SPM Additional Science cheat sheet

Variables: manipulated (independent) variable is changed deliberately; responding (dependent) variable is measured; fixed variables are kept constant.

Hypothesis must be testable and state a relationship between manipulated and responding variables, e.g. 'As temperature increases, reaction rate increases'.

Accuracy = closeness to true value; precision = consistency of repeated readings; a systematic error shifts all readings the same way, a random error scatters them.

Mean = sum of readings / number of readings; reduce random error by repeating and averaging, reduce systematic error by calibrating or correcting the instrument.

SI base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity).

Prefixes: k = 10^3, c = 10^-2, m = 10^-3, µ = 10^-6, n = 10^-9; convert before substituting into formulas.

Uncertainty of a measuring instrument is usually ± half the smallest scale division; percentage error = (uncertainty / reading) × 100.

A valid conclusion must be supported by data, refer back to the hypothesis, and state whether the hypothesis is accepted or rejected.

Atom: protons (+1, mass 1) and neutrons (0, mass 1) in the nucleus; electrons (-1, negligible mass) in shells. Proton number Z defines the element; nucleon number A = protons + neutrons.

Isotopes have the same proton number but different neutron numbers, so identical chemistry but different mass; relative atomic mass is the weighted mean of isotope masses.

Electron shell filling: 2, 8, 8 (up to 20); valence electrons determine group number, number of shells determines period.

Ion formation: metals lose electrons to form cations (e.g. Na → Na+ + e−); non-metals gain electrons to form anions (e.g. Cl + e− → Cl−).

Three states of matter differ in particle arrangement and energy: solid (fixed lattice, vibrate), liquid (close but mobile), gas (far apart, fast random motion).

Diffusion rate increases with temperature and decreases with particle mass; Graham's law: rate ∝ 1/√molar mass.

Kinetic particle model explains Brownian motion, gas pressure (particle collisions with walls), and expansion on heating.

Mixtures are separated by physical methods (filtration, distillation, chromatography, magnetism); compounds by chemical reactions.

Ionic compounds: high melting point, conduct when molten or aqueous; covalent simple molecules: low melting point, do not conduct; metals: conduct, malleable.

Balanced equation conserves atoms of each element; coefficients only, never change subscripts.

Mole concept: 1 mol = 6.02 × 10^23 particles; mass = moles × molar mass; gas volume at s.t.p. = moles × 22.4 dm³.

Concentration (mol/dm³) = moles of solute / volume of solution in dm³; dilution: C1V1 = C2V2.

Acid + base → salt + water (neutralisation); acid + metal → salt + hydrogen; acid + carbonate → salt + water + carbon dioxide.

pH < 7 acidic, 7 neutral, > 7 alkaline; strong acids ionise completely, weak acids partially.

Oxidation = loss of electrons/increase in oxidation number; reduction = gain of electrons/decrease in oxidation number (OIL RIG).

Rate of reaction increases with concentration, temperature, surface area and catalyst; catalyst lowers activation energy without being consumed.

Exothermic reactions release heat (ΔH negative); endothermic absorb heat (ΔH positive); bond breaking absorbs, bond forming releases energy.

Tests: hydrogen - lighted splint 'pop'; oxygen - relights glowing splint; carbon dioxide - turns limewater milky; water - turns anhydrous copper(II) sulphate blue.

Newton's second law: F = ma; weight W = mg with g ≈ 9.8 N/kg (or 10 N/kg).

Equations of motion: v = u + at; s = ut + ½at²; v² = u² + 2as.

Momentum p = mv; principle of conservation of momentum applies in collisions and explosions.

Work done W = Fs (force along displacement); power P = W/t; kinetic energy Ek = ½mv²; gravitational PE = mgh.

Principle of conservation of energy: energy cannot be created or destroyed, only transformed; efficiency = useful output / total input × 100%.

Pressure P = F/A; liquid pressure P = ρgh; Pascal's principle underlies hydraulic systems.

Hooke's law: F = kx up to the elastic limit; spring constant k in N/m.

Moments: clockwise moments = anticlockwise moments for equilibrium; moment = force × perpendicular distance from pivot.

Friction opposes relative motion, produces heat, and can be reduced by lubricants or streamlining.

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

Series circuit: same current everywhere, voltages add, R_total = R1 + R2 + ...

Parallel circuit: same voltage across branches, currents add, 1/R_total = 1/R1 + 1/R2 + ...

Electrical power P = VI = I²R = V²/R; energy E = Pt (joules) or kWh for domestic meters.

Charge Q = It (coulombs); 1 coulomb = 1 ampere × 1 second.

Magnetic field lines run from north to south outside a magnet; a current-carrying conductor produces a circular field (right-hand grip rule).

Force on a current-carrying conductor in a magnetic field: F = BIL sin θ; direction given by Fleming's left-hand rule.

