Maths 3ème année : Testez vos connaissances en algèbre et géométrie

Question 1 sur 10 10:00

[{"id":9933,"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":"A","explication":"En soustrayant 2x des deux côtés, on obtient x + 5 = -7. Puis en soustrayant 5, on trouve x = -12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9934,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"6 cm","option_d":"4,5 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9935,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 12 = 4 \u003E 0, donc la fonction s'annule en x = 1 et x = 3. Elle n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9936,"question":"Quel est le coefficient directeur de la droite d'équation y = 2x - 5 ?","option_a":"2","option_b":"-5","option_c":"5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation réduite y = mx + p, m représente le coefficient directeur. Ici, m = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9937,"question":"L'aire d'un cercle de rayon r est donnée par la formule πr².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de l'aire d'un cercle est bien πr², où r est le rayon.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9938,"question":"Résolvez l'inéquation 2x - 3 ≤ 7.","option_a":"x ≤ 5","option_b":"x ≥ 5","option_c":"x ≤ 2","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En ajoutant 3 des deux côtés, on obtient 2x ≤ 10, puis en divisant par 2, x ≤ 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9939,"question":"Dans un triangle isocèle, les angles à la base sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, un triangle isocèle a deux côtés égaux et les angles opposés à ces côtés sont égaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9940,"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":9941,"question":"La médiatrice d'un segment est la droite qui passe par son milieu et est perpendiculaire à ce segment.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la médiatrice d'un segment vérifie ces deux propriétés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9942,"question":"Calculez f(2) pour la fonction f(x) = 3x² - 2x + 1.","option_a":"7","option_b":"9","option_c":"11","option_d":"5","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(2) = 3*(2)² - 2*2 + 1 = 12 - 4 + 1 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]