Quiz Maths Bac : Testez vos connaissances en 10 questions !

Question 1 sur 10 10:00

[{"id":55601,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55602,"question":"La fonction f(x) = x³ - 3x² + 2 admet-elle un extremum local en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En calculant f'(x) = 3x² - 6x, on trouve f'(1) = -3 ≠ 0, donc pas d'extremum local en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55603,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 0.5","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule des racines, Δ = 25 - 16 = 9, donc x = (5 ± 3)\/4 → x = 2 ou x = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55604,"question":"La probabilité d'un événement A est P(A) = 0.3. Quelle est la probabilité de l'événement contraire ?","option_a":"0.3","option_b":"0.7","option_c":"0.5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 0.7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55605,"question":"Une suite géométrique a pour premier terme u₀ = 2 et raison q = 3. Quel est le terme u₃ ?","option_a":"54","option_b":"18","option_c":"6","option_d":"162","option_e":"","option_f":"","bonne_reponse":"A","explication":"uₙ = u₀ × qⁿ → u₃ = 2 × 3³ = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55606,"question":"La fonction f(x) = ln(x) est-elle définie pour x = -1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction logarithme est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55607,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient lim (2 + 3\/x) \/ (1 - 1\/x²) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55608,"question":"Un dé équilibré est lancé. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles → P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55609,"question":"La dérivée seconde d'une fonction permet-elle de déterminer la concavité de sa courbe ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si f''(x) \u003E 0, la courbe est convexe (concave vers le haut). Si f''(x) \u003C 0, elle est concave (vers le bas).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55610,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme u₀ = 3 et de raison r = 2 ?","option_a":"25","option_b":"35","option_c":"40","option_d":"50","option_e":"","option_f":"","bonne_reponse":"B","explication":"Sₙ = n\/2 × (2u₀ + (n-1)r) → S₅ = 5\/2 × (6 + 8) = 5\/2 × 14 = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]