Quiz — Devoir n°2.doc

Question 1 sur 10 20:00

[{"id":25684,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 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 = -12\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":25685,"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.","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":25686,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 12x² - 4x + 5","option_b":"f'(x) = 12x² - 4x + 5x","option_c":"f'(x) = 12x² - 4x - 1","option_d":"f'(x) = 4x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 4x³ est 12x², celle de -2x² est -4x, celle de 5x est 5, et celle de -1 est 0.","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 + 5\", \"b\": \"f'(x) = 12x² - 4x + 5x\", \"c\": \"f'","_debug_options_count":4},{"id":25687,"question":"Si sin(θ) = 3\/5, quelle est la valeur de cos(θ) dans un triangle rectangle ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"2\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant l'identité sin²(θ) + cos²(θ) = 1, on trouve cos(θ) = √(1 - (3\/5)²) = 4\/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\": \"4\/5\", \"b\": \"3\/4\", \"c\": \"5\/3\", \"d\": \"2\/5\"}}","_debug_options_count":4},{"id":25688,"question":"La fonction f(x) = x² - 4x + 4 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et la dérivée seconde f''(x) = 2 \u003E 0, donc c'est un minimum.","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":25689,"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, on obtient 2x \u003E 4 → 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":25690,"question":"Dans un triangle ABC, si AB = 5 cm, AC = 12 cm et BC = 13 cm, alors ce triangle est rectangle en A.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérification avec le théorème de Pythagore : 5² + 12² = 13² → 25 + 144 = 169, donc le triangle est rectangle en A.","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":25691,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (3 - 2\/x + 1\/x²)\/(1 + 1\/x²) → 3\/1 = 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\": \"3\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":25692,"question":"Le point d'intersection de la droite y = 2x + 1 et de la parabole y = x² - 3x + 2 est en x = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant 2x + 1 = x² - 3x + 2 → x² - 5x + 1 = 0, les solutions sont x = (5 ± √21)\/2, donc x = 1 n'est pas une solution.","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":25693,"question":"Quelle est la valeur de l'expression (2a + 3b)² si a = 1 et b = -1 ?","option_a":"1","option_b":"-1","option_c":"25","option_d":"16","option_e":"","option_f":"","bonne_reponse":"c","explication":"En développant (2a + 3b)² = 4a² + 12ab + 9b² → 4(1) + 12(1)(-1) + 9(1) = 4 - 12 + 9 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\", \"b\": \"-1\", \"c\": \"25\", \"d\": \"16\"}}","_debug_options_count":4}]