Panhellenic EPAL - 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.

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.

For a sinusoid V_rms = V_peak/√2; the stated impedance magnitude is for a series RLC model.

Q_C = P(tan φ₁ − tan φ₂) for power-factor correction

Transformer: V₁/V₂ = N₁/N₂ = I₂/I₁

Induction motor: n = (1 − s)·60f/p

Thévenin voltage is open-circuit voltage; deactivate independent sources to obtain resistance while preserving dependent-source behavior.

Karnaugh: give the minimum sum of products

State the system boundary and assumptions before calculation.

Units, sign conventions and uncertainty are part of the answer.

Verification against a specification differs from validation for an intended use.

Drawings need a declared convention and controlled revision.

Classroom models do not authorize physical operation or structural approval.

Recursion needs a base case and progress toward that base case.

Overloading uses different signatures; overriding replaces an inherited method.

Unit tests isolate units; integration tests combine them.

Short-circuit evaluation can skip the right operand.

Pass-by-value copies arguments; pass-by-reference can mutate the caller's object.

Decomposition breaks problems down; abstraction removes irrelevant detail.

Binary search requires sorted data and is O(log n).

Merge sort is O(n log n) worst case; bubble sort is O(n^2).

Trace tables prevent guessing about loop output.

Update search bounds to mid + 1 or mid - 1, not mid.

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.

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

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.