Quiz Mathématiques : 4ème année secondaire — Série 1

Question 1 sur 10 10:00

[{"id":21608,"question":"Quelle est la solution de l'équation 3x - 5 = 16 ?","option_a":"x = 7","option_b":"x = 9","option_c":"x = 11","option_d":"x = 13","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 16, on ajoute 5 des deux côtés : 3x = 21, puis on divise par 3 : x = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21609,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[. Elle n'est donc pas toujours croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21610,"question":"Quel est le résultat de (2x + 3)(x - 4) ?","option_a":"2x² - 5x - 12","option_b":"2x² - 11x - 12","option_c":"2x² + 5x - 12","option_d":"2x² + 11x - 12","option_e":"","option_f":"","bonne_reponse":"B","explication":"En développant (2x + 3)(x - 4), on obtient 2x² - 8x + 3x - 12 = 2x² - 5x - 12. Attention à bien regrouper les termes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21611,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21612,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + 5x - 7 ?","option_a":"f'(x) = 12x² - 4x + 5","option_b":"f'(x) = 12x² - 4x - 7","option_c":"f'(x) = 4x² - 2x + 5","option_d":"f'(x) = 12x² - 4x + 5x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = 4x³ - 2x² + 5x - 7 est f'(x) = 12x² - 4x + 5 (dérivée terme à terme).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21613,"question":"L'équation x² + 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation x² + 4x + 4 = 0 peut s'écrire (x + 2)² = 0, qui admet une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21614,"question":"Quel est le périmètre d'un cercle de rayon 5 cm ?","option_a":"10π cm","option_b":"25π cm","option_c":"5π cm","option_d":"20π cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le périmètre d'un cercle est donné par P = 2πr. Avec r = 5 cm, P = 2π × 5 = 10π cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21615,"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 interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21616,"question":"Quelle est la solution de l'inéquation 2x - 7 \u003E 5 ?","option_a":"x \u003E 6","option_b":"x \u003E 1","option_c":"x \u003C 6","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 2x - 7 \u003E 5, on ajoute 7 des deux côtés : 2x \u003E 12, puis on divise par 2 : x \u003E 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21617,"question":"Le vecteur u(3, -2) et le vecteur v(-3, 2) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs u(3, -2) et v(-3, 2) sont colinéaires car v = -1 × u. Ils ont donc la même direction.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]