Quiz Maths — 4ème année secondaire : Algèbre, Géométrie & Fonctions

Question 1 sur 10 10:00

[{"id":75307,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75309,"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":75311,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 3 ?","option_a":"f(x) = (x-2)² - 1","option_b":"f(x) = (x-1)² + 2","option_c":"f(x) = (x+2)² - 1","option_d":"f(x) = (x-2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient en complétant le carré : f(x) = (x² - 4x + 4) - 1 = (x-2)² - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75313,"question":"Si deux droites sont parallèles, leurs coefficients directeurs sont :","option_a":"égaux","option_b":"opposés","option_c":"inverses","option_d":"nuls","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont le même coefficient directeur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75315,"question":"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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75317,"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 = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant le système, on trouve x = 2 et y = 1. Vérification : 2*2 + 1 = 5 et 2 - 1 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75318,"question":"Dans un triangle rectangle, le cosinus d'un angle est égal au rapport :","option_a":"côté adjacent \/ hypoténuse","option_b":"côté opposé \/ hypoténuse","option_c":"côté opposé \/ côté adjacent","option_d":"hypoténuse \/ côté adjacent","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le cosinus d'un angle est défini comme le rapport du côté adjacent à l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75319,"question":"La fonction f(x) = 2x + 3 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 s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75320,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + x - 1 ?","option_a":"f'(x) = 3x² - 4x + 1","option_b":"f'(x) = 3x² - 2x + 1","option_c":"f'(x) = x² - 4x + 1","option_d":"f'(x) = 3x² - 4x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée s'obtient en appliquant la règle de dérivation : f'(x) = 3x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":75321,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = 4b² - ac","option_d":"Δ = a² - 4bc","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est calculé par la formule Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]