GCE A/L Science for Technology cheat sheet

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

Derived units are products or quotients of base units: 1 N = 1 kg·m·s⁻²; 1 J = 1 N·m; 1 W = 1 J·s⁻¹; 1 Pa = 1 N·m⁻².

Prefixes: T = 10¹², G = 10⁹, M = 10⁶, k = 10³, c = 10⁻², m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹².

Dimensional consistency test: both sides of any physical equation must have identical base-unit dimensions; a mismatch proves the equation wrong.

Relative uncertainty of a product or quotient equals the sum of the relative uncertainties of the factors; for powers multiply the relative uncertainty by the exponent.

Absolute uncertainty of a sum or difference equals the sum of the absolute uncertainties of the terms.

Random error reduces by averaging repeated readings (uncertainty falls as 1/√n); systematic error shifts all readings and is removed only by calibration or correction.

Significant figures of a result are limited by the least precise input; a measuring instrument is read to half its smallest scale division for analogue scales.

Precision describes repeatability; accuracy describes closeness to the true value. A calibrated instrument can be precise but inaccurate.

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.

Newton's second law: F = ma; weight W = mg with g ≈ 9.81 m·s⁻² near Earth's surface.

Momentum p = mv is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Work W = Fs cos θ; power P = W/t = Fv; kinetic energy ½mv²; gravitational potential energy mgh.

Circular motion: centripetal acceleration a = v²/r = ω²r, with ω = 2π/T.

Hooke's law: F = kx within the elastic limit; elastic strain energy = ½Fx = ½kx².

Stress σ = F/A; strain ε = Δl/l; Young's modulus E = σ/ε applies in the linear region of the stress–strain curve.

Pressure in a fluid at depth h is p = p₀ + ρgh; upthrust equals the weight of fluid displaced (Archimedes' principle).

Torque τ = F × perpendicular distance; a body in equilibrium has zero resultant force and zero resultant torque about any point.

Heat transfer modes: conduction (through solids via lattice vibration and free electrons), convection (bulk fluid motion), radiation (electromagnetic, needs no medium).

Specific heat capacity: Q = mcΔθ; specific latent heat: Q = mL for a change of state at constant temperature.

Thermal conductivity: rate of heat flow = kAΔθ/l for a slab of thickness l and area A.

Boyle's law: pV = constant at constant T; Charles's law: V/T = constant at constant p; pressure law: p/T = constant at constant V (T in kelvin).

Ideal gas equation: pV = nRT with R ≈ 8.31 J·mol⁻¹·K⁻¹; average kinetic energy of a molecule = (3/2)kT.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; for an isothermal process ΔU = 0.

Efficiency of a heat engine = (Q_in − Q_out)/Q_in = W/Q_in; Carnot limit η = 1 − T_cold/T_hot (kelvin).

Stefan–Boltzmann law: power radiated per unit area = εσT⁴, with σ ≈ 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴.

Absolute zero is 0 K = −273.15 °C; a temperature in kelvin is obtained by adding 273 to the Celsius value.

Wave equation: v = fλ; for a stretched string v = √(T/µ) where µ is mass per unit length.

Transverse waves oscillate perpendicular to propagation (light, string waves); longitudinal waves oscillate parallel (sound in air).

Refraction obeys Snell's law: n₁ sin θ₁ = n₂ sin θ₂, with refractive index n = c/v.

Total internal reflection occurs only when light travels from denser to rarer medium and the angle of incidence exceeds the critical angle sin C = n₂/n₁.

Thin lens and mirror equation: 1/f = 1/v + 1/u; magnification m = v/u; power of a lens P = 1/f (in dioptres, f in metres).

Two-source interference condition: constructive when path difference = nλ, destructive when path difference = (n + ½)λ.

Diffraction grating: d sin θ = nλ, where d is the slit spacing; smaller d gives a wider spread of orders.

Sound intensity level in decibels: L = 10 log₁₀(I/I₀) with I₀ = 1 × 10⁻¹² W·m⁻².

Doppler effect for sound: observed frequency rises as source and observer approach; f' = f(v ± v_o)/(v ∓ v_s).

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = ρl/A.

