Quiz Mathématiques — 3ème année secondaire : Algèbre, Géométrie & Analyse

Question 1 sur 10 10:00

[{"id":41316,"question":"Quelle est la solution de l'équation 3x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2\/3","option_b":"x = -1 ou x = 2\/3","option_c":"x = 1 ou x = -2\/3","option_d":"x = -1 ou x = -2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation 3x² - 5x + 2 = 0 a pour discriminant Δ = 25 - 24 = 1. Les solutions sont x = (5 ± 1)\/6, soit x = 1 ou x = 2\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41317,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) = ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"1\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, si sin(θ) = 3\/5, alors le côté opposé est 3, l'hypoténuse est 5, et le côté adjacent est 4. Donc cos(θ) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41318,"question":"La fonction f(x) = x³ - 3x + 2 est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1, 1], donc elle n'est pas croissante sur [-2, 2].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41319,"question":"Quel est le produit scalaire de deux vecteurs u(2, -1) et v(3, 4) ?","option_a":"10","option_b":"2","option_c":"6","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire u·v = (2×3) + (-1×4) = 6 - 4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41320,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41321,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n) \/ (n² - 5) quand n tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (2 + 3\/n) \/ (1 - 5\/n²). Quand n → ∞, uₙ → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41322,"question":"Le centre de gravité d'un triangle est l'intersection de ses médianes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le centre de gravité (ou barycentre) d'un triangle est bien l'intersection de ses trois médianes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41323,"question":"Soit f(x) = 2x + 1. Quelle est l'image de -3 par f ?","option_a":"-5","option_b":"-6","option_c":"7","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(-3) = 2×(-3) + 1 = -6 + 1 = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41324,"question":"La dérivée de f(x) = x⁴ - 2x² + 1 est f'(x) = 4x³ - 4x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x⁴ est 4x³, celle de -2x² est -4x, et celle de 1 est 0. Donc f'(x) = 4x³ - 4x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":41325,"question":"Quel est le déterminant d'une matrice 2x2 [[a, b], [c, d]] ?","option_a":"ad - bc","option_b":"a + d","option_c":"ac - bd","option_d":"ab + cd","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le déterminant d'une matrice 2x2 [[a, b], [c, d]] est ad - bc.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]