Quiz : Maîtrisez les fonctions dérivées et la trigonométrie — 2ème année Secondaire

Question 1 sur 10 10:00

[{"id":26718,"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 - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26719,"question":"L'équation sin(x) = √2\/2 admet-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans [0, π], sin(x) = √2\/2 admet deux solutions : x = π\/4 et x = 3π\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26720,"question":"Soit f(x) = x³ - 3x² + 2. Quel est le coefficient directeur de la tangente à la courbe au point d'abscisse x = 1 ?","option_a":"A. -3","option_b":"B. 0","option_c":"C. 3","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur de la tangente est f'(1). f'