Quiz : Les incontournables du programme de mathématiques pour le bac

Question 1 sur 10 10:00

[{"id":16778,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A) 2x + 3","option_b":"B) x + 3","option_c":"C) 2x² + 3x","option_d":"D) 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16779,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une limite fondamentale en analyse : lim(x→0) sin(x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16780,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₃ ?","option_a":"A) 18","option_b":"B) 54","option_c":"C) 162","option_d":"D) 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"uₙ = u₀ × qⁿ, donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16781,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-4)² - 4×1×4 = 0, donc une seule solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16782,"question":"Quelle est l'intégrale de f(x) = 2x entre 0 et 3 ?","option_a":"A) 3","option_b":"B) 6","option_c":"C) 9","option_d":"D) 12","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 2x est x². Évaluée entre 0 et 3 : 3² - 0² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16783,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16784,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"A) 0.6826","option_b":"B) 0.8413","option_c":"C) 0.9772","option_d":"D) 0.5","option_e":"","option_f":"","bonne_reponse":"B","explication":"D'après les tables de la loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16785,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16786,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"A) x \u003E 8","option_b":"B) x \u003C 8","option_c":"C) x \u003E 6","option_d":"D) x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 \u003E 2x + 1 ⇒ x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16787,"question":"La fonction f(x) = x³ est impaire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ = -x³ = -f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]