Quiz — 4Maths DS3 Reg sousse 2022 .pdf

Question 1 sur 10 20:00

[{"id":23754,"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: x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de x² est 2x, celle de 3x est 3, et celle de -5 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\": \"A: 2x + 3\", \"b\": \"B: x² + 3\", \"c\": \"C: 2x - 5\", \"d\": \"D: x + 3\"}","_debug_options_count":4},{"id":23755,"question":"L'équation x² - 4x + 4 = 0 admet une solution double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, ce qui signifie qu'il y a une solution double (x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":23756,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"A: 0","option_b":"B: 3","option_c":"C: -1","option_d":"D: +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour x tendant vers l'infini, on divise numérateur et dénominateur par x² : f(x) ≈ (3 + 2\/x) \/ (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\": \"b\", \"options\": {\"a\": \"A: 0\", \"b\": \"B: 3\", \"c\": \"C: -1\", \"d\": \"D: +∞\"}}","_debug_options_count":4},{"id":23757,"question":"La fonction f(x) = sin(x) est périodique de période 2π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction sinus est bien 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":23758,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A: x \u003C -6","option_b":"B: x \u003E -6","option_c":"C: x \u003C 6","option_d":"D: x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant : 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6 (en divisant par -1, on inverse le sens de l'inégalité).","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 \u003C -6\", \"b\": \"B: x \u003E -6\", \"c\": \"C: x \u003C 6\", \"d\": \"D: x \u003E 6\"}}","_debug_options_count":4},{"id":23759,"question":"Le vecteur u(2, -3) et le vecteur v(-4, 6) sont colinéaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont colinéaires si l'un est un multiple de l'autre. Ici, v = -2 * u, donc ils sont colinéaires.","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":23760,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"A: 1\/6","option_b":"B: 1\/3","option_c":"C: 1\/2","option_d":"D: 2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé a 6 faces, dont 3 sont paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A: 1\/6\", \"b\": \"B: 1\/3\", \"c\": \"C: 1\/2\", \"d\": \"D: 2\/3\"}}","_debug_options_count":4},{"id":23761,"question":"La fonction f(x) = e^(2x) est une fonction exponentielle de base e.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction e^(2x) peut s'écrire (e²)^x, donc c'est une fonction exponentielle de base e², pas e.","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":23762,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A: x = e","option_b":"B: x = e²","option_c":"C: x = 1","option_d":"D: x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition du logarithme népérien, ln(x) = 2 équivaut à x = e².","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: x = e\", \"b\": \"B: x = e²\", \"c\": \"C: x = 1\", \"d\": \"D: x = 2\"}}","_debug_options_count":4},{"id":23763,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","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}]