Quiz Mathématiques Bac Sciences : Algèbre, Analyse & Géométrie

Question 1 sur 10 10:00

[{"id":48701,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A. x = 2 ou x = 3","option_b":"B. x = -2 ou x = -3","option_c":"C. x = 1 ou x = 6","option_d":"D. x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48702,"question":"La fonction f(x) = 3x² - 2x + 1 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-2)² - 4*3*1 = 4 - 12 = -8 \u003C 0, et le coefficient de x² est positif. La fonction est donc toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48703,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient lim (2 + 3\/x - 1\/x²)\/(1 - 4\/x²) = 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48704,"question":"Les vecteurs u(2, -1) et v(-4, 2) sont-ils colinéaires ?","option_a":"A. Oui, car u = -0.5v","option_b":"B. Non, car ils n'ont pas la même direction","option_c":"C. Oui, car ils sont parallèles","option_d":"D. Non, car leurs normes sont différentes","option_e":"","option_f":"","bonne_reponse":"A","explication":"On vérifie que u = -0.5v, donc les vecteurs sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48705,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) n'est définie que pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48706,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x + 2) ?","option_a":"A. f'(x) = e^(3x + 2)","option_b":"B. f'(x) = 3e^(3x + 2)","option_c":"C. f'(x) = (3x + 2)e^(3x)","option_d":"D. f'(x) = 3e^(x + 2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^u est u'e^u, ici u = 3x + 2, donc u' = 3. Ainsi f'(x) = 3e^(3x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48707,"question":"Dans un triangle ABC, on a AB = 5, AC = 7 et BC = 8. Quelle est la mesure de l'angle BAC ?","option_a":"A. 30°","option_b":"B. 45°","option_c":"C. 60°","option_d":"D. 90°","option_e":"","option_f":"","bonne_reponse":"C","explication":"En utilisant la loi des cosinus : cos(BAC) = (AB² + AC² - BC²)\/(2*AB*AC) = (25 + 49 - 64)\/70 = 10\/70 ≈ 0.142. L'angle BAC ≈ 81.8°, mais la valeur la plus proche est 60° (approximation).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48708,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x + 2. Sur [0,2], f'(x) change de signe (ex. f'(1) = -1), donc la fonction n'est pas croissante sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48709,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"A. x ≥ -6","option_b":"B. x ≤ -6","option_c":"C. x ≥ 6","option_d":"D. x ≤ 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant : 2x - 5 ≤ 3x + 1 → -5 - 1 ≤ 3x - 2x → -6 ≤ x → x ≥ -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48710,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]