DNB 2025 – Centres Étrangers

Groupe I · 16 juin 2025 · Correction interactive

100 points 5 exercices Durée : 2h00
💡 Toutes les réponses doivent être justifiées, sauf indication contraire. Pour chaque question, si le travail n'est pas terminé, laisse tout de même une trace de la recherche. Clique sur « Voir la correction » pour chaque exercice, et utilise les indices si tu bloques.
⏳ 2:00:00
Lance le chrono pour simuler les conditions d'examen
Progression
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Correction complète !

★★★★★

Tu as consulté toutes les corrections. Revois les points délicats et refais le sujet sans aide !

Ex.1 – 20 pts Ex.2 – 19 pts Ex.3 – 21 pts Ex.4 – 21 pts Ex.5 – 19 pts
✓ Vu
Questionnaire à choix multiple 5 questions · 4 points chacune · aucune justification demandée
Q1
La décomposition en produit de facteurs premiers de 120 est :
A : 2×3×4×5    B : 15×2×2×2    C : 2³×3×5    D : 53+67
Q2
Dans la cellule A2, la formule « = −4 * A1 − 12 » a été saisie. On l'étire jusqu'à la cellule B2. Sachant que B1 = 5, la valeur obtenue dans B2 est :
A : −32    B : −20    C : 8    D : 68
Q3
Sur la figure, le carré B a des côtés deux fois plus grands que le carré A. Le rapport de l'homothétie de centre O qui transforme le carré A en le carré B est :
A : −2    B : −0,5    C : 0,5    D : 2
Figure – carrés A et B avec centre O
Q4
Une écriture factorisée de 4x²−1 est :
A : (2x−1)(2x+1)    B : (4x−1)(4x+1)    C : 4(x−1)(x+1)    D : (2x−1)²
Q5
Dans le triangle TER rectangle en R, TE = 7,4 cm et l'angle en E vaut 39°. La mesure de RE arrondie au centième est :
Triangle TER rectangle en R
A : 4,66 cm    B : 5,75 cm    C : 9,52 cm    D : 11,76 cm

💡 Indices

Commence par le plus petit facteur premier possible. Divise successivement jusqu'à tomber sur 1.
Quand on étire une formule d'une colonne vers la suivante, quelle lettre de colonne change dans la formule ?
Le rapport d'une homothétie se calcule en comparant une longueur du carré image à la longueur correspondante du carré original.
4x² − 1 est une différence de deux carrés. Quelle identité remarquable te permet de factoriser une expression de la forme a² − b² ?
Identifie d'abord les trois côtés du triangle : lequel est l'hypoténuse ? Lequel est adjacent à l'angle en E ? Quelle fonction trigonométrique relie ces deux côtés ?

Q1 – Décomposition de 120 → Réponse C

120 2
60 2
30 2
15 3
5 5
1
\(120 = 2^3 \times 3 \times 5\) ✓
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" alt="" style="max-width:260px;width:100%;border-radius:10px;box-shadow:0 2px 12px var(--shadow);">
Exemple de décomposition en facteurs premiers (méthode du tableau)
\(120 = 2^3 \times 3 \times 5\) ✓
A : 2×3×4×5 — 4 n'est pas premier
B : 15×2×2×2 — 15 n'est pas premier
C : 2³×3×5 ✓
D : 53+67 — c'est une somme

Q2 – Formule tableur → Réponse A

La formule étirée vers B2 devient =−4*B1−12. Or B1 = 5, donc :

\(-4 \times 5 - 12 = -20 - 12 = -32\)
\(\text{B2} = -32\) ✓

Q3 – Rapport de l'homothétie → Réponse D

Le carré B a des dimensions doubles de celles du carré A. Le rapport est donc 2 (positif car même sens, O est à l'extérieur).

