Quiz de révision : Algèbre et Analyse pour la 4ème année secondaire

Question 1 sur 10 10:00

[{"id":50811,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'équation : 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50812,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est un polynôme du second degré avec un discriminant positif (Δ = 4), donc elle change de signe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50813,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 5 ?","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 6x² - 4x + 1","option_c":"f'(x) = 3x² - 2x + 1","option_d":"f'(x) = 9x² - 4x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme à terme : (3x³)' = 9x², (-2x²)' = -4x, (x)' = 1, (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50814,"question":"Le nombre 0,000001 peut s'écrire en notation scientifique comme :","option_a":"1 × 10⁻⁶","option_b":"1 × 10⁻⁵","option_c":"1 × 10⁶","option_d":"1 × 10⁵","option_e":"","option_f":"","bonne_reponse":"A","explication":"En notation scientifique, on écrit un nombre sous la forme a × 10ⁿ où 1 ≤ a \u003C 10 et n est un entier. Ici, 0,000001 = 1 × 10⁻⁶.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50815,"question":"La limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) quand x tend vers +∞ est égale à :","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les limites à l'infini des fonctions rationnelles, on compare les degrés des polynômes. Ici, les degrés sont égaux (2), donc la limite est le rapport des coefficients dominants : 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50816,"question":"Un événement certain a une probabilité égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un événement certain a une probabilité de 1 (ou 100%).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50817,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'inéquation : 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50818,"question":"La fonction f(x) = √(x - 2) est définie pour :","option_a":"x ≥ 2","option_b":"x \u003E 2","option_c":"x ≤ 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La racine carrée est définie pour les valeurs où l'expression sous la racine est positive ou nulle : x - 2 ≥ 0 → x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50819,"question":"Le centre de symétrie de la fonction f(x) = x³ - 3x est :","option_a":"O(0,0)","option_b":"A(1, -2)","option_c":"B(-1, 2)","option_d":"C(0, -3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une fonction polynôme de degré impair, le centre de symétrie est l'origine O(0,0) si la fonction est impaire. Vérification : f(-x) = -x³ + 3x = -f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50820,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est :","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces, dont 3 paires (2, 4, 6). La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]