Quiz — Examen 2eme math-phys 2022 sem1-Corrigé.pdf

Question 1 sur 10 20:00

[{"id":28140,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. 2x + 3","option_b":"B. x² + 3","option_c":"C. 2x + 5","option_d":"D. 3x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 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. 2x + 3\", \"b\": \"B. x² + 3\", \"c\": \"C. 2x + 5\", \"d\": \"D. 3x - 5\"","_debug_options_count":4},{"id":28141,"question":"La loi de Newton F = m·a s'applique-t-elle à un mouvement circulaire uniforme ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans un mouvement circulaire uniforme, l'accélération est centripète (a = v²\/r), mais la force résultante n'est pas nulle. La loi F = m·a reste valable.","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":28142,"question":"Quel est le résultat de l'intégrale ∫(3x² + 2x) dx ?","option_a":"A. x³ + x² + C","option_b":"B. 6x + 2 + C","option_c":"C. x³ + x + C","option_d":"D. 3x³ + x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². Donc ∫(3x² + 2x) dx = x³ + x² + C.","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. x³ + x² + C\", \"b\": \"B. 6x + 2 + C\", \"c\": \"C. x³ + x + C\", \"","_debug_options_count":4},{"id":28143,"question":"Un circuit électrique en série avec une résistance R = 10Ω et une tension U = 20V a un courant I = 2A. Quelle est la puissance dissipée ?","option_a":"A. 20 W","option_b":"B. 40 W","option_c":"C. 10 W","option_d":"D. 5 W","option_e":"","option_f":"","bonne_reponse":"b","explication":"La puissance P = U·I = 20V × 2A = 40 W. On peut aussi utiliser P = R·I² = 10Ω × (2A)² = 40 W.","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. 20 W\", \"b\": \"B. 40 W\", \"c\": \"C. 10 W\", \"d\": \"D. 5 W\"}}","_debug_options_count":4},{"id":28144,"question":"La fonction f(x) = sin(x) est-elle périodique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction sin(x) est périodique avec une période de 2π, car sin(x + 2π) = sin(x) pour tout 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28145,"question":"Quelle est la solution de l'équation différentielle y' + y = 0 ?","option_a":"A. y = Ce^x","option_b":"B. y = Ce^{-x}","option_c":"C. y = Cx","option_d":"D. y = C","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation y' + y = 0 a pour solution générale y = Ce^{-x}, où C est une constante.","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. y = Ce^x\", \"b\": \"B. y = Ce^{-x}\", \"c\": \"C. y = Cx\", \"d\": \"D. y","_debug_options_count":4},{"id":28146,"question":"Un objet de masse m = 2 kg est lancé verticalement vers le haut avec une vitesse initiale v₀ = 10 m\/s. Quelle est son énergie cinétique au point le plus haut ?","option_a":"A. 100 J","option_b":"B. 0 J","option_c":"C. 20 J","option_d":"D. 50 J","option_e":"","option_f":"","bonne_reponse":"b","explication":"Au point le plus haut, la vitesse est nulle, donc l'énergie cinétique E_c = ½mv² = 0 J.","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. 100 J\", \"b\": \"B. 0 J\", \"c\": \"C. 20 J\", \"d\": \"D. 50 J\"}}","_debug_options_count":4},{"id":28147,"question":"La dérivée de la fonction f(x) = ln(x) est-elle 1\/x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est bien 1\/x, c'est une propriété fondamentale des logarithmes.","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":28148,"question":"Quel est le résultat de l'expression (a + b)² - (a - b)² ?","option_a":"A. 4ab","option_b":"B. 2ab","option_c":"C. a² + b²","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant, (a + b)² = a² + 2ab + b² et (a - b)² = a² - 2ab + b². Donc (a + b)² - (a - b)² = 4ab.","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. 4ab\", \"b\": \"B. 2ab\", \"c\": \"C. a² + b²\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":28149,"question":"La tension aux bornes d'un conducteur ohmique est-elle proportionnelle à l'intensité du courant qui le traverse ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, selon la loi d'Ohm U = R·I, où U est proportionnelle à I si R est constante.","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}]