Quiz — 63317f38e84ba_Exercice 19.pdf

Question 1 sur 5 10:00

[{"id":2378,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il s'agit d'une équation du second degré. En utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9, on trouve les solutions x = (5 ± √9)\/4, soit x = 2 ou x = 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\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":2379,"question":"Soit f(x) = x³ - 3x² + 4. Quelle est la dérivée de f en x = 2 ?","option_a":"f'(2) = 0","option_b":"f'(2) = 3","option_c":"f'(2) = -3","option_d":"f'(2) = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) est f'(x) = 3x² - 6x. En x = 2, f'(2) = 3*(4) - 6*(2) = 12 - 12 = 0. Cela indique un extremum local en ce point.","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'(2) = 0\", \"b\": \"f'(2) = 3\", \"c\": \"f'(2) = -3\", \"d\": \"f'(2) = 4\"","_debug_options_count":4},{"id":2380,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, quelle est la valeur de cos(θ) ?","option_a":"cos(θ) = 4\/5","option_b":"cos(θ) = 3\/4","option_c":"cos(θ) = 5\/3","option_d":"cos(θ) = 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, si sin(θ) = opposé\/hypoténuse = 3\/5, alors le côté adjacent vaut √(5² - 3²) = 4. Ainsi, cos(θ) = adjacent\/hypoténuse = 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\": \"cos(θ) = 4\/5\", \"b\": \"cos(θ) = 3\/4\", \"c\": \"cos(θ) = 5\/3\", \"d\": ","_debug_options_count":4},{"id":2381,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"La limite est 3","option_b":"La limite est 0","option_c":"La limite est ∞","option_d":"La limite est -∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x tendant vers l'infini, on divise le numérateur et le dénominateur par x². On obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²) → 3\/1 = 3 lorsque x → ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"La limite est 3\", \"b\": \"La limite est 0\", \"c\": \"La limite est ∞","_debug_options_count":4},{"id":2382,"question":"Soit une suite définie par uₙ = 2n + 1. Quelle est la nature de cette suite ?","option_a":"Arithmétique de raison 2","option_b":"Géométrique de raison 2","option_c":"Arithmétique de raison 1","option_d":"Constante","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = (2(n+1) + 1) - (2n + 1) = 2, donc la raison est 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\": \"Arithmétique de raison 2\", \"b\": \"Géométrique de raison 2\", \"c\"","_debug_options_count":4}]