CSET Science, general interdisciplinary foundations - independent foundations cheat sheet

State resolution and uncertainty convention for each instrument

Random errors → repeats and means; systematic errors → correction

For first-order worst-case bounds, add relative contributions; independent standard uncertainties use quadrature

Gradient from two points on the best-fit line, with units

Average repeated timings and time many oscillations to cut reaction error

Never quote more significant figures than the data justify

Hypothesis = testable prediction; theory = broad supported explanation; law = consistent regularity.

Independent variable is manipulated; dependent is measured; controls are held constant.

Random assignment supports experimental causal inference; an observed association alone does not establish causation.

Accuracy = closeness to truth; precision = repeatability.

Replication and sample size reduce the influence of random chance.

Relative atomic mass is an abundance-weighted mean of isotope masses, calculated from mass-spectrum data.

Across a period effective nuclear charge rises, so radius falls and ionisation energy and electronegativity rise.

Large jumps in successive ionisation energies reveal the number of electrons in the outer shell.

Cr and Cu adopt 3d5 4s1 and 3d10 4s1 configurations; 4s electrons are removed first on ionisation.

Transition metals require a partially filled d subshell in at least one common oxidation state.

VSEPR: count all electron domains, then apply lone pair–lone pair > lone pair–bond pair > bond pair–bond pair repulsion.

Molecular polarity requires both polar bonds and an asymmetric arrangement of those bonds.

Higher bond order gives a shorter, stronger bond; resonance spreads the order over equivalent positions.

Only period 3 elements and below can expand their octet; N, O, F and C cannot.

Ionic lattice strength increases with ion charge and decreases with ion radius.

Convert to K and m3 before using PV = nRT; R = 8.314 J mol−1 K−1.

Real gases deviate from ideality at high pressure and low temperature.

n = m/M, n = cV (V in dm3) and n = V/24.0 for gases at RTP are the three key conversions.

The limiting reagent is the one with the smallest moles ÷ coefficient; product amount depends on it.

Percentage yield measures practical success; atom economy measures how much reactant mass is useful.

Dilution uses c1V1 = c2V2 because the moles of solute do not change.

Always balance the equation before applying any molar ratio.

ΔH is negative for exothermic reactions; standard enthalpy of formation of an element in its standard state is zero.

q = mcΔT uses the total mass of solution, and ΔH per mole = −q/n.

Hess's law lets you combine any route; combustion data are used in the reverse order to formation data.

Resolve vectors before applying F = ma or the SUVAT equations

Momentum is a vector: conserve each component only when the corresponding net external impulse is zero

Equilibrium requires both zero resultant force and zero resultant moment

The centripetal component points to the centre; uniform circular motion has constant speed but changing velocity

SHM signature: a = −ω²x, giving T = 2π/ω

State g and sign conventions explicitly at the start of a solution

Define the system boundary before applying energy conservation.

Constant-force work is F s cos(theta); variable-force work is a signed area or integral.

Net work equals kinetic-energy change for a constant-mass nonrelativistic particle.

m g delta-h is a local uniform-gravity potential-energy approximation.

Mechanical-energy loss can become internal energy while total energy is conserved.

Average power is transferred energy divided by time; instantaneous mechanical power is force dot velocity.

Phase difference = 2π × path difference/λ

Stationary waves: node spacing λ/2, node–antinode λ/4, no energy transfer

Grating equation d sinθ = nλ with d = 1/N in metres

Young's slits: x = λD/a for small angles

Snell: n₁ sinθ₁ = n₂ sinθ₂; critical angle sinθc = n₂/n₁ requires n₁ > n₂

Keep one lens sign convention throughout and state it

hf = φ + KEmax; intensity affects rate, not maximum energy

Threshold frequency f₀ = φ/h in the ordinary single-photon model; below it that model predicts no photoemission

Prokaryotes lack a membrane-bound nucleus; bacterial peptidoglycan walls are not universal and archaeal walls differ.

