MSI Concours d'Admission flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax²+bx+c=0 with a≠0, the solutions are x=(−b±√(b²−4ac))/(2a). The discriminant Δ=b²−4ac indicates two real roots if positive, one if zero, complex conjugates if negative.

Derivative of composite function

Chain rule: if h(x)=f(g(x)), then h′(x)=f′(g(x))·g′(x). For example, derivative of sin(3x) is 3cos(3x). Essential for differentiating nested functions.

Integration by parts

∫u dv = uv − ∫v du. Choose u to simplify when differentiated and dv easy to integrate. Useful for products such as x·eˣ or ln x.

Bayes' theorem

P(A|B) = P(B|A)·P(A)/P(B). Updates prior probability P(A) with evidence B. Denominator can be expanded as P(B|A)P(A)+P(B|¬A)P(¬A).

Binomial coefficient

C(n,k)=n!/(k!(n−k)!) counts subsets of size k from n distinct items. Appears in binomial expansion (a+b)ⁿ=Σ C(n,k)aⁿ⁻ᵏbᵏ.

Newton's second law

The net force on an object equals mass times acceleration: ΣF=ma. Weight is W=mg with g≈9.81 m/s². Used to solve dynamics problems with forces and motion.

Ohm's law and power

Voltage U=RI for a resistor; electrical power P=UI=I²R=U²/R. In series resistances add; in parallel reciprocals add. Basis for circuit analysis.

Ideal gas law

PV=nRT relates pressure, volume, amount in moles, and absolute temperature; R≈8.314 J/(mol·K). At STP one mole occupies about 22.4 L.

pH definition

pH=−log[H₃O⁺]. At 25°C, pH+pOH=14. Strong acids fully dissociate; buffers resist pH change and follow Henderson–Hasselbalch pH=pKa+log([A⁻]/[HA]).

Snell's law

n₁sinθ₁=n₂sinθ₂ describes refraction at an interface, where n=c/v is refractive index. Total internal reflection occurs when light travels from denser to less dense medium beyond critical angle.

DNA base pairing

In DNA, adenine pairs with thymine via two hydrogen bonds, and guanine pairs with cytosine via three. In RNA, uracil replaces thymine. Strands are antiparallel in a double helix.

Central dogma

Genetic information flows DNA→RNA (transcription)→protein (translation). The code is triplet, non-overlapping, degenerate; AUG is start codon; UAA, UAG, UGA are stop codons.

Mitosis versus meiosis

Mitosis produces two identical diploid cells for growth and repair. Meiosis produces four haploid gametes with genetic recombination via crossing-over in prophase I.

Mendel's law of segregation

Each organism carries two alleles per gene; during gamete formation they separate so each gamete receives one. Explains 3:1 phenotypic ratio in monohybrid F2 crosses.

Photosynthesis equation

6CO₂+6H₂O+light energy → C₆H₁₂O₆+6O₂. Light reactions in thylakoids produce ATP and NADPH; Calvin cycle in stroma fixes CO₂ using rubisco.

Accord du participe passé

Avec être, le participe passé s'accorde avec le sujet (elle est partie). Avec avoir, il ne s'accorde pas avec le sujet mais avec le COD placé avant le verbe (les lettres qu'il a écrites).

Subjonctif présent

Mode exprimant volonté, doute, émotion ou nécessité. Employé après des verbes comme vouloir que, douter que, et des conjonctions comme bien que, pour que, avant que.

Métaphore et comparaison

La comparaison rapproche deux éléments avec un outil (comme, tel que). La métaphore est une comparaison implicite sans outil. L'oxymore allie deux termes contradictoires.

Mouvements littéraires français

Humanisme (XVIᵉ), classicisme (XVIIᵉ), Lumières (XVIIIᵉ), romantisme, réalisme et naturalisme (XIXᵉ), surréalisme (XXᵉ). Chacun définit des thèmes et esthétiques propres.

Present perfect

Formed with have/has + past participle. Links a past action to present relevance, used with for, since, already, yet, ever. Contrasts with past simple for finished actions at a definite time.

Third conditional

If + past perfect, would have + past participle: 'If I had studied, I would have passed.' Expresses unreal past situations and their imagined consequences.

Passive voice

Formed with be + past participle. Used when the agent is unknown, unimportant, or to focus on the action. Only transitive verbs can be made passive.

Reported speech backshift

When reporting, shift tense one step back: present→past, past→past perfect, will→would. Pronouns and time/place expressions also change (today→that day, here→there).

French Revolution key dates

1789 Bastille and Declaration of the Rights of Man; 1792 First Republic; 1793–94 Reign of Terror; 1799 Napoleon's coup. Marks the end of absolute monarchy in France.

Cold War

Geopolitical tension 1947–1991 between US-led NATO and Soviet-led Warsaw Pact. Key events: Berlin Blockade, Cuban Missile Crisis 1962, Berlin Wall 1961–1989, USSR dissolution 1991.

French Fifth Republic

Established in 1958 under Charles de Gaulle. Its constitution strengthened the presidency. Institutions include President, Prime Minister, Assemblée nationale, and Sénat.

Map projections

Ways to represent Earth's curved surface on a plane. Mercator preserves angles but distorts area near poles; Peters preserves area; all projections distort some property.

Descartes' cogito

'Cogito ergo sum'-I think, therefore I am. Descartes uses methodical doubt to find an indubitable foundation for knowledge, leading to mind-body dualism.

Kant's categorical imperative

Act only according to maxims you could will as universal law, and treat humanity always as an end, never merely as a means. Central to deontological ethics.

Social contract theories

Hobbes: absolute sovereignty to escape state of nature. Locke: natural rights and limited government. Rousseau: general will and popular sovereignty. Montesquieu: separation of powers.

Deductive validity

An argument is valid if conclusion necessarily follows from premises. Soundness requires validity plus true premises. Validity concerns form, not factual truth of premises.

Contrapositive

For 'If P then Q', the contrapositive 'If not Q then not P' is logically equivalent. Converse 'If Q then P' and inverse 'If not P then not Q' are not equivalent.