Quiz — ccp-2013-pc-maths-2-epreuve.pdf

Question 1 sur 10 20:00

[{"id":47278,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 6","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez l'équation : 2x - 5 = 3x + 1 → 2x - 3x = 1 + 5 → -x = 6 → x = -6.","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 = -6\", \"b\": \"x = -4\", \"c\": \"x = 6\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":47279,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est une parabole de coefficient directeur positif (1), donc elle admet un minimum en x = -b\/(2a) = 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":47280,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 9x² - 4x + 5","option_b":"f'(x) = 9x² - 4x + 5x","option_c":"f'(x) = 3x² - 2x + 5","option_d":"f'(x) = 6x² - 4x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x³ est 9x², 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) = 9x² - 4x + 5\", \"b\": \"f'(x) = 9x² - 4x + 5x\", \"c\": \"f'(x","_debug_options_count":4},{"id":47281,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","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, donc elle est arithmétique.","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":47282,"question":"Quelle est la valeur de la limite lim (x→∞) (3x² + 2x - 1)\/(2x² - x + 4) ?","option_a":"3\/2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Divisez le numérateur et le dénominateur par x² : (3 + 2\/x - 1\/x²)\/(2 - 1\/x + 4\/x²) → 3\/2 quand 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\": \"3\/2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":47283,"question":"L'inéquation 2x + 3 \u003E 5x - 2 a-t-elle pour solution x \u003C 5\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvez l'inéquation : 2x + 3 \u003E 5x - 2 → -3x \u003E -5 → x \u003C 5\/3. La solution est donc x \u003C 5\/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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47284,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 3x² + 2x - 1 ?","option_a":"F(x) = x⁴ - x³ + x² - x + C","option_b":"F(x) = 12x² - 6x + 2","option_c":"F(x) = x⁴ - x³ + x² - x","option_d":"F(x) = 4x⁴ - 3x³ + 2x² - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 4x³ est x⁴, celle de -3x² est -x³, celle de 2x est x², et celle de -1 est -x. Ajoutez la constante 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\": \"F(x) = x⁴ - x³ + x² - x + C\", \"b\": \"F(x) = 12x² - 6x + 2\", \"","_debug_options_count":4},{"id":47285,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet-elle 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, car le dénominateur s'annule. Elle admet donc une asymptote verticale en 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47286,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ ]2, 3[","option_d":"x ∈ {2, 3}","option_e":"","option_f":"","bonne_reponse":"a","explication":"Factorisez : (x - 2)(x - 3) ≤ 0. La solution est l'intervalle entre les racines, soit x ∈ [2, 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\": \"x ∈ [2, 3]\", \"b\": \"x ∈ ]-∞, 2] ∪ [3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":47287,"question":"La suite définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 3 est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite est géométrique si le rapport entre deux termes consécutifs est constant. Ici, uₙ₊₁\/uₙ = 2 + 3\/uₙ, qui n'est pas constant.","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}]