Rapport = 2 ✓

Q4 – Factorisation de 4x²−1 → Réponse A

On utilise l'identité \(a^2 - b^2 = (a+b)(a-b)\) avec \(a = 2x\) et \(b = 1\) :

\(4x^2 - 1 = (2x)^2 - 1^2 = (2x+1)(2x-1)\)
\((2x+1)(2x-1)\) ✓

Q5 – Triangle TER rectangle en R → Réponse B

On a : Le triangle TER est rectangle en R. \(\text{TE} = 7{,}4\) cm est l'hypoténuse  ;  angle en E \(= 39°\) RE est le côté adjacent à l'angle en E Or : d'après la définition du cosinus (C·A·H) :
\(\cos\!\left(\widehat{TER}\right) = \dfrac{RE}{TE}\)
\(\dfrac{\cos(39°)}{1} = \dfrac{RE}{7{,}4}\)
\(RE = \cos(39°) \times 7{,}4 \div 1\)
\(RE \approx 0{,}777 \times 7{,}4 \div 1 \approx 5{,}75\)
Donc : RE mesure environ 5,75 cm. ✓
✓ Vu
Statistiques & masse volumique Probabilité · Volume · Calcul numérique
L'entreprise Transport Rapide doit livrer cinq colis A, B, C, D et E ayant les masses suivantes :
ColisABCDE
Masse (kg)492711
Les colis ont la forme d'un pavé droit de longueur L, largeur l et hauteur h :
Pavé droit de longueur L, largeur l et hauteur h
ColisL (m)l (m)h (m)
A0,40,30,5
B0,50,40,8
C0,30,10,5
D0,40,30,7
E0,50,40,6
Q1
Calculer la moyenne des masses des colis en kg.
Q2
Déterminer la médiane des masses des colis en kg. Interpréter ce résultat.
Q3
Le transporteur choisit au hasard un colis parmi les cinq. Calculer la probabilité qu'il sélectionne un colis de masse inférieure à 8 kg.
Q4a
Vérifier que le volume du colis E est de 0,12 m³.
Q4b
Montrer que la masse volumique du colis E arrondie au dixième est 91,7 kg/m³.
Rappel :   masse volumique (kg/m³)  =  masse  (kg)volume (m³)
Q4c
Le transporteur affirme : « Le colis E est plus lourd que le colis C, donc sa masse volumique est plus grande. » A-t-il raison ?

💡 Indices

Rappelle-toi la formule de la moyenne : comment combiner toutes les masses pour obtenir une seule valeur représentative ?
Pour trouver la médiane, commence par ranger les 5 masses dans l'ordre. Quelle position occupe la valeur centrale sur 5 valeurs ?
Repère, dans le tableau, quels colis vérifient la condition. La probabilité se calcule en faisant le rapport entre les cas favorables et le total.
Calcule le volume du colis C à partir de ses dimensions, puis sa masse volumique. Compare-la ensuite avec celle du colis E.

Q1 – Moyenne des masses

\(\text{Moyenne} = \dfrac{4 + 9 + 2 + 7 + 11}{5} = \dfrac{33}{5} = 6{,}6 \text{ kg}\)
Moyenne = 6,6 kg ✓

Q2 – Médiane

Ordre croissant : 2 ; 4 ; 7 ; 9 ; 11

Médiane = 7 kg ✓

Interprétation : la moitié des colis pèsent au plus 7 kg, l'autre moitié pèsent au moins 7 kg.

Q3 – Probabilité (masse < 8 kg)

Colis de masse < 8 kg : A (4 kg), C (2 kg), D (7 kg) → 3 colis favorables sur 5.

\(p = \dfrac{3}{5} = 0{,}6\)
\(p = \dfrac{3}{5} = 0{,}6\) ✓

Q4a – Volume du colis E

\(V_E = L \times l \times h = 0{,}5 \times 0{,}4 \times 0{,}6 = 0{,}12 \text{ m}^3 \checkmark\)

Q4b – Masse volumique du colis E

\(\rho_E = \dfrac{\text{masse}}{\text{volume}} = \dfrac{11}{0{,}12} = \dfrac{1100}{12} \approx 91{,}7 \text{ kg/m}^3 \checkmark\)

Q4c – Le transporteur a-t-il raison ?

\(V_C = 0{,}3 \times 0{,}1 \times 0{,}5 = 0{,}015 \text{ m}^3\)
\(\rho_C = \dfrac{2}{0{,}015} \approx 133{,}3 \text{ kg/m}^3\)

Or \(\rho_C \approx 133{,}3 > \rho_E \approx 91{,}7\).

