Quiz Mathématiques : Équations, Fonctions et Géométrie — 3ème Secondaire

Question 1 sur 10 10:00

[{"id":21748,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21749,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est un polynôme du second degré avec un discriminant positif (Δ = 4), donc elle s'annule en deux points et n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21750,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 7 ?","option_a":"7","option_b":"-2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est le nombre devant x, ici -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21751,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"6 cm","option_c":"√34 cm","option_d":"2 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : 3² + x² = 5² → x² = 16 → x = 4 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21752,"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 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":21753,"question":"Résolvez l'inéquation 2x + 3 ≤ 7.","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≤ 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 2x ≤ 4 → x ≤ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21754,"question":"Quel est le discriminant de l'équation x² - 6x + 9 = 0 ?","option_a":"0","option_b":"12","option_c":"36","option_d":"9","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est Δ = b² - 4ac = (-6)² - 4(1)(9) = 36 - 36 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21755,"question":"La somme des angles d'un triangle est-elle toujours égale à 180° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle, la somme des angles est toujours égale à 180°, que ce soit en géométrie plane ou dans l'espace.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21756,"question":"Quelle est la forme factorisée de 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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21757,"question":"Si f(x) = 3x + 2 et g(x) = 2x - 1, quelle est la valeur de f(g(2)) ?","option_a":"11","option_b":"7","option_c":"14","option_d":"5","option_e":"","option_f":"","bonne_reponse":"B","explication":"g(2) = 2(2) - 1 = 3 → f(g(2)) = f(3) = 3(3) + 2 = 11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]