Quiz : Algèbre, Géométrie et Analyse — 4ème année secondaire

Question 1 sur 10 10:00

[{"id":58406,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58407,"question":"Dans un triangle rectangle, si un angle mesure 30°, alors l'autre angle aigu mesure 60°. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des angles d'un triangle est de 180°. Si un angle est de 90° et un autre de 30°, le troisième mesure bien 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58408,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 1) quand x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x tendant vers l'infini, on garde uniquement les termes de plus haut degré : f(x) ≈ 2x²\/x² = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58409,"question":"Le théorème de Thalès s'applique uniquement dans un triangle rectangle. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique à tout triangle, pas seulement aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58410,"question":"Quelle est la forme canonique de l'équation x² - 4x + 3 = 0 ?","option_a":"(x-2)² - 1 = 0","option_b":"(x-1)² - 4 = 0","option_c":"(x+2)² - 1 = 0","option_d":"(x-3)² - 1 = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est obtenue en complétant le carré : x² - 4x + 3 = (x-2)² - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58411,"question":"Dans un repère orthonormé, les vecteurs u(2; -3) et v(-4; 6) sont-ils colinéaires ?","option_a":"Oui","option_b":"Non","option_c":"Parfois","option_d":"On ne peut pas savoir","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs u et v sont colinéaires car v = -2u (les coordonnées sont proportionnelles).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58412,"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":58413,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x - 5","option_d":"f'(x) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58414,"question":"Un parallélépipède rectangle a 6 faces, 12 arêtes et 8 sommets. Vrai ou Faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un parallélépipède rectangle (ou pavé droit) a bien 6 faces, 12 arêtes et 8 sommets.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58415,"question":"Quelle est l'équation de l'asymptote horizontale de la fonction f(x) = (3x² + 2)\/(x² - 1) ?","option_a":"y = 3","option_b":"y = 2","option_c":"y = 0","option_d":"y = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x tendant vers l'infini, f(x) ≈ 3x²\/x² = 3. L'asymptote horizontale est donc y = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]