Le transporteur a tort : le colis C est plus dense que le colis E, malgré une masse plus faible. ✓
✓ Vu
Algèbre & représentation graphique Équation · Fonction affine · Graphique
On considère le programme de calcul suivant :
Choisir un nombre
↓
Multiplier par −2
↓
Ajouter 4
↓
Multiplier par 4
Q1
Montrer que si l'on choisit 1 comme nombre de départ, le résultat obtenu est 8.
Q2
Quel est le résultat si le nombre de départ est −2 ?
Q3
Si l'on note x le nombre de départ, montrer que le résultat peut s'écrire −8x + 16.
Q4a
Résoudre l'équation −8x + 16 = 4.
Q4b
En déduire le nombre de départ qu'il faut choisir pour obtenir 4 comme résultat.
Q5
Parmi les trois représentations graphiques ci-dessous, laquelle représente la fonction f définie par f(x) = −8x + 16 ? Expliquer la démarche.
Les trois représentations graphiques

💡 Indices

Suit le programme pas à pas, en notant le résultat après chaque opération.
Remplace le nombre de départ par x, puis applique chaque opération du programme l'une après l'autre. Développe l'expression finale.
Pour isoler x, pense à effectuer les mêmes opérations des deux côtés de l'égalité, dans le bon ordre.
Calcule f(0) pour trouver où la droite coupe l'axe des ordonnées. Pense aussi au signe du coefficient directeur : la droite est-elle croissante ou décroissante ?

Q1 – Nombre de départ : 1

\(1 \xrightarrow{\times(-2)} -2 \xrightarrow{+4} 2 \xrightarrow{\times 4} 8\)
Résultat \(= 8\) ✓

Q2 – Nombre de départ : −2

\(-2 \xrightarrow{\times(-2)} 4 \xrightarrow{+4} 8 \xrightarrow{\times 4} 32\)
Résultat \(= 32\) ✓

Q3 – Expression algébrique

\(x \xrightarrow{\times(-2)} -2x \xrightarrow{+4} -2x+4 \xrightarrow{\times 4} 4(-2x+4) = -8x+16\)
Le résultat s\'écrit bien \(-8x + 16\) ✓

Q4a – Résoudre −8x + 16 = 4

\(-8x\) \(+16\) \(\;=\; 4\)
\(-16\)
\(-16\)
\(-8\)\(x \;=\; 4 - 16 \;=\; -12\)
\(\div(-8)\)
\(\div(-8)\)
\(x \;=\; \dfrac{-12}{-8} \;=\; \dfrac{3}{2} \;=\; 1{,}5\)
La solution de l'équation est \(x = 1{,}5\). ✓

Q4b – Nombre de départ

Il faut choisir \(1{,}5\) comme nombre de départ pour obtenir \(4\). ✓

Q5 – Identification du graphique

• Ordonnée à l'origine : \(f(0) = 16\). Le graphique 2 ne passe pas par \((0\,;\,16)\) → éliminé.

• Coefficient directeur \(= -8\) : la droite est très raide et décroissante. Sur la représentation 3, les valeurs de \(x\) vont de \(-0{,}5\) à \(2\) environ et la droite descend de \(16\) vers \(0\), ce qui est cohérent avec une pente de \(-8\).

C'est la Représentation graphique 3 ✓
✓ Vu
Pythagore · Thalès · Proportionnalité Partie A – Géométrie · Partie B – Budget graines
Un agriculteur cultive un champ représenté par le triangle ABC (figure non à l'échelle) :
• Le triangle ABC est rectangle en B.
• Les points C, E et A sont alignés ; les points C, D et B sont alignés.
• AB = 600 m  ;  BC = 450 m  ;  CD = 270 m.
Figure du terrain (non à l'échelle) – triangle ABC avec points D et E

📌 Partie A – Étude géométrique du terrain

Q1
Montrer que le segment [AC] mesure 750 mètres.
Q2a
Montrer que les droites (ED) et (AB) sont parallèles.
Q2b
Montrer que le segment [DE] mesure 360 mètres.
Q3
Montrer que l'aire du triangle CDE est 48 600 m².

