Révisons les maths : Algèbre, Analyse et Géométrie — 3ème année secondaire

Question 1 sur 10 10:00

[{"id":67362,"question":"Quelle est la solution de l’équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons l’équation 2x² - 5x + 2 = 0 en utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67363,"question":"La dérivée de la fonction 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 de f(x) = x³ + 2x² - 5x + 1 est bien f’(x) = 3x² + 4x - 5, car la dérivée de x³ est 3x², celle de 2x² est 4x, et celle de -5x est -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67364,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"3","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x → +∞, on divise le numérateur et le dénominateur par x² : f(x) = (3 + 2\/x - 1\/x²)\/(1 - 4\/x²). La limite est donc 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67365,"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, sin²(θ) + cos²(θ) = 1. Donc sin(θ) = √(1 - (3\/5)²) = √(16\/25) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67366,"question":"L’équation x² + y² - 4x + 6y - 3 = 0 représente un cercle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En complétant les carrés, on obtient (x-2)² + (y+3)² = 16, ce qui est l’équation d’un cercle de centre (2, -3) et de rayon 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67367,"question":"Quelle est la valeur de la suite définie par uₙ = 2n² - 3n + 1 pour n = 4 ?","option_a":"17","option_b":"25","option_c":"33","option_d":"41","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour n = 4, u₄ = 2*(4)² - 3*4 + 1 = 32 - 12 + 1 = 21. La réponse correcte est 21 (aucune option proposée ne correspond).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67368,"question":"La probabilité de tirer un as dans un jeu de 52 cartes est de 1\/13.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un jeu de 52 cartes contient 4 as. La probabilité est donc 4\/52 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67369,"question":"Quelle est la solution de l’inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 ≤ 2x + 5 → x ≤ 12. La solution est donc x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67370,"question":"La fonction f(x) = 1\/x est décroissante sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f’(x) = -1\/x² est négative pour tout x ≠ 0, donc la fonction est décroissante sur ]-∞,0[ et ]0,+∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":67371,"question":"Quelle est la moyenne d’une série statistique dont les valeurs sont 5, 7, 9, 11 et 13 ?","option_a":"7","option_b":"9","option_c":"11","option_d":"13","option_e":"","option_f":"","bonne_reponse":"B","explication":"La moyenne est (5 + 7 + 9 + 11 + 13)\/5 = 45\/5 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]