Quiz — Spring 2015 4M.pdf

Question 1 sur 10 20:00

[{"id":15609,"question":"Quel est le résultat de l'expression : 3 × (5 + 2) - 4 ?","option_a":"17","option_b":"23","option_c":"13","option_d":"21","option_e":"","option_f":"","bonne_reponse":"a","explication":"On applique d'abord la règle des parenthèses : 5 + 2 = 7, puis la multiplication : 3 × 7 = 21, et enfin la soustraction : 21 - 4 = 17.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"17\", \"b\": \"23\", \"c\": \"13\", \"d\": \"21\"}}","_debug_options_count":4},{"id":15610,"question":"L'équation x² - 5x + 6 = 0 a pour solutions x = 2 et x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 2 et 3 dans l'équation, on obtient 0 = 0, ce qui est vrai. Les solutions sont bien 2 et 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":15611,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + 5 ?","option_a":"12x² - 4x","option_b":"12x² - 4x + 5","option_c":"12x² - 4x + 1","option_d":"8x² - 4x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n·a·x^(n-1). Ici, f'(x) = 12x² - 4x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"12x² - 4x\", \"b\": \"12x² - 4x + 5\", \"c\": \"12x² - 4x + 1\", \"d\": \"","_debug_options_count":4},{"id":15612,"question":"Un triangle rectangle a un angle de 30°. Quel est la mesure de son troisième angle ?","option_a":"60°","option_b":"45°","option_c":"90°","option_d":"120°","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle rectangle, la somme des angles est 180°. Si un angle est 90° et un autre 30°, le troisième angle mesure 180° - 90° - 30° = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"60°\", \"b\": \"45°\", \"c\": \"90°\", \"d\": \"120°\"}}","_debug_options_count":4},{"id":15613,"question":"La fonction f(x) = 2x + 1 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine f(x) = ax + b est croissante si a \u003E 0. Ici, a = 2 \u003E 0, donc la fonction est croissante.","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":15614,"question":"Quelle est la solution de l'inéquation : 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003E 6","option_c":"x \u003C 8","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 2x des deux côtés : x - 7 \u003E 1, puis on ajoute 7 : x \u003E 8.","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 \u003E 8\", \"b\": \"x \u003E 6\", \"c\": \"x \u003C 8\", \"d\": \"x \u003C 6\"}}","_debug_options_count":4},{"id":15615,"question":"Le périmètre d'un cercle de rayon r est donné par la formule :","option_a":"2πr","option_b":"πr²","option_c":"4πr","option_d":"πr","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du périmètre (circonférence) d'un cercle est 2πr, où r est le rayon.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2πr\", \"b\": \"πr²\", \"c\": \"4πr\", \"d\": \"πr\"}}","_debug_options_count":4},{"id":15616,"question":"Si a et b sont deux nombres réels, alors (a + b)² = a² + 2ab + b².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une identité remarquable : (a + b)² = a² + 2ab + b² est toujours vraie.","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":15617,"question":"Quelle est la valeur de sin(30°) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle rectangle, sin(30°) = côté opposé \/ hypoténuse = 1\/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\": \"1\/2\", \"b\": \"√2\/2\", \"c\": \"√3\/2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":15618,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ? Si oui, quelle est sa valeur ?","option_a":"Oui, minimum = -1","option_b":"Oui, minimum = 1","option_c":"Non","option_d":"Oui, minimum = -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une fonction du second degré avec a = 1 \u003E 0, donc elle admet un minimum. Le sommet a pour ordonnée f(2) = 2² - 4×2 + 3 = -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\": \"Oui, minimum = -1\", \"b\": \"Oui, minimum = 1\", \"c\": \"Non\", \"d\": \"Ou","_debug_options_count":4}]