🌿 Partie B – Étude du prix du mélange de graines

L'agriculteur veut semer un mélange sur les 48 600 m² du triangle CDE. Indication 1 – Prix au kg : blé 1,40 €, seigle 1,30 €, pois 2,10 €. Indication 2 – Pour 10 000 m² : blé 80 kg, seigle 60 kg, pois 50 kg.
Q1
Un vendeur propose un mélange selon le ratio 16 : 12 : 8. Montrer que ce ratio ne respecte pas l'indication 2.
Q2
Justifier que l'agriculteur doit prévoir 388,80 kg de blé pour les 48 600 m².
Q3
L'agriculteur dispose d'un budget de 1 500 €. Il doit acheter 388,80 kg de blé, 291,6 kg de seigle et 243 kg de pois. Dispose-t-il d'un budget suffisant ?

💡 Indices

Dans un triangle rectangle, quel est le côté opposé à l'angle droit ? Quelle relation relie les carrés des trois côtés ?
Regarde les angles droits en B et en D. Que sait-on sur (AB) et (ED) par rapport à (BC) ? Quelle propriété sur les droites perpendiculaires à une même droite peux-tu utiliser ?
Vérifie que les conditions du théorème de Thalès sont bien réunies (droites parallèles, points alignés). Écris ensuite l'égalité des rapports, puis résous avec un produit en croix.
Quel est le type du triangle CDE ? Quelle formule permet de calculer l'aire d'un triangle connaissant sa base et sa hauteur ?
Pour vérifier un ratio, divise chaque quantité par le nombre correspondant dans le ratio proposé. Les quotients doivent tous être égaux. Pour les quantités, utilise la proportionnalité entre surface et masse.

A – Q1 : AC = 750 m (Théorème de Pythagore)

On a : Le triangle ABC est rectangle en B. AB = 600 m  ;  BC = 450 m  ;  Hypoténuse : AC Or : d'après le théorème de Pythagore :
\(AC^2 = AB^2 + BC^2\)
\(AC^2 = 600^2 + 450^2 = 360\,000 + 202\,500 = 562\,500\)
\(AC = \sqrt{562\,500} = 750\)
Donc : AC mesure bien 750 m ✓

A – Q2a : (ED) est parallèle à (AB)

On a : L'angle en B est droit, donc (AB) est perpendiculaire à (BC). L'angle en D est droit, donc (ED) est perpendiculaire à (BC). Or : Deux droites perpendiculaires à une même droite sont parallèles entre elles. Donc : (ED) est parallèle à (AB). ✓

A – Q2b : DE = 360 m (Théorème de Thalès)

On a : Les points C, E, A sont alignés. Les points C, D, B sont alignés. (ED) est parallèle à (AB). Or : d'après le théorème de Thalès dans le triangle CAB :
Rapport 1
CB
CD
=
Rapport 2
CA
CE
=
Rapport 3
AB
ED

On utilise les rapports 1 et 3 :

450
270
=
600
ED

Produit en croix :

\(ED = 600 \times 270 \div 450 = 360 \text{ m}\)
Donc : DE mesure 360 m. ✓

A – Q3 : Aire du triangle CDE

Le triangle CDE est rectangle en D (ED est perpendiculaire à DC). DE = 360 m et DC = 270 m.

\(\mathcal{A} = \dfrac{DE \times DC}{2} = \dfrac{360 \times 270}{2} = \dfrac{97\,200}{2} = 48\,600 \text{ m}^2 \checkmark\)

B – Q1 : Le ratio 16 : 12 : 8 respecte-t-il l'indication 2 ?

\(\text{Blé}: 80 \div 16 = 5 \quad \text{Seigle}: 60 \div 12 = 5 \quad \text{Pois}: 50 \div 8 = 6{,}25\)
Les quotients sont différents \((5 \neq 6{,}25)\) : le ratio 16:12:8 ne respecte pas l'indication 2. ✓

B – Q2 : Justification des 388,80 kg de blé

Surface (m²)10 00048 600
Blé (kg)80?
\(? = 80 \times 48\,600 \div 10\,000 = 388{,}8 \text{ kg}\) ✓

B – Q3 : Budget suffisant ?

