Quiz : Isométries et dérivation — 4ème année secondaire

Question 1 sur 10 10:00

[{"id":22278,"question":"Quelle transformation géométrique conserve les distances mais pas nécessairement l'orientation ?","option_a":"Translation","option_b":"Rotation","option_c":"Symétrie axiale","option_d":"Homothétie","option_e":"","option_f":"","bonne_reponse":"C","explication":"La symétrie axiale conserve les distances mais inverse l'orientation, contrairement aux autres transformations qui la conservent.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22279,"question":"La dérivée de la fonction f(x) = x² + 3x + 2 est f'(x) = 2x + 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de 2 est 0. Donc f'(x) = 2x + 3 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22280,"question":"Quel est le résultat de la composition d'une translation de vecteur (2, 3) suivie d'une rotation de 90° autour de l'origine ?","option_a":"Une translation","option_b":"Une rotation","option_c":"Une symétrie","option_d":"Une homothétie","option_e":"","option_f":"","bonne_reponse":"B","explication":"La composition d'une translation et d'une rotation est une rotation (ou une translation si la rotation est de 0°).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22281,"question":"La dérivée de la fonction f(x) = 1\/x est f'(x) = -1\/x².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 1\/x est bien -1\/x², car d\/dx (x⁻¹) = -x⁻².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22282,"question":"Quelle est l'image du point A(2, -1) par la symétrie centrale de centre O(0, 0) ?","option_a":"A'(2, 1)","option_b":"A'(-2, 1)","option_c":"A'(-2, -1)","option_d":"A'(1, -2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'image d'un point (x, y) par une symétrie centrale de centre O est (-x, -y). Donc A'(-2, 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22283,"question":"La dérivée de la fonction f(x) = sin(x) est f'(x) = cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est bien cos(x), selon les règles de dérivation des fonctions trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22284,"question":"Quelle transformation géométrique conserve à la fois les distances et l'orientation ?","option_a":"Symétrie axiale","option_b":"Rotation","option_c":"Translation","option_d":"Homothétie","option_e":"","option_f":"","bonne_reponse":"C","explication":"La translation conserve les distances et l'orientation, contrairement aux autres transformations qui peuvent inverser l'orientation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22285,"question":"La dérivée de la fonction f(x) = e^x est f'(x) = e^x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^x est bien e^x, car c'est la seule fonction égale à sa dérivée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22286,"question":"Quelle est l'image du point B(3, 4) par une rotation de 180° autour de l'origine ?","option_a":"B'(-3, -4)","option_b":"B'(4, -3)","option_c":"B'(-3, 4)","option_d":"B'(3, -4)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une rotation de 180° autour de l'origine transforme (x, y) en (-x, -y). Donc B'(-3, -4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22287,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est bien 1\/x, selon les règles de dérivation des fonctions logarithmiques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]