Series: R_total = R₁ + R₂ + …; parallel: 1/R_total = 1/R₁ + 1/R₂ + ….

Electrical power P = VI = I²R = V²/R; energy = power × time.

Kirchhoff's laws: sum of currents at a junction is zero; sum of e.m.f.s equals sum of p.d.s around any closed loop.

Capacitance C = Q/V; energy stored = ½QV = ½CV²; capacitors in series add reciprocally, in parallel directly.

Force on a current-carrying conductor F = BIl sin θ; force on a moving charge F = qvB sin θ (motor effect).

Electromagnetic induction: induced e.m.f. = −N dΦ/dt (Faraday); Lenz's law states the induced current opposes the change producing it.

Transformer relation: V_s/V_p = N_s/N_p; for an ideal transformer V_pI_p = V_sI_s.

Diode conducts in forward bias above about 0.7 V (silicon); a Zener diode in reverse breakdown provides voltage regulation.

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes have equal Z but different A.

Electron configuration fills in order of increasing energy: 1s 2s 2p 3s 3p 4s 3d, following the Aufbau principle and Hund's rule.

Ionic bonding: metal loses electrons to non-metal; high melting points, conduct when molten or in solution.

Covalent bonding: shared electron pairs; polar covalent bonds arise from electronegativity difference between atoms.

Metallic bonding: positive ions in a sea of delocalised electrons, explaining conductivity and malleability.

Mole concept: n = m/M; one mole contains 6.022 × 10²³ particles; molar gas volume is 22.4 dm³ at s.t.p.

Acid–base neutralisation: H⁺ + OH⁻ → H₂O; pH = −log₁₀[H⁺]; strong acids ionise completely.

Oxidation is loss of electrons and increase in oxidation number; reduction is gain. Redox reactions pair these processes.

Le Chatelier's principle: a system at equilibrium shifts to oppose a change in concentration, pressure or temperature.

Homologous series differ by CH₂; general formulas: alkanes CₙH₂ₙ₊₂, alkenes CₙH₂ₙ, alkynes CₙH₂ₙ₋₂.

Alkanes undergo free-radical substitution with halogens in UV light; alkenes undergo electrophilic addition across the C=C bond.

Markovnikov's rule: in addition of HX to an alkene, H adds to the carbon already bearing more hydrogen.

Functional groups: hydroxyl (alcohol), carboxyl (carboxylic acid), ester, amine, amide, aldehyde and ketone determine chemical behaviour.

Esterification: carboxylic acid + alcohol ⇌ ester + water, usually acid-catalysed and reversible.

Addition polymerisation opens C=C bonds (e.g. ethene → poly(ethene)); condensation polymerisation releases a small molecule such as water (e.g. nylon, PET).

Thermoplastics soften on heating and can be remoulded; thermosets have cross-linked networks and char rather than melt.

Degree of polymerisation n = molar mass of polymer / molar mass of repeat unit.

Crude oil fractions separate by fractional distillation according to boiling point; cracking converts long chains into shorter, more useful alkenes.

Prokaryotic cells lack a membrane-bound nucleus and organelles; eukaryotic cells contain a nucleus, mitochondria and other membrane-bound structures.

Mitochondria carry out aerobic respiration releasing ATP; chloroplasts carry out photosynthesis; ribosomes synthesise protein.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four haploid gametes with crossing over and independent assortment.

DNA structure: double helix of two antiparallel strands, base pairs A–T and G–C joined by hydrogen bonds.

Transcription copies DNA to mRNA in the nucleus; translation at the ribosome assembles amino acids in codon-specified order.

Mendel's monohybrid cross of heterozygotes gives a 3:1 phenotype ratio; a test cross with a homozygous recessive reveals genotype.

Sex-linked traits carried on the X chromosome appear more often in males, who have only one X.

Bacteria reproduce by binary fission; growth phases are lag, exponential (log), stationary and decline.

Sterilisation kills all microorganisms including endospores; disinfectants reduce numbers on surfaces; antibiotics target bacterial structures absent in human cells.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, light-dependent reactions in thylakoids and the Calvin cycle in the stroma.

