Maths 3ème année secondaire : Testez vos connaissances en 10 questions !

Question 1 sur 10 10:00

[{"id":49061,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la formule des racines du second degré : x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4. Les solutions sont donc 2 et 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49062,"question":"La dérivée de f(x) = x³ + 2x² - 5x + 1 est f'(x) = 3x² + 4x - 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée correcte est f'(x) = 3x² + 4x - 5, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49063,"question":"Quel est le résultat de ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x²","option_c":"3x³ + x² + C","option_d":"x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². On ajoute la constante C pour l'intégrale indéfinie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49064,"question":"Dans un triangle rectangle, si cos(θ) = 3\/5, alors sin(θ) = ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"2\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, sin(θ) = √(1 - cos²(θ)) = √(1 - 9\/25) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49065,"question":"La fonction f(x) = x² est toujours croissante sur ℝ.","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":49066,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49067,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements incompatibles, la probabilité de leur union est bien la somme de leurs probabilités individuelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49068,"question":"La limite de (x² + 1)\/x quand x tend vers +∞ est :","option_a":"0","option_b":"+∞","option_c":"1","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x, on obtient x + 1\/x, dont la limite est +∞ quand x tend vers +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49069,"question":"Le vecteur u(2, -3) a pour norme :","option_a":"√5","option_b":"√13","option_c":"5","option_d":"13","option_e":"","option_f":"","bonne_reponse":"B","explication":"La norme d'un vecteur u(a, b) est √(a² + b²) = √(4 + 9) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49070,"question":"Si f(x) = ln(x), alors f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction logarithme népérien est bien f'(x) = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]