Quiz — 65f1a3f94978b_corrigé_EOT test 2 review.pdf

Question 1 sur 10 20:00

[{"id":11403,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A. x = 2 ou x = 3","option_b":"B. x = -2 ou x = -3","option_c":"C. x = 1 ou x = 6","option_d":"D. x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et 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\": \"A. x = 2 ou x = 3\", \"b\": \"B. x = -2 ou x = -3\", \"c\": \"C. x = 1 ou","_debug_options_count":4},{"id":11404,"question":"La dérivée de la fonction f(x) = 3x² - 4x + 1 est f'(x) = 6x - 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation, f'(x) = 6x - 4 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":11405,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x³ au point d'abscisse x = 1 ?","option_a":"A. y = 3x - 2","option_b":"B. y = 2x + 1","option_c":"C. y = x + 2","option_d":"D. y = 3x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(1) = 1 et f'(x) = 3x², donc f'(1) = 3. L'équation de la tangente est y = 3(x-1) + 1 = 3x - 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\": \"A. y = 3x - 2\", \"b\": \"B. y = 2x + 1\", \"c\": \"C. y = x + 2\", \"d\": \"","_debug_options_count":4},{"id":11406,"question":"Le volume d'une pyramide à base carrée de côté 4 cm et de hauteur 6 cm est :","option_a":"A. 32 cm³","option_b":"B. 48 cm³","option_c":"C. 64 cm³","option_d":"D. 96 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'une pyramide est V = (1\/3) × aire de la base × hauteur = (1\/3) × 16 × 6 = 32 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 32 cm³\", \"b\": \"B. 48 cm³\", \"c\": \"C. 64 cm³\", \"d\": \"D. 96 cm","_debug_options_count":4},{"id":11407,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet une asymptote verticale en x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction n'est pas définie en x = 3, ce qui crée une asymptote verticale 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":11408,"question":"Quelle est la dérivée de la fonction g(x) = √(x² + 1) ?","option_a":"A. g'(x) = x\/√(x² + 1)","option_b":"B. g'(x) = 2x\/√(x² + 1)","option_c":"C. g'(x) = 1\/√(x² + 1)","option_d":"D. g'(x) = x\/√(x² - 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la règle de dérivation des fonctions composées, g'(x) = (1\/2)(x² + 1)^(-1\/2) × 2x = x\/√(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. g'(x) = x\/√(x² + 1)\", \"b\": \"B. g'(x) = 2x\/√(x² + 1)\", \"c","_debug_options_count":4},{"id":11409,"question":"Le théorème de Thalès s'applique uniquement dans les 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.","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":11410,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. -3","option_d":"D. ∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient lim (3 + 2\/x - 1\/x²)\/(1 - 4\/x²) = 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\": \"A. 3\", \"b\": \"B. 0\", \"c\": \"C. -3\", \"d\": \"D. ∞\"}}","_debug_options_count":4},{"id":11411,"question":"La fonction f(x) = x³ - 3x² + 4 admet un minimum local en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"f'(x) = 3x² - 6x et f''(x) = 6x - 6. En x = 2, f'(2) = 0 et f''(2) = 6 \u003E 0, donc c'est un minimum local.","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":11412,"question":"Quelle est l'aire d'un triangle de côtés 5 cm, 6 cm et 7 cm ?","option_a":"A. 14,7 cm²","option_b":"B. 15 cm²","option_c":"C. 12 cm²","option_d":"D. 10 cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule de Héron : p = (5+6+7)\/2 = 9, aire = √(9×4×3×2) = √216 ≈ 14,7 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 14,7 cm²\", \"b\": \"B. 15 cm²\", \"c\": \"C. 12 cm²\", \"d\": \"D. 10 ","_debug_options_count":4}]