Limiting factors of photosynthesis: light intensity, CO₂ concentration and temperature; the rate plateaus when another factor becomes limiting.

Soil pH, texture and nutrient content (N, P, K) determine crop suitability; legumes fix nitrogen via Rhizobium in root nodules.

Transpiration pulls water up the xylem; stomata regulate gas exchange and water loss, closing under water stress.

Plant tissue culture uses sterile explants on nutrient medium with auxin and cytokinin to regenerate whole plants.

Genetic engineering steps: isolation of the gene, insertion into a vector (plasmid), transfer into host cells, selection and expression.

PCR amplifies DNA through repeated cycles of denaturation, primer annealing and extension by a thermostable polymerase.

Integrated pest management combines biological control, resistant varieties and limited pesticide use to reduce resistance build-up.

Fermentation in biotechnology uses microorganisms in controlled bioreactors to produce antibiotics, enzymes and single-cell protein.

Sensor output is usually conditioned (amplified, filtered, digitised) before display or control; a transducer converts one energy form into another.

Operational amplifier basics: inverting gain = −R_f/R_in; non-inverting gain = 1 + R_f/R_in; a virtual earth exists at the inverting input.

Digital logic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are universal gates.

Binary to decimal conversion weights each bit by powers of two; an 8-bit unsigned number ranges 0–255.

Microcontroller control loop: read sensor, compare with set point, compute error, drive actuator (e.g. PWM output for motor speed).

Pneumatic and hydraulic systems transmit force via fluid pressure F = pA; hydraulics suit high force, pneumatics suit fast, clean, low-force action.

Gear ratio = driven teeth / driving teeth; output torque increases and speed decreases with a larger driven gear.

Mechanical advantage = load/effort; velocity ratio = distance moved by effort / distance moved by load; efficiency = MA/VR × 100%.

Strain gauges, thermocouples and LVDTs are analogue transducers; a thermocouple produces a small e.m.f. proportional to temperature difference.

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

Derived units are products or quotients of base units: 1 N = 1 kg·m·s⁻²; 1 J = 1 N·m; 1 W = 1 J·s⁻¹; 1 Pa = 1 N·m⁻².

Prefixes: T = 10¹², G = 10⁹, M = 10⁶, k = 10³, c = 10⁻², m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹, p = 10⁻¹².

Dimensional consistency test: both sides of any physical equation must have identical base-unit dimensions; a mismatch proves the equation wrong.

Relative uncertainty of a product or quotient equals the sum of the relative uncertainties of the factors; for powers multiply the relative uncertainty by the exponent.

Absolute uncertainty of a sum or difference equals the sum of the absolute uncertainties of the terms.

Random error reduces by averaging repeated readings (uncertainty falls as 1/√n); systematic error shifts all readings and is removed only by calibration or correction.

Significant figures of a result are limited by the least precise input; a measuring instrument is read to half its smallest scale division for analogue scales.

Precision describes repeatability; accuracy describes closeness to the true value. A calibrated instrument can be precise but inaccurate.

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.

Newton's second law: F = ma; weight W = mg with g ≈ 9.81 m·s⁻² near Earth's surface.

Momentum p = mv is conserved in all collisions; kinetic energy is conserved only in elastic collisions.

Work W = Fs cos θ; power P = W/t = Fv; kinetic energy ½mv²; gravitational potential energy mgh.

Circular motion: centripetal acceleration a = v²/r = ω²r, with ω = 2π/T.

Hooke's law: F = kx within the elastic limit; elastic strain energy = ½Fx = ½kx².

Stress σ = F/A; strain ε = Δl/l; Young's modulus E = σ/ε applies in the linear region of the stress–strain curve.

Pressure in a fluid at depth h is p = p₀ + ρgh; upthrust equals the weight of fluid displaced (Archimedes' principle).

Torque τ = F × perpendicular distance; a body in equilibrium has zero resultant force and zero resultant torque about any point.

Heat transfer modes: conduction (through solids via lattice vibration and free electrons), convection (bulk fluid motion), radiation (electromagnetic, needs no medium).

Specific heat capacity: Q = mcΔθ; specific latent heat: Q = mL for a change of state at constant temperature.

