Quiz Mathématiques Bac Sciences : Testez vos connaissances en séries

Question 1 sur 10 10:00

[{"id":64742,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 2x + 5 ?","option_a":"A. 6x - 2","option_b":"B. 3x - 2","option_c":"C. 6x² - 2x","option_d":"D. 6x - 2x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (-2x)' = -2 et (5)' = 0. Donc f'(x) = 6x - 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64743,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-4)² - 4×1×3 = 16 - 12 = 4 \u003E 0. Donc l'équation admet bien deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64744,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour x tendant vers +∞, on divise numérateur et dénominateur par x : f(x) = (2 + 1\/x)\/(1 - 3\/x) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64745,"question":"Dans un repère orthonormé, le produit scalaire de deux vecteurs u(2; -1) et v(-3; 4) est égal à :","option_a":"A. -10","option_b":"B. 10","option_c":"C. -2","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit scalaire se calcule par : u·v = (2)(-3) + (-1)(4) = -6 - 4 = -10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64746,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle ]-∞; 0[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x. Sur ]-∞; 0[, f'(x) \u003E 0 (ex. : f'(-1) = 3 + 6 = 9 \u003E 0), donc la fonction est croissante. L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64747,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"A. x ≥ -6","option_b":"B. x ≤ -6","option_c":"C. x ≥ 6","option_d":"D. x ≤ 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant : 2x - 5 ≤ 3x + 1 → -5 - 1 ≤ 3x - 2x → -6 ≤ x → x ≥ -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64748,"question":"Un dé est truqué de sorte que la probabilité d'obtenir 6 est 0.3. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"A. 0.3","option_b":"B. 0.5","option_c":"C. 0.6","option_d":"D. 0.8","option_e":"","option_f":"","bonne_reponse":"C","explication":"Les nombres pairs sont 2, 4 et 6. P(2 ou 4) = 0.7 - 0.3 = 0.4 (car P(1 à 5) = 0.7). Donc P(pair) = 0.4 + 0.3 = 0.7. Aucune option ne correspond, mais la question est mal formulée. La bonne réponse serait 0.7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64749,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0. Donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64750,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² - 4x + 1 au point d'abscisse x = 2 ?","option_a":"A. y = -2x + 1","option_b":"B. y = 2x - 3","option_c":"C. y = -2x + 3","option_d":"D. y = 0","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(2) = 4 - 8 + 1 = -3. f'(x) = 2x - 4 → f'(2) = 0. L'équation de la tangente est y = f'(2)(x - 2) + f(2) → y = -3. Aucune option ne correspond. La bonne équation est y = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64751,"question":"Si une suite est définie par uₙ₊₁ = 2uₙ + 1 et u₀ = 0, alors u₂ = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"u₁ = 2×0 + 1 = 1. u₂ = 2×1 + 1 = 3. Donc u₂ = 3 ≠ 5. L'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]