Electromagnetic induction: changing magnetic flux induces an emf (Faraday); direction opposes change (Lenz).

Transformers: Vp/Vs = Np/Ns; ideal transformer Pp = Ps; step-up increases voltage, decreases current.

Wave equation: v = fλ; period T = 1/f; frequency in hertz.

Transverse waves oscillate perpendicular to propagation (light); 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; Snell's law n1 sin θ1 = n2 sin θ2; n = c/v.

Total internal reflection occurs when light travels from denser to less dense medium and angle of incidence exceeds the critical angle; sin c = 1/n.

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

Sound needs a medium; speed in air ≈ 340 m/s, faster in solids; pitch depends on frequency, loudness on amplitude.

Resonance occurs when driving frequency equals natural frequency, producing maximum amplitude.

Electromagnetic spectrum order (increasing frequency): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Cell theory: all living things are made of cells; the cell is the basic unit of life; cells arise from pre-existing cells.

Prokaryotic cells lack a membrane-bound nucleus and organelles; eukaryotic cells have a nucleus and membrane-bound organelles.

Plant cells have cellulose cell walls, chloroplasts, and a large permanent vacuole; animal cells have none of these.

Organelles: nucleus (genetic control), mitochondrion (aerobic respiration), ribosome (protein synthesis), chloroplast (photosynthesis), vacuole (storage/turgor).

Photosynthesis: 6CO2 + 6H2O → C6H12O6 + 6O2, in chloroplasts using chlorophyll and light energy.

Aerobic respiration: C6H12O6 + 6O2 → 6CO2 + 6H2O + energy (ATP); anaerobic in muscle gives lactic acid.

Enzymes are biological catalysts; activity peaks at optimum pH and temperature; denaturation above optimum destroys the active site.

Diffusion moves particles down a concentration gradient; osmosis is water movement across a semi-permeable membrane; active transport requires energy.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four haploid gametes with genetic variation.

Neurone structure: dendrites receive, axon conducts, myelin insulates; synapse transmits via neurotransmitters across a gap.

Reflex arc: receptor → sensory neurone → relay neurone in spinal cord → motor neurone → effector; involuntary and rapid.

Hormones are chemical messengers secreted by endocrine glands into the blood; insulin lowers blood glucose, glucagon raises it.

Negative feedback restores a variable to its set point (e.g. body temperature, blood glucose, water balance).

Homeostasis: thermoregulation via sweating, vasodilation, shivering; osmoregulation by kidneys via ADH.

Male gametes: sperm made in testes, testosterone; female gametes: ova released from ovaries, controlled by oestrogen and progesterone.

Menstrual cycle: FSH matures follicle, LH triggers ovulation around day 14, progesterone maintains the uterine lining.

Fertilisation occurs in the fallopian tube; the zygote implants in the uterus; placenta exchanges nutrients, gases and wastes.

Auxins in plants cause phototropism; auxin accumulates on the shaded side, causing cells to elongate and the shoot to bend toward light.

Food chain: producer → primary consumer → secondary consumer; arrows show direction of energy flow.

Only about 10% of energy passes to the next trophic level; the rest is lost as heat, movement and excretion.

Pyramid of numbers, biomass, or energy represents trophic levels; energy pyramids are always upright.

Population size is affected by birth rate, death rate, immigration and emigration; sampling uses quadrats or capture–recapture.

Carbon cycle: photosynthesis removes CO2; respiration, combustion and decomposition release it.

Nitrogen cycle: nitrogen fixation, nitrification, assimilation, denitrification; legumes fix nitrogen via root nodules.

Greenhouse gases (CO2, CH4, water vapour) trap infrared radiation; enhanced greenhouse effect causes global warming.

Eutrophication: excess nitrates and phosphates cause algal bloom, oxygen depletion, and death of aquatic organisms.

Conservation strategies: protected areas, captive breeding, seed banks, reducing pollution and habitat destruction.

Semiconductors (silicon, germanium) conduct only when doped; n-type adds electron donors, p-type adds electron acceptors.

Diode allows current in one direction only; LED emits light when forward biased; a p–n junction is the basis of solar cells.

Transistor acts as an amplifier or switch; integrated circuits pack many transistors onto a chip.

Electromagnetic induction in generators converts mechanical energy to electrical energy; motors convert electrical to mechanical.

Renewable energy sources: solar, wind, hydroelectric, geothermal, biomass; non-renewable: coal, oil, natural gas, nuclear fuel.

Nuclear fission releases energy from splitting heavy nuclei; fusion joins light nuclei; both release energy per E = mc².

Biotechnology applications: fermentation, antibiotics, vaccines, genetic engineering, gene therapy.

Nanotechnology manipulates matter at 1–100 nm scale, producing materials with enhanced strength, conductivity or reactivity.

Materials science: alloys, polymers, composites, and ceramics chosen for strength, conductivity, or corrosion resistance.