Maths 4ème année secondaire : Devoir de contrôle – Révision des notions clés

Question 1 sur 10 10:00

[{"id":8853,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -2","option_c":"x = 5","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x = 7 + 5, soit x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8854,"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 f(x) = ax + b. Ici, f(x) est un polynôme du second degré (terme en x²), donc ce n'est pas une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8855,"question":"Quel est le développement de (x + 3)(2x - 5) ?","option_a":"2x² + x - 15","option_b":"2x² - 5x + 6","option_c":"x² + 6x - 15","option_d":"2x² + 6x - 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 2x² - 5x + 6x - 15 = 2x² + x - 15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8856,"question":"Dans une série statistique, la moyenne est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La moyenne et la médiane sont égales uniquement si la série est symétrique. Dans le cas général, elles peuvent être différentes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8857,"question":"Résolvez l'inéquation : -2x + 4 \u003E 6.","option_a":"x \u003C -1","option_b":"x \u003E -1","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient -2x \u003E 2, soit x \u003C -1 (car on divise par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8858,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 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},{"id":8859,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"√25","option_d":"10","option_e":"","option_f":"","bonne_reponse":"A","explication":"√(16) = 4 et √(9) = 3, donc 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8860,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, a² + b² = c² où c est l'hypoténuse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8861,"question":"Factorisez l'expression : x² - 9.","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, donc (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":8862,"question":"La dérivée de f(x) = x³ est f'(x) = 3x².","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}]