Quiz Mathématiques : 4ème année secondaire — Série 40809

Question 1 sur 10 10:00

[{"id":51701,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51702,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51703,"question":"Quelle est la solution de l'équation 2x - 3 = 7 ?","option_a":"x = 5","option_b":"x = 2","option_c":"x = 10","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 2x = 10, donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51704,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51705,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé à 6 faces ?","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, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51706,"question":"L'intégrale de f(x) = 2x entre 0 et 3 est égale à :","option_a":"9","option_b":"6","option_c":"3","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x², donc [x²] de 0 à 3 = 9 - 0 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51707,"question":"Un triangle rectangle a des côtés de longueurs 3, 4 et 5. L'hypoténuse est-elle le côté de longueur 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle, l'hypoténuse est le côté opposé à l'angle droit, ici 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51708,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51709,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante (uₙ₊₁ - uₙ = 2), donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51710,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 1 ?","option_a":"x \u003E 2","option_b":"x \u003E 1","option_c":"x \u003C 2","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x \u003E 6, donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]