Quiz — Lycée Pilote Sfax - DS 2 2016.pdf

Question 1 sur 10 20:00

[{"id":33710,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"On isole x en soustrayant 2x des deux côtés, puis en ajoutant 5 : 3x - 2x = 7 + 5 → x = 12.","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 = 12\", \"b\": \"x = 2\", \"c\": \"x = -2\", \"d\": \"x = 5\"}}","_debug_options_count":4},{"id":33711,"question":"Le théorème de Thalès s'applique-t-il uniquement aux triangles rectangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles, à condition que les droites soient parallèles.","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":33712,"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":"On complète le carré : x² - 6x + 5 = (x² - 6x + 9) - 9 + 5 = (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":33713,"question":"Dans un triangle ABC, si AB = 5 cm, AC = 7 cm et BC = 10 cm, peut-on appliquer le théorème de Thalès ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès nécessite que les droites soient parallèles, ce qui n'est pas le cas ici. Il faut vérifier la configuration géométrique.","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":33714,"question":"Quelle est la solution de l'inéquation 2x + 3 ≤ 5x - 6 ?","option_a":"x ≥ 3","option_b":"x ≤ 3","option_c":"x ≥ -3","option_d":"x ≤ -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"On isole x : 2x - 5x ≤ -6 - 3 → -3x ≤ -9 → x ≥ 3 (en divisant par un nombre négatif, 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\": \"x ≥ 3\", \"b\": \"x ≤ 3\", \"c\": \"x ≥ -3\", \"d\": \"x ≤ -3\"}}","_debug_options_count":4},{"id":33715,"question":"Si f(x) = 2x + 1, quelle est l'image de 3 par f ?","option_a":"5","option_b":"7","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"On remplace x par 3 : f(3) = 2*3 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"6\", \"d\": \"8\"}}","_debug_options_count":4},{"id":33716,"question":"Dans un triangle rectangle, le cosinus d'un angle est toujours inférieur à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le cosinus d'un angle dans un triangle rectangle est toujours compris entre 0 et 1, car il représente le rapport de deux longueurs.","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":33717,"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 possibles, donc la probabilité est 3\/6 = 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\": \"1\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":33718,"question":"Si deux vecteurs sont colinéaires, alors ils sont nécessairement parallèles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs colinéaires sont toujours parallèles, car ils ont la même direction ou des directions opposées.","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":33719,"question":"Quelle est la solution de l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"On reconnaît une identité remarquable : (x - 2)² = 0 → x = 2 (solution double).","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 = 2\", \"b\": \"x = -2\", \"c\": \"x = 4\", \"d\": \"x = 0\"}}","_debug_options_count":4}]