GraineQuantité (kg)Prix (€/kg)Coût (€)
Blé388,81,40\(388{,}8 \times 1{,}40 = 544{,}32\)
Seigle291,61,30\(291{,}6 \times 1{,}30 = 379{,}08\)
Pois2432,10\(243 \times 2{,}10 = 510{,}30\)
\(\text{Total} = 544{,}32 + 379{,}08 + 510{,}30 = 1\,433{,}70 \text{ €}\)
\(1\,433{,}70 \text{ €} < 1\,500 \text{ €}\) : le budget est suffisant. ✓
✓ Vu
Probabilités & Algorithmique Dénombrement · Probabilités · Scratch
Léna a oublié le code de la maison de sa grand-mère. Elle sait qu'il est composé d'une lettre parmi A, B ou C, suivie d'un chiffre entre 0 et 9.
Q1
Proposer deux codes différents que Léna peut tester.
Q2
Quelle est la probabilité que la grand-mère ait choisi la lettre C dans son code ?
Q3
Montrer que la probabilité que le code contienne le chiffre 7 est 1/10.
Q4
La grand-mère aime les nombres premiers. Quelle est la probabilité que le code comporte un nombre premier ?
Q5a
Léna teste tous les codes possibles à raison de 5 secondes par code. Réussira-t-elle en moins de 3 minutes ?
Q5b
Ce format de code garantit-il la sécurité ? Comment pourrait-on améliorer le système ?
Q6
Le programme Scratch affiche « Code correct » si la lettre saisie est B ET le chiffre saisi est 7, sinon « Code faux ».
Programme Scratch du digicode
a) Léna saisit B5. Qu'affiche le programme ?
b) Quel est le code correct d'après ce programme ?

💡 Indices

Pour compter le nombre de codes possibles, réfléchis au nombre de choix pour chaque position du code.
Combien de codes contiennent le chiffre 7 ? Pense à combien de lettres différentes peuvent l'accompagner.
Rappelle-toi la définition d'un nombre premier. Quels chiffres entre 0 et 9 sont premiers ? Pour chacun, combien de codes différents peut-on former ?
Lis attentivement la condition du programme. Avec un opérateur ET, que faut-il pour que le résultat soit « Code correct » ?

Q1 – Deux codes possibles

Exemples : B3 ou C9 ✓

Q2 – Nombre total de codes et P(lettre C)

3 lettres possibles × 10 chiffres possibles :

Nombre total de codes = 3 × 10 = 30

10 codes commencent par C (C0, C1, …, C9) :

\(P(\text{lettre C}) = \dfrac{10}{30} = \dfrac{1}{3}\)

Q3 – P(chiffre 7) = 1/10

3 codes se terminent par 7 : A7, B7, C7.

\(P(\text{chiffre 7}) = \dfrac{3}{30} = \dfrac{1}{10} = 0{,}1 \checkmark\)

Q4 – P(nombre premier)

Nombres premiers entre 0 et 9 : 2, 3, 5 et 7 → 4 chiffres.

Pour chacun, 3 codes (A, B ou C) → 4 × 3 = 12 codes favorables.

\(P(\text{nb premier}) = \dfrac{12}{30} = \dfrac{2}{5} = 0{,}4\)

Q5a – Durée maximale

30 codes × 5 s = 150 s = 2 min 30 s
2 min 30 s < 3 min → Léna réussira en moins de 3 minutes. ✓

Q5b – Sécurité et amélioration

Ce code n'est pas sécurisé : il peut être cracké en 2 min 30 s maximum.

Amélioration : utiliser les 26 lettres de l'alphabet → 26×10 = 260 codes → durée max ≈ 21 min 40 s (plus de 8 fois plus long). On peut aussi ajouter davantage de chiffres.

Q6a – Léna saisit B5

Condition : lettre = B ET chiffre = 7. Ici 5 ≠ 7 → condition fausse.

Le programme affiche : « Code faux » ✓

Q6b – Code correct

Le programme affiche « Code correct » uniquement si lettre = B ET chiffre = 7.

Le code correct est : B7 ✓
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