Thermal conductivity: rate of heat flow = kAΔθ/l for a slab of thickness l and area A.

Boyle's law: pV = constant at constant T; Charles's law: V/T = constant at constant p; pressure law: p/T = constant at constant V (T in kelvin).

Ideal gas equation: pV = nRT with R ≈ 8.31 J·mol⁻¹·K⁻¹; average kinetic energy of a molecule = (3/2)kT.

First law of thermodynamics: ΔU = Q − W, where W is work done by the gas; for an isothermal process ΔU = 0.

Efficiency of a heat engine = (Q_in − Q_out)/Q_in = W/Q_in; Carnot limit η = 1 − T_cold/T_hot (kelvin).

Stefan–Boltzmann law: power radiated per unit area = εσT⁴, with σ ≈ 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴.

Absolute zero is 0 K = −273.15 °C; a temperature in kelvin is obtained by adding 273 to the Celsius value.

Wave equation: v = fλ; for a stretched string v = √(T/µ) where µ is mass per unit length.

Transverse waves oscillate perpendicular to propagation (light, string waves); longitudinal waves oscillate parallel (sound in air).

Refraction obeys Snell's law: n₁ sin θ₁ = n₂ sin θ₂, with refractive index n = c/v.

Total internal reflection occurs only when light travels from denser to rarer medium and the angle of incidence exceeds the critical angle sin C = n₂/n₁.

Thin lens and mirror equation: 1/f = 1/v + 1/u; magnification m = v/u; power of a lens P = 1/f (in dioptres, f in metres).

Two-source interference condition: constructive when path difference = nλ, destructive when path difference = (n + ½)λ.

Diffraction grating: d sin θ = nλ, where d is the slit spacing; smaller d gives a wider spread of orders.

Sound intensity level in decibels: L = 10 log₁₀(I/I₀) with I₀ = 1 × 10⁻¹² W·m⁻².

Doppler effect for sound: observed frequency rises as source and observer approach; f' = f(v ± v_o)/(v ∓ v_s).

Ohm's law V = IR holds for ohmic conductors at constant temperature; resistance R = ρl/A.

Series: R_total = R₁ + R₂ + …; parallel: 1/R_total = 1/R₁ + 1/R₂ + ….

Electrical power P = VI = I²R = V²/R; energy = power × time.

Kirchhoff's laws: sum of currents at a junction is zero; sum of e.m.f.s equals sum of p.d.s around any closed loop.

Capacitance C = Q/V; energy stored = ½QV = ½CV²; capacitors in series add reciprocally, in parallel directly.

Force on a current-carrying conductor F = BIl sin θ; force on a moving charge F = qvB sin θ (motor effect).

Electromagnetic induction: induced e.m.f. = −N dΦ/dt (Faraday); Lenz's law states the induced current opposes the change producing it.

Transformer relation: V_s/V_p = N_s/N_p; for an ideal transformer V_pI_p = V_sI_s.

Diode conducts in forward bias above about 0.7 V (silicon); a Zener diode in reverse breakdown provides voltage regulation.

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes have equal Z but different A.

Electron configuration fills in order of increasing energy: 1s 2s 2p 3s 3p 4s 3d, following the Aufbau principle and Hund's rule.

Ionic bonding: metal loses electrons to non-metal; high melting points, conduct when molten or in solution.

Covalent bonding: shared electron pairs; polar covalent bonds arise from electronegativity difference between atoms.

Metallic bonding: positive ions in a sea of delocalised electrons, explaining conductivity and malleability.

Mole concept: n = m/M; one mole contains 6.022 × 10²³ particles; molar gas volume is 22.4 dm³ at s.t.p.

Acid–base neutralisation: H⁺ + OH⁻ → H₂O; pH = −log₁₀[H⁺]; strong acids ionise completely.

Oxidation is loss of electrons and increase in oxidation number; reduction is gain. Redox reactions pair these processes.

Le Chatelier's principle: a system at equilibrium shifts to oppose a change in concentration, pressure or temperature.

Homologous series differ by CH₂; general formulas: alkanes CₙH₂ₙ₊₂, alkenes CₙH₂ₙ, alkynes CₙH₂ₙ₋₂.

