Bac Général Djibouti - independent subject foundations cheat sheet
Bac Général Djibouti - independent subject foundations · Keep the key ideas within reach.
Upper-secondary functions, calculus, geometry and probability
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.
Mechanics, fields, thermal behavior, waves and modern models
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
Chemical structure, reactions and organic models
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.
Biological organization, inheritance, regulation and ecosystems
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.
Physical Science: The Earth: Atmosphere, Hydrosphere, Structure Features, Geologic Processes, and History
S-waves cannot pass liquids, revealing a liquid outer core
Divergent, convergent, and transform boundaries produce distinct features
Cross-cutting relationships and superposition establish relative ages
Igneous (intrusive vs extrusive), sedimentary, and metamorphic rocks cycle
Atmosphere: 78% N2, 21% O2; weather occurs in the troposphere
End-Cretaceous extinction linked to asteroid impact and iridium layer
French reading, grammar and structured written expression
Identifier genre, paratexte et situation d’énonciation avant de répondre.
Citer précisément puis expliquer l’effet du procédé, sans paraphrase.
Distinguer auteur, narrateur et personnage.
Respecter la langue et les deux temps de la consigne.
Ne pas importer des connaissances extérieures au texte.
Learn subjunctive triggers by pairs: bien que/parce que, avant que/après que.
il est probable que + indicative, il est possible que + subjunctive.
In hypothetical si clauses, use the relevant indicative pattern; si in an indirect question is a different construction.
Pronominal agreement depends on whether the reflexive pronoun is direct or indirect.
In se rendre compte, the past participle rendu remains invariable; the entire expression is not grammatically invariant.
Problématiser le sujet avant de choisir le plan.
Un paragraphe = une idée, un exemple, une explication.
Meaning, paragraph organization and warranted inference
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.
Philosophical reasoning and normative ethical frameworks
Separate premises, conclusion, validity and soundness.
Reconstruct the actual claim without strengthening it.
Compare reason, experience and justification carefully.
Distinguish what exists from how it can be known.
Support philosophical commentary with concepts, evidence and argument.
Distinguish descriptive, normative, metaethical and applied questions.
Kantian reasoning examines maxims, duty and respect for persons.
Utilitarian arguments require an account of welfare and consequences.
Virtue ethics emphasizes cultivated character and practical wisdom.
Compare justifications, not only whether conclusions happen to agree.
Physical and human geography with spatial 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.
Markets, macroeconomic models and development evidence
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.
Recording, costing, organization and business decisions
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
Scientific questions, evidence and quantitative reasoning
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.