Quiz — dm17.pdf

Question 1 sur 10 20:00

[{"id":89116,"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","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) x = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":89117,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ est f'(x) = 3x², qui est toujours positive ou nulle. La fonction est donc croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":89118,"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 f(x) = (2 + 3\/x - 1\/x²)\/(1 - 4\/x²). Lorsque x tend vers l'infini, les termes en 1\/x tendent vers 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 2\", \"c\": \"C) -∞\", \"d\": \"D) +∞\"}}","_debug_options_count":4},{"id":89119,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"A) 5 cm","option_b":"B) 7 cm","option_c":"C) √7 cm","option_d":"D) 25 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25. Donc BC = √25 = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 5 cm\", \"b\": \"B) 7 cm\", \"c\": \"C) √7 cm\", \"d\": \"D) 25 cm\"}}","_debug_options_count":4},{"id":89120,"question":"La dérivée de la fonction f(x) = sin(x) est-elle cos(x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction sinus est bien la fonction cosinus, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":89121,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A) x \u003C -6","option_b":"B) x \u003E -6","option_c":"C) x \u003C 6","option_d":"D) x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'inéquation : 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6 (en multipliant par -1, on change le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) x \u003C -6\", \"b\": \"B) x \u003E -6\", \"c\": \"C) x \u003C 6\", \"d\": \"D) x \u003E 6\"}}","_debug_options_count":4},{"id":89122,"question":"Un cercle a un rayon de 5 cm. Quelle est son aire ?","option_a":"A) 25π cm²","option_b":"B) 10π cm²","option_c":"C) 5π cm²","option_d":"D) 100π cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle est donnée par la formule A = πr². Avec r = 5 cm, A = π × 5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 25π cm²\", \"b\": \"B) 10π cm²\", \"c\": \"C) 5π cm²\", \"d\": \"D) ","_debug_options_count":4},{"id":89123,"question":"La fonction f(x) = 1\/x est-elle définie en 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. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":89124,"question":"Quelle est la valeur de la dérivée de f(x) = ln(x) en x = 1 ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) e","option_d":"D) -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de la fonction logarithme népérien est f'(x) = 1\/x. En x = 1, f'(1) = 1\/1 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 1\", \"c\": \"C) e\", \"d\": \"D) -1\"}}","_debug_options_count":4},{"id":89125,"question":"Un parallélogramme a des côtés de 6 cm et 8 cm. Quelle est son aire si la hauteur relative au côté de 6 cm est de 5 cm ?","option_a":"A) 30 cm²","option_b":"B) 48 cm²","option_c":"C) 24 cm²","option_d":"D) 14 cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un parallélogramme est donnée par A = base × hauteur. Ici, A = 6 cm × 5 cm = 30 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) 30 cm²\", \"b\": \"B) 48 cm²\", \"c\": \"C) 24 cm²\", \"d\": \"D) 14 cm","_debug_options_count":4}]