Curaçao Eindexamen HAVO - independent subject foundations cheat sheet

State domain restrictions before simplifying; cancelled factors still exclude values.

Composition f(g(x)) is evaluated inside-out and is generally not commutative.

Inverses require one-to-one functions; domain and range swap.

Horizontal transformations act opposite to the sign or factor shown.

Log laws convert sums to products, enabling solution of log equations.

Always check candidate solutions against original domain restrictions.

Chain rule: never drop the inner derivative g'(x).

Integration by parts: choose u so du is simpler than u.

Change limits immediately when substituting in a definite integral.

Improper integrals require an explicit limit, not direct substitution.

Implicit differentiation collects dy/dx terms after differentiating both sides.

Similarity scales lengths by k, areas by k², volumes by k³.

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

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.

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.

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

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

Opportunity cost is the next-best alternative forgone and can have a monetary valuation.

A shortage at a price is different from scarcity of resources across competing uses.

An own-price movement differs from a demand or supply shift.

State the point, initial-base or midpoint elasticity convention.

Revenue and profit can move in different directions.

Distinguish a budget flow, a debt stock and the financing transactions.

A bank loan can create a corresponding deposit; a 1/r multiplier is a deliberately simplified model.

Policy rates influence, but do not equal, every retail borrowing rate.

Real and nominal measures need the relevant price index and base normalization.

Spending and tax multipliers require their model and sign conventions.

Separate business activity and owner transactions while recording capital and drawings appropriately.

Apply the supplied earning and expense-allocation model rather than cash timing alone.

Prudence requires caution without deliberate bias.

Identify the applicable framework and version before applying detailed recognition rules.

Distinguish changes in estimates, policies and genuine errors.

Debit assets and expenses; credit liabilities, income and capital

Trade discount is deducted before recording; cash discount is recorded on payment

Credit notes issued go to sales returns; credit notes received go to purchases returns

A trial balance proves arithmetical equality, not accuracy

Errors of principle, commission, omission and reversal do not affect trial balance agreement

One-sided postings and addition errors do affect the difference

Corrections are made by journal, not by changing source documents

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.

Frame answers as process chains with controlling variables, not lists of landforms.

North German Plain: young glacial relief; moraine, Sander, Urstromtal, Geschiebemergel; determines both drainage and soil type.

Use P = ET + R + ΔS; distinguish potential from actual evapotranspiration.

Soil patterns reflect climate, organisms, relief, parent material, time and human influence; substrate alone does not uniquely determine a soil class.

Risk depends on hazard, exposure and vulnerability; adaptation options require site-specific evaluation.

Never mix timescales: glacial sculpture versus storm-surge frequency are separate arguments.

Distinguish natural population change from net migration in every analysis.

The demographic transition model is descriptive; adapt for stalled fertility and migration-driven growth.

Dependency ratios indicate structure, not actual labour participation.

Migration models identify selectivity and intervening obstacles; their historical patterns are not universal laws.

Von Thünen: land rent and intensity vary with distance, given uniform plain, one market, transport costs proportional to distance and weight.

Weber's least-cost triangle: transport, labour and agglomeration orientation.

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.