Quiz Maths 4M : Équations, Fonctions et Géométrie

Question 1 sur 10 10:00

[{"id":8743,"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":8744,"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 est de la forme f(x) = ax + b, donc f(x) = 2x + 3 est bien affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8745,"question":"Quelle est la pente de la droite représentative de la fonction f(x) = -4x + 7 ?","option_a":"4","option_b":"-4","option_c":"7","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans une fonction affine f(x) = ax + b, 'a' représente la pente. Ici, a = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8746,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"4 cm","option_c":"10 cm","option_d":"12 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : 6² + x² = 10² → 36 + x² = 100 → x² = 64 → x = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8747,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8748,"question":"Quelle est la représentation graphique d'une fonction linéaire ?","option_a":"Une parabole","option_b":"Une droite passant par l'origine","option_c":"Une droite quelconque","option_d":"Un cercle","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction linéaire f(x) = ax passe toujours par l'origine (0,0) et est représentée par une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8749,"question":"Si deux droites sont parallèles, leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont le même coefficient directeur (pente), car elles ne se croisent jamais.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8750,"question":"Résolvez l'équation suivante : 2(x + 3) = 5x - 1","option_a":"x = 7\/3","option_b":"x = 7","option_c":"x = -7\/3","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant : 2x + 6 = 5x - 1 → 6 + 1 = 5x - 2x → 7 = 3x → x = 7\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8751,"question":"Dans un triangle ABC rectangle en A, si AB = 3 cm et AC = 4 cm, quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"1 cm","option_d":"6 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : BC² = AB² + AC² = 9 + 16 = 25 → BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8752,"question":"La fonction f(x) = x² - 2x + 1 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette fonction est un carré parfait : f(x) = (x - 1)² ≥ 0 pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]