Public Institution Category C (Natural Sciences) - independent foundations cheat sheet

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

EMF is per unit charge from the source; terminal p.d. is E − Ir

Kirchhoff's laws follow from conservation of charge and energy

Capacitor energy is ½CV²; discharge is exponential with time constant RC

Magnetic-force magnitude is |q|vB sinθ and its vector is perpendicular to velocity, so magnetic force does no work

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.

Condensation forms glycosidic, ester and peptide bonds; hydrolysis reverses them.

Reducing-sugar test interpretation requires suitable assay conditions and controls; hydrolysis can change sucrose test results.

Cellulose = β-1,4 glucose, straight H-bonded microfibrils; starch and glycogen = α-glucose.

Triglyceride = glycerol + 3 fatty acids; phospholipid = phosphate head + 2 tails, amphipathic.

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.

ΔH = Σ bonds broken − Σ bonds formed, and mean bond enthalpies are averages.

Feasibility is determined by ΔG = ΔH − TΔS, not by ΔH alone.

Orders are determined experimentally, not from stoichiometric coefficients.

Rate constant units depend on overall order: for second order overall, dm3 mol−1 s−1; for third order overall, dm6 mol−2 s−1.

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

A conditional and its contrapositive are equivalent; its converse generally is not.

Use a counterexample to test whether a conclusion is necessary.

Distinguish at least one, at most one and exactly one.

Identify the missing evidential link when testing assumptions.

An analogy must preserve a relationship, not just share words.

Identify units, time periods and denominators before calculating.

Percentage change and percentage-point difference are different operations.

Combine rates only under the supplied process assumptions.

Choose ordered or unordered counting according to the actual selection task.

Check both arithmetic and the meaning of the measured quantity.

Identify whether the task asks for gist, detail, order, inference or an exception.

Respect qualifiers and the limits of the passage.

Check antecedents and logical dependence when ordering sentences.

Evaluate meaning, grammar and register together.

Do not treat a passage claim as independently verified real-world evidence.