Quiz — Devoir Contrôle N°2 Avec Correction - Mathématique - Lycée 15 Novembre sfax - 2012.pdf

Question 1 sur 10 20:00

[{"id":26464,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 5","option_c":"x = -12","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 2x + 7, on soustrait 2x des deux côtés : x - 5 = 7, puis on ajoute 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 = 5\", \"c\": \"x = -12\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":26465,"question":"L'inéquation 2x + 3 \u003E 5 a pour solution x \u003E 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 3 des deux côtés, on obtient 2x \u003E 2, puis en divisant par 2 : x \u003E 1. L'affirmation est donc 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":26466,"question":"Quel est le développement de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - 5x + 6","option_c":"x² + x + 6","option_d":"x² - x - 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule (a+b)(a-b) = a² - b² ou en développant manuellement, on obtient x² + x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x - 6\", \"b\": \"x² - 5x + 6\", \"c\": \"x² + x + 6\", \"d\": \"x² ","_debug_options_count":4},{"id":26467,"question":"La somme des angles d'un triangle est toujours égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la géométrie euclidienne : la somme des angles internes d'un triangle est toujours de 180°.","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":26468,"question":"Résolvez l'inéquation -3x + 4 ≤ 10.","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En soustrayant 4 des deux côtés : -3x ≤ 6, puis en divisant par -3 (attention au changement de sens) : x ≥ -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\": \"x ≥ -2\", \"b\": \"x ≤ -2\", \"c\": \"x ≥ 2\", \"d\": \"x ≤ 2\"}}","_debug_options_count":4},{"id":26469,"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 énonce que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Il ne s'applique donc qu'aux triangles rectangles.","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":26470,"question":"Quelle est la valeur de x dans 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":"En factorisant : (x - 2)(x - 3) = 0, donc x = 2 ou 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":26471,"question":"Un parallélogramme a ses diagonales qui se coupent en leur milieu.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété caractéristique des parallélogrammes : leurs diagonales se coupent en leur milieu.","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":26472,"question":"Calculez la valeur de l'expression 2a + 3b pour a = 4 et b = -1.","option_a":"5","option_b":"11","option_c":"-5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant : 2(4) + 3(-1) = 8 - 3 = 5. La bonne réponse est donc 5.","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\": \"11\", \"c\": \"-5\", \"d\": \"1\"}}","_debug_options_count":4},{"id":26473,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du discriminant est bien Δ = b² - 4ac, c'est une définition fondamentale en algèbre.","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}]