Quiz Mathématiques : Algèbre, Fonctions et Géométrie pour la 4ème secondaire

Question 1 sur 10 10:00

[{"id":54021,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_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":54022,"question":"La fonction f(x) = 3x + 2 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit f(x)=ax+b, ce qui correspond ici à a=3 et b=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54023,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 3x² - 4x + 5","option_b":"f'(x) = x² - 2x + 5","option_c":"f'(x) = 3x² - 4x","option_d":"f'(x) = 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée se calcule terme par terme : (x³)'=3x², (-2x²)'=-4x, (5x)'=5, et (-1)'=0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54024,"question":"Le triangle ABC avec AB=5, BC=12 et AC=13 est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 13² (25+144=169), donc le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54025,"question":"Quelle est la solution de l'inéquation 2x - 7 \u003E 3x + 1 ?","option_a":"x \u003C -8","option_b":"x \u003E -8","option_c":"x \u003C 8","option_d":"x \u003E 8","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E 8, soit x \u003C -8 (en multipliant par -1, on inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54026,"question":"La fonction f(x) = 1\/x est-elle définie pour x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x)=1\/x n'est pas définie en x=0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54027,"question":"Quelle est la limite de la suite uₙ = (2n+1)\/(n-3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 - 3\/n), donc la limite est 2\/1=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54028,"question":"Un angle de 120° est-il un angle aigu ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un angle aigu mesure moins de 90°, donc 120° est un angle obtus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54029,"question":"Quelle est la solution de l'équation 3^(x+1) = 27 ?","option_a":"x = 2","option_b":"x = 3","option_c":"x = 1","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"On écrit 27 comme 3³, donc 3^(x+1)=3³ implique x+1=3, soit x=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":54030,"question":"La probabilité d'un événement impossible est-elle égale à 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la probabilité d'un événement impossible est 0, tandis que celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]