Quiz — synt 2 4 Math 2014.pdf

Question 1 sur 10 20:00

[{"id":32630,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = 1 ou x = 6","option_c":"x = -2 ou x = -3","option_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, donc les solutions sont 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\": \"x = 2 ou x = 3\", \"b\": \"x = 1 ou x = 6\", \"c\": \"x = -2 ou x = -3\", ","_debug_options_count":4},{"id":32631,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est positive sur [-2, -1] et [1, 2], mais négative sur [-1, 1], donc la fonction n'est pas croissante sur tout l'intervalle.","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":32632,"question":"Quel est le volume d'une pyramide à base carrée de côté 4 cm et de hauteur 6 cm ?","option_a":"32 cm³","option_b":"48 cm³","option_c":"64 cm³","option_d":"96 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'une pyramide est donné par V = (1\/3) × aire de la base × hauteur. Ici, aire de la base = 4² = 16 cm², donc V = (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\": \"32 cm³\", \"b\": \"48 cm³\", \"c\": \"64 cm³\", \"d\": \"96 cm³\"}}","_debug_options_count":4},{"id":32633,"question":"Si A et B sont deux événements indépendants, alors P(A ∩ B) = ?","option_a":"P(A) + P(B)","option_b":"P(A) × P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, deux événements sont indépendants si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) × P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"P(A)","_debug_options_count":4},{"id":32634,"question":"La droite d'équation y = 2x + 1 est-elle asymptote à la courbe de f(x) = (2x² + x + 1)\/(x - 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La droite y = 2x + 3 est l'asymptote oblique de f(x), car en effectuant la division polynomiale, on obtient f(x) = 2x + 3 + 4\/(x-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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":32635,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² + 3x en x = 1 ?","option_a":"1","option_b":"3","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le coefficient directeur de la tangente est donné par la dérivée f'(x) = 2x + 3. En x = 1, f'(1) = 2(1) + 3 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\", \"b\": \"3\", \"c\": \"5\", \"d\": \"7\"}}","_debug_options_count":4},{"id":32636,"question":"Dans un triangle rectangle, si les côtés de l'angle droit mesurent 3 cm et 4 cm, alors l'hypoténuse mesure ?","option_a":"5 cm","option_b":"6 cm","option_c":"7 cm","option_d":"8 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, l'hypoténuse mesure √(3² + 4²) = √25 = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5 cm\", \"b\": \"6 cm\", \"c\": \"7 cm\", \"d\": \"8 cm\"}}","_debug_options_count":4},{"id":32637,"question":"La probabilité de tirer un as dans un jeu de 52 cartes est de 1\/13.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 4 as dans un jeu de 52 cartes, donc la probabilité est 4\/52 = 1\/13.","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":32638,"question":"Quelle est la limite de f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant le numérateur et le dénominateur par x², on obtient f(x) = (3 + 2\/x - 1\/x²)\/(1 - 4\/x²). Lorsque x tend vers l'infini, f(x) tend vers 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":32639,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux droites parallèles ont des coefficients directeurs égaux, car elles ont la même pente.","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}]