Quiz — Ds 5 Salmane 2011-2012 Cor.pdf

Question 1 sur 10 20:00

[{"id":8665,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution est obtenue en isolant x : 3x = 15, donc 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 = 15\/3\", \"c\": \"x = 5\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":8666,"question":"La fonction f(x) = 2x² - 3x + 1 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, f(x) est une fonction du second degré (présence de x²).","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":8667,"question":"Quel est le volume d'un cube de côté 4 cm ?","option_a":"16 cm³","option_b":"32 cm³","option_c":"64 cm³","option_d":"12 cm³","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le volume d'un cube est donné par V = côté³. Ici, V = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"16 cm³\", \"b\": \"32 cm³\", \"c\": \"64 cm³\", \"d\": \"12 cm³\"}}","_debug_options_count":4},{"id":8668,"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":8669,"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 + 3)² - 4","option_c":"f(x) = (x - 3)² + 4","option_d":"f(x) = (x + 3)² + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient par complétion du 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 + 3)² - 4\", \"c\": \"f(x) = ","_debug_options_count":4},{"id":8670,"question":"Un parallélépipède rectangle a pour dimensions 2 cm, 3 cm et 4 cm. Quelle est son aire totale ?","option_a":"24 cm²","option_b":"28 cm²","option_c":"52 cm²","option_d":"62 cm²","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'aire totale est calculée par la formule 2(ab + bc + ac). Ici, A = 2(2×3 + 3×4 + 2×4) = 2(6 + 12 + 8) = 52 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"24 cm²\", \"b\": \"28 cm²\", \"c\": \"52 cm²\", \"d\": \"62 cm²\"}}","_debug_options_count":4},{"id":8671,"question":"La fonction f(x) = -2x + 7 est décroissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine est décroissante si son coefficient directeur est négatif. Ici, a = -2 \u003C 0, donc la fonction est décroissante.","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":8672,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x : 2x \u003E 4, donc 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 \u003C 2\", \"c\": \"x \u003E -2\", \"d\": \"x \u003C -2\"}}","_debug_options_count":4},{"id":8673,"question":"Le volume d'une pyramide est égal à un tiers du volume d'un prisme de même base et même hauteur.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du volume d'une pyramide est V = (1\/3) × aire de la base × hauteur, ce qui correspond bien à un tiers du volume d'un prisme de même base et hauteur.","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":8674,"question":"Quelle est l'image de 3 par la fonction f(x) = 4x² - 5x + 1 ?","option_a":"22","option_b":"16","option_c":"28","option_d":"32","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 3 : f(3) = 4×9 - 5×3 + 1 = 36 - 15 + 1 = 22. (Correction : la bonne réponse est 22, donc l'option correcte devrait être 22. L'explication est correcte.)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"22\", \"b\": \"16\", \"c\": \"28\", \"d\": \"32\"}}","_debug_options_count":4}]