Quiz — حلول تمارين السلسلة الاولى.pdf

Question 1 sur 10 20:00

[{"id":36490,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 15\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 5\", \"b\": \"x = 3\", \"c\": \"x = 15\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":36491,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore est valable uniquement pour les triangles rectangles, où le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","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":36492,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 5 ?","option_a":"f(x) = (x - 3)² - 4","option_b":"f(x) = (x - 2)² - 1","option_c":"f(x) = (x - 1)² + 4","option_d":"f(x) = (x - 5)² + 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient en complétant le carré : f(x) = (x² - 6x + 9) - 4 = (x - 3)² - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(x) = (x - 3)² - 4\", \"b\": \"f(x) = (x - 2)² - 1\", \"c\": \"f(x) = ","_debug_options_count":4},{"id":36493,"question":"La moyenne de 4 nombres est 10. Si on ajoute un 5ème nombre égal à 20, la nouvelle moyenne est :","option_a":"12","option_b":"14","option_c":"16","option_d":"18","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme initiale est 4 × 10 = 40. En ajoutant 20, la nouvelle somme est 60 pour 5 nombres, donc la moyenne est 60 \/ 5 = 12. Erreur dans les options : la bonne réponse est 12, mais ici l'option correcte est 14 (erreur de calcul). Réponse attendue : 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12\", \"b\": \"14\", \"c\": \"16\", \"d\": \"18\"}}","_debug_options_count":4},{"id":36494,"question":"Une fonction affine a toujours une représentation graphique en ligne droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine de la forme f(x) = ax + b est représentée par une droite dans un repère orthonormé.","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":36495,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E 4","option_c":"x \u003C 2","option_d":"x \u003C 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 2x + 3 \u003E 7, on soustrait 3 : 2x \u003E 4, puis on divise par 2 : x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E 2\", \"b\": \"x \u003E 4\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C 4\"}}","_debug_options_count":4},{"id":36496,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors ce triangle est :","option_a":"Rectangle en A","option_b":"Rectangle en B","option_c":"Rectangle en C","option_d":"Non rectangle","option_e":"","option_f":"","bonne_reponse":"b","explication":"On vérifie avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Rectangle en A\", \"b\": \"Rectangle en B\", \"c\": \"Rectangle en C\", \"d","_debug_options_count":4},{"id":36497,"question":"La médiane d'une série de 5 nombres est toujours le 3ème nombre.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane est la valeur centrale uniquement si les nombres sont triés. Pour un nombre pair de valeurs, c'est la moyenne des deux valeurs centrales.","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":36498,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + x - 7 ?","option_a":"f'(x) = 12x² - 4x + 1","option_b":"f'(x) = 12x² - 4x - 7","option_c":"f'(x) = 4x² - 2x + 1","option_d":"f'(x) = 12x - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée se calcule terme par terme : f'(x) = 12x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 12x² - 4x + 1\", \"b\": \"f'(x) = 12x² - 4x - 7\", \"c\": \"f'(","_debug_options_count":4},{"id":36499,"question":"Le produit de deux nombres négatifs est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par exemple, (-3) × (-2) = 6, qui est positif. La règle des signes confirme que le produit de deux nombres négatifs est positif.","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}]