Quiz — devoir-de-contrôle-n°2--2010-2011(lazreg-imed).pdf

Question 1 sur 10 20:00

[{"id":7905,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A : x = 2 ou x = 3","option_b":"B : x = -2 ou x = -3","option_c":"C : x = 1 ou x = 6","option_d":"D : x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc 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\": \"A : x = 2 ou x = 3\", \"b\": \"B : x = -2 ou x = -3\", \"c\": \"C : x = 1","_debug_options_count":4},{"id":7906,"question":"Dans un triangle rectangle, le cosinus d'un angle est égal à :","option_a":"A : Opposé \/ Hypoténuse","option_b":"B : Adjacent \/ Hypoténuse","option_c":"C : Opposé \/ Adjacent","option_d":"D : Hypoténuse \/ Adjacent","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, le cosinus d'un angle dans un triangle rectangle est le rapport entre le côté adjacent et l'hypoténuse.","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 : Opposé \/ Hypoténuse\", \"b\": \"B : Adjacent \/ Hypoténuse\", \"c","_debug_options_count":4},{"id":7907,"question":"Vrai ou Faux ? La somme de deux vecteurs est commutative.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme de deux vecteurs est commutative, c'est-à-dire que u + v = v + u.","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":7908,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"A : 6x + 2","option_b":"B : 3x + 2","option_c":"C : 6x² + 2","option_d":"D : 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2, car la dérivée de x² est 2x et celle de x est 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\": \"A : 6x + 2\", \"b\": \"B : 3x + 2\", \"c\": \"C : 6x² + 2\", \"d\": \"D : 3x","_debug_options_count":4},{"id":7909,"question":"Vrai ou Faux ? Une fonction affine est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine f(x) = ax + b est croissante si a \u003E 0 et décroissante si a \u003C 0. Elle n'est donc pas toujours croissante.","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":7910,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A : x \u003E 4","option_b":"B : x \u003C 4","option_c":"C : x \u003E 1","option_d":"D : x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, donc x \u003E 4.","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 \u003E 4\", \"b\": \"B : x \u003C 4\", \"c\": \"C : x \u003E 1\", \"d\": \"D : x \u003C 1\"}","_debug_options_count":4},{"id":7911,"question":"Vrai ou Faux ? 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":"Deux vecteurs orthogonaux ont un produit scalaire égal à zéro, car cos(90°) = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7912,"question":"Quelle est la valeur de sin(30°) ?","option_a":"A : 0","option_b":"B : 1\/2","option_c":"C : √2\/2","option_d":"D : 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La valeur de sin(30°) est 1\/2, d'après le cercle trigonométrique.","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 : 1\/2\", \"c\": \"C : √2\/2\", \"d\": \"D : 1\"}}","_debug_options_count":4},{"id":7913,"question":"Quelle est la forme canonique de l'expression x² - 6x + 5 ?","option_a":"A : (x-3)² - 4","option_b":"B : (x-2)² - 1","option_c":"C : (x-5)² - 20","option_d":"D : (x-1)² - 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique de x² - 6x + 5 est (x-3)² - 4, car (x-3)² = x² - 6x + 9, donc x² - 6x + 5 = (x-3)² - 4.","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-3)² - 4\", \"b\": \"B : (x-2)² - 1\", \"c\": \"C : (x-5)² - 20\"","_debug_options_count":4},{"id":7914,"question":"Vrai ou Faux ? La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 1.","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}]