Quiz Maths : Algèbre, Géométrie et Analyse — 4ème Année Secondaire

Question 1 sur 10 10:00

[{"id":14133,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On soustrait 2x des deux côtés : x - 5 = 7, puis on ajoute 5 : x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14134,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14135,"question":"Quelle est la dérivée de la fonction f(x) = 4x² - 3x + 2 ?","option_a":"f'(x) = 8x - 3","option_b":"f'(x) = 4x - 3","option_c":"f'(x) = 8x² - 3x","option_d":"f'(x) = 4x² - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 4x² est 8x, celle de -3x est -3, et la dérivée de 2 est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14136,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors ce triangle est :","option_a":"Acute","option_b":"Rectangle","option_c":"Obtus","option_d":"Isocèle","option_e":"","option_f":"","bonne_reponse":"B","explication":"5² + 12² = 25 + 144 = 169 = 13², donc le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14137,"question":"La fonction f(x) = x² + 4x - 5 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 + 20 = 36 \u003E 0, donc la fonction s'annule en deux points et n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14138,"question":"Quelle est la solution du système d'équations : { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 2","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations, on obtient 3x = 6 ⇒ x = 2, puis y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14139,"question":"L'aire d'un cercle de rayon r est donnée par la formule :","option_a":"πr²","option_b":"2πr","option_c":"4πr²","option_d":"πr","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de l'aire d'un cercle est π multiplié par le carré du rayon.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14140,"question":"La fonction f(x) = 3x + 2 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine est de la forme f(x) = ax + b, ce qui correspond ici à a = 3 et b = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14141,"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":"sin(30°) = 1\/2, une valeur fondamentale en trigonométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14142,"question":"La somme des angles d'un quadrilatère convexe est égale à :","option_a":"180°","option_b":"360°","option_c":"540°","option_d":"720°","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des angles d'un quadrilatère convexe est toujours de 360°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]