Maths 3ème année : Évaluation des compétences clés

Question 1 sur 10 10:00

[{"id":50301,"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 + 2","option_d":"D. 6x + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50302,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-4)² - 4*1*4 = 16 - 16 = 0. Une seule solution double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50303,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A. x \u003E 1","option_b":"B. x \u003C 4","option_c":"C. x \u003E 4","option_d":"D. x \u003C 1","option_e":"","option_f":"","bonne_reponse":"C","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50304,"question":"La fonction f(x) = x³ est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Sa dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc f est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50305,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² en x = 1 ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 0","option_d":"D. -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 2x donne le coefficient directeur. En x=1, f'(1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50306,"question":"L'équation 5x + 7 = 0 a pour solution x = -7\/5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"5x + 7 = 0 ⇒ 5x = -7 ⇒ x = -7\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50307,"question":"Quelle est l'image de 2 par la fonction f(x) = 4x - 1 ?","option_a":"A. 7","option_b":"B. 5","option_c":"C. 8","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(2) = 4*2 - 1 = 8 - 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50308,"question":"La fonction f(x) = -x² + 4x est-elle concave sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Sa dérivée seconde f''(x) = -2 est négative, donc la fonction est concave.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50309,"question":"Quelle est la solution de l'équation |x - 3| = 5 ?","option_a":"A. x = 8 ou x = -2","option_b":"B. x = 2 ou x = -8","option_c":"C. x = 3 ou x = -5","option_d":"D. x = 5 ou x = -5","option_e":"","option_f":"","bonne_reponse":"A","explication":"|x - 3| = 5 ⇒ x - 3 = 5 ou x - 3 = -5 ⇒ x = 8 ou x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50310,"question":"La dérivée de la fonction f(x) = √x est-elle f'(x) = 1\/(2√x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","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}]