Quiz Maths : Testez vos connaissances en 4ème année secondaire

Question 1 sur 10 10:00

[{"id":50261,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 1","option_d":"x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50262,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50263,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3)\/(x² - 1) quand x 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 le numérateur et le dénominateur par x², on obtient lim (2 + 3\/x²)\/(1 - 1\/x²) = 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50264,"question":"Le triangle ABC avec AB=5, BC=12 et AC=13 est rectangle en B.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifiez le théorème de Pythagore : AB² + BC² = 25 + 144 = 169 = AC². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50265,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 5 ?","option_a":"x \u003E 12","option_b":"x \u003C 12","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x \u003E 5 + 7 → x \u003E 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50266,"question":"La fonction f(x) = x³ est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ x³, donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50267,"question":"Quelle est l'aire d'un cercle de rayon r = 4 cm ? (π ≈ 3,14)","option_a":"16π cm²","option_b":"8π cm²","option_c":"50,24 cm²","option_d":"25,12 cm²","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'aire d'un cercle est A = πr² = 3,14 × 16 = 50,24 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50268,"question":"La suite définie par uₙ = 2n + 1 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si uₙ₊₁ - uₙ est constant. Ici, uₙ₊₁ - uₙ = 2(n+1)+1 - (2n+1) = 2, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50269,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 2","option_b":"x = 1","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"2^(x+1) = 2³ → x+1 = 3 → x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50270,"question":"Le vecteur u(3; -2) et v(-1; 4) sont orthogonaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux vecteurs sont orthogonaux si leur produit scalaire est nul. u·v = 3×(-1) + (-2)×4 = -3 -8 = -11 ≠ 0. Ils ne sont pas orthogonaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]