Quiz Mathématiques : Équations, Fonctions et Dérivées — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":66712,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 2x + 7 → 3x - 2x = 7 + 5 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66713,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction a un minimum en x=2 (f(2)=-1), donc elle n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66714,"question":"Quelle est la dérivée de f(x) = 4x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 12x² - 4x + 5","option_b":"f'(x) = 12x² - 4x + 5x","option_c":"f'(x) = 4x² - 2x + 5","option_d":"f'(x) = 12x - 4x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², donc 4x³ donne 12x². La dérivée de -2x² est -4x, et celle de 5x est 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66715,"question":"L'inéquation 2x + 3 \u003E 5x - 4 a pour solution :","option_a":"x \u003C 7\/3","option_b":"x \u003E 7\/3","option_c":"x \u003C -7\/3","option_d":"x \u003E -7\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 5x - 4 → 3 + 4 \u003E 5x - 2x → 7 \u003E 3x → x \u003C 7\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66716,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet une asymptote verticale en x = 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le dénominateur s'annule en x=3, ce qui crée une asymptote verticale en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66717,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"x ∈ ]2 ; 3[","option_b":"x ∈ ]-∞ ; 2[ ∪ ]3 ; +∞[","option_c":"x ∈ [2 ; 3]","option_d":"x ∈ ]-∞ ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x=2 et x=3. Le polynôme est négatif entre les racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66718,"question":"La dérivée de f(x) = √(x) est égale à :","option_a":"f'(x) = 1\/(2√x)","option_b":"f'(x) = 1\/√x","option_c":"f'(x) = √x \/ 2","option_d":"f'(x) = 2\/√x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de √x = x^(1\/2) est (1\/2)x^(-1\/2) = 1\/(2√x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66719,"question":"L'équation x² + 4x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66720,"question":"Quelle est la valeur de f(2) pour f(x) = 3x² - 2x + 1 ?","option_a":"f(2) = 9","option_b":"f(2) = 11","option_c":"f(2) = 7","option_d":"f(2) = 5","option_e":"","option_f":"","bonne_reponse":"B","explication":"f(2) = 3*(2)² - 2*2 + 1 = 12 - 4 + 1 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66721,"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 \u003C 0 pour tout x ≠ 0, donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]