charge carriers in metals are electrons; in electrolytes, ions move to the electrodes.

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

Electromagnetic induction: a changing magnetic field through a conductor induces a voltage; faster motion or more turns give a larger induced voltage.

Temperature measures average kinetic energy of particles; thermal energy transfers from hotter to colder bodies until thermal equilibrium.

Specific heat capacity: E = mcΔT, where c is the energy needed to raise 1 kg by 1 °C.

Specific latent heat: E = mL for a change of state at constant temperature; latent heat of vaporisation is larger than of fusion.

Thermal conduction in solids occurs by particle vibration and free-electron transfer; metals conduct well.

Convection is bulk movement of fluid caused by density differences; it cannot occur in solids.

Thermal radiation is infrared emission; dark, matt surfaces absorb and emit best, shiny light surfaces reflect.

Absolute temperature T (K) = θ (°C) + 273; gas pressure is proportional to absolute temperature at constant volume.

Boyle's law: pV = constant at constant temperature; p₁V₁ = p₂V₂.

Reducing heat loss uses insulation, trapped air, double glazing and reflective surfaces, all limiting conduction, convection or radiation.

Earth's structure: crust, mantle, outer core (liquid), inner core (solid); tectonic plate movement causes earthquakes, volcanoes and mountain building.

Rock cycle: igneous (cooled magma), sedimentary (compacted deposited layers), metamorphic (heat and pressure).

The Sun's energy comes from nuclear fusion of hydrogen into helium; it reaches Earth mainly by radiation.

Solar System order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune; planets orbit the Sun with gravity providing the centripetal force.

Gravity follows an inverse-square law: doubling distance reduces gravitational force to one quarter.

Seasons arise from the tilt of Earth's axis, not from distance from the Sun; day and night arise from rotation on the axis.

Moon phases arise from the changing angle between Earth, Moon and Sun; eclipses occur when the bodies are aligned.

The greenhouse effect: gases such as CO₂, CH₄ and water vapour absorb and re-emit infrared, warming the surface.

Human impacts include acid rain from sulfur dioxide and nitrogen oxides, and ozone depletion by CFCs.

Burning fuels is exothermic: chemical energy in bonds converts to thermal energy, which can drive turbines via steam.

Electrolysis uses electrical energy to drive a non-spontaneous reaction; electroplating and metal extraction are applications.

Batteries convert chemical energy to electrical energy; charging reverses the reaction and stores energy chemically.

Fuel cells combine hydrogen and oxygen to give water and electrical energy with no carbon dioxide at the point of use.

Exothermic reactions release energy (temperature rises); endothermic reactions absorb it (temperature falls).

Bond breaking requires energy; bond forming releases energy; the overall energy change depends on the balance.

Corrosion of iron needs oxygen and water; rusting is prevented by painting, greasing, galvanising or sacrificial protection with a more reactive metal.

Thermistors (resistance falls as temperature rises) and LDRs (resistance falls as light intensity rises) link physical properties to control circuits.

Recycling metals saves energy because extraction by reduction or electrolysis is energy-intensive.