Fluid mosaic membranes contain a lipid bilayer and proteins; sterol and carbohydrate composition depends on the cell.

Facilitated diffusion is passive; primary active transport may use ATP directly and secondary transport uses a gradient.

Water potential ψ = ψs + ψp; water moves from higher (less negative) to lower ψ.

Mitosis (P-M-A-T) after S-phase replication maintains chromosome number.

Cytokinesis: cleavage furrow in animals, cell plate in plants.

A–T has 2 hydrogen bonds, G–C has 3; strands are antiparallel with 3′–5′ phosphodiester bonds.

Semi-conservative replication: helicase, DNA polymerase (5′→3′), ligase on the lagging strand.

The standard code is triplet and degenerate, nearly universal; AUG is a common start codon with biological exceptions.

Meiosis I separates homologues; crossing over in prophase I produces recombinants.

A test cross is with a homozygous recessive to reveal an unknown genotype.

Informative linked-locus crosses often give excess parentals; recombination percentage approximates short map distances, not all intervals exactly.

Negative feedback reverses a deviation; positive feedback amplifies and must terminate.

Surface area to volume ratio drives the need for specialized exchange surfaces.

Pulmonary arteries carry deoxygenated blood away from the heart.

Xylem moves water up (cohesion–tension); phloem moves sugars by pressure flow.

Insulin lowers blood glucose; glucagon raises it - both are negative feedback.

Los virus son acelulares; los ciclos lítico y lisogénico son modelos de determinados bacteriófagos, no de todos los virus.

Retrovirus: retrotranscriptasa convierte ARN en ADN e integra el provirus.

Muchas bacterias tienen peptidoglicano; pared, plásmidos y otros rasgos deben comprobarse en cada organismo.

Lithosphere = crust + uppermost mantle; it is not the same as the crust.

S-wave shadow beyond 103° and P-wave shadow between 103° and 142° prove a liquid outer core.

Slab pull is the dominant plate-driving force; ridge push is secondary.

Calc-alkaline andesite–granodiorite suites mark subduction; tholeiitic MORB marks ridges.

Weathering breaks rock in place; erosion removes and transports it.

The Hjulström curve explains why cohesive clay resists erosion but stays suspended.

Cross-cutting relationships and inclusions date events relative to one another.

Angular unconformity = folding and erosion before renewed deposition; nonconformity = sediments over basement.

Mineral definition requires natural, inorganic, solid, crystalline and a definite composition.

Silicate classes follow tetrahedron arrangement: neso, soro, cyclo, ino, phyllo, tecto.

A prescribed 6.5°C/km environmental gradient differs from a dry adiabatic parcel rate; most ordinary weather occurs in the troposphere.

Earth's average albedo is about 30 %; greenhouse gases re-emit long-wave radiation.

Biodiversity has genetic, species and ecosystem levels; richness plus evenness describe diversity.

Soil horizons O-A-B-C-R; formation depends on climate, organisms, relief, parent material and time.

Risk depends jointly on hazard, exposure and vulnerability; define quantities before calculating a product.

Lorca 2011 and the Betic cordillera illustrate Spanish seismic risk; La Palma 2021 illustrates volcanic risk.

Convert scale before computing: 1:50,000 means 1 cm = 500 m.

Gradient (%) = vertical difference / horizontal distance × 100.

Main sequence stars fuse hydrogen into helium

H–R diagram plots luminosity against temperature; OBAFGKM from hot to cool

Distinguish hypotheses, models, empirical support and proof claims.

Peer review is scrutiny, not a guarantee of truth.

Separate evidence about effects from values used to choose among options.

Risk requires exposure and consequences, not a hazard label alone.

State uncertainty, affected groups, alternatives and a way to monitor outcomes.

Criteria define success; constraints restrict possible solutions.

Choose models and prototypes for a stated question and disclose their limits.

Test alternatives using comparable conditions and consistent boundaries.

A design can involve trade-offs rather than one universally best solution.

Iteration uses measured evidence to revise and retest a feature.