Alkanes undergo free-radical substitution with halogens in UV light; alkenes undergo electrophilic addition across the C=C bond.

Markovnikov's rule: in addition of HX to an alkene, H adds to the carbon already bearing more hydrogen.

Functional groups: hydroxyl (alcohol), carboxyl (carboxylic acid), ester, amine, amide, aldehyde and ketone determine chemical behaviour.

Esterification: carboxylic acid + alcohol ⇌ ester + water, usually acid-catalysed and reversible.

Addition polymerisation opens C=C bonds (e.g. ethene → poly(ethene)); condensation polymerisation releases a small molecule such as water (e.g. nylon, PET).

Thermoplastics soften on heating and can be remoulded; thermosets have cross-linked networks and char rather than melt.

Degree of polymerisation n = molar mass of polymer / molar mass of repeat unit.

Crude oil fractions separate by fractional distillation according to boiling point; cracking converts long chains into shorter, more useful alkenes.

Prokaryotic cells lack a membrane-bound nucleus and organelles; eukaryotic cells contain a nucleus, mitochondria and other membrane-bound structures.

Mitochondria carry out aerobic respiration releasing ATP; chloroplasts carry out photosynthesis; ribosomes synthesise protein.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four haploid gametes with crossing over and independent assortment.

DNA structure: double helix of two antiparallel strands, base pairs A–T and G–C joined by hydrogen bonds.

Transcription copies DNA to mRNA in the nucleus; translation at the ribosome assembles amino acids in codon-specified order.

Mendel's monohybrid cross of heterozygotes gives a 3:1 phenotype ratio; a test cross with a homozygous recessive reveals genotype.

Sex-linked traits carried on the X chromosome appear more often in males, who have only one X.

Bacteria reproduce by binary fission; growth phases are lag, exponential (log), stationary and decline.

Sterilisation kills all microorganisms including endospores; disinfectants reduce numbers on surfaces; antibiotics target bacterial structures absent in human cells.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, light-dependent reactions in thylakoids and the Calvin cycle in the stroma.

Limiting factors of photosynthesis: light intensity, CO₂ concentration and temperature; the rate plateaus when another factor becomes limiting.

Soil pH, texture and nutrient content (N, P, K) determine crop suitability; legumes fix nitrogen via Rhizobium in root nodules.

Transpiration pulls water up the xylem; stomata regulate gas exchange and water loss, closing under water stress.

Plant tissue culture uses sterile explants on nutrient medium with auxin and cytokinin to regenerate whole plants.

Genetic engineering steps: isolation of the gene, insertion into a vector (plasmid), transfer into host cells, selection and expression.

PCR amplifies DNA through repeated cycles of denaturation, primer annealing and extension by a thermostable polymerase.

Integrated pest management combines biological control, resistant varieties and limited pesticide use to reduce resistance build-up.

Fermentation in biotechnology uses microorganisms in controlled bioreactors to produce antibiotics, enzymes and single-cell protein.

Sensor output is usually conditioned (amplified, filtered, digitised) before display or control; a transducer converts one energy form into another.

Operational amplifier basics: inverting gain = −R_f/R_in; non-inverting gain = 1 + R_f/R_in; a virtual earth exists at the inverting input.

Digital logic gates: AND outputs 1 only when all inputs are 1; OR outputs 1 when any input is 1; NOT inverts; NAND and NOR are universal gates.

Binary to decimal conversion weights each bit by powers of two; an 8-bit unsigned number ranges 0–255.

Microcontroller control loop: read sensor, compare with set point, compute error, drive actuator (e.g. PWM output for motor speed).

Pneumatic and hydraulic systems transmit force via fluid pressure F = pA; hydraulics suit high force, pneumatics suit fast, clean, low-force action.

Gear ratio = driven teeth / driving teeth; output torque increases and speed decreases with a larger driven gear.

Mechanical advantage = load/effort; velocity ratio = distance moved by effort / distance moved by load; efficiency = MA/VR × 100%.

Strain gauges, thermocouples and LVDTs are analogue transducers; a thermocouple produces a small e.m.f. proportional to temperature difference.