Maths 4ème : Évaluation des compétences du 1er trimestre

Question 1 sur 10 10:00

[{"id":26288,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = -12","option_b":"x = 12","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26289,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine est de la forme ax + b. Ici, le terme x² indique qu'il s'agit d'une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26290,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"-4","option_b":"7","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est le nombre devant x, soit -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26291,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, une propriété fondamentale de la géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26292,"question":"Résolvez l'inéquation : 2x + 3 \u003E 5x - 6","option_a":"x \u003C 3","option_b":"x \u003E 3","option_c":"x \u003C -3","option_d":"x \u003E -3","option_e":"","option_f":"","bonne_reponse":"C","explication":"En soustrayant 2x et en ajoutant 6, on obtient 9 \u003E 3x, soit x \u003C 3. Mais attention à l'inversion du sens de l'inégalité si on divise par un nombre négatif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26293,"question":"La dérivée de la fonction f(x) = x³ est f'(x) = 3x². Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est bien 3x², selon la règle de dérivation des puissances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26294,"question":"Quel est le discriminant de l'équation x² - 4x + 4 = 0 ?","option_a":"0","option_b":"8","option_c":"16","option_d":"-8","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4(1)(4) = 16 - 16 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26295,"question":"Dans un cercle de rayon r, l'aire est donnée par la formule A = πr². Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la formule standard pour calculer l'aire d'un cercle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26296,"question":"Résolvez le 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":"A","explication":"En additionnant les deux équations, on obtient 3x = 6, soit x = 2. En remplaçant, y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26297,"question":"La fonction f(x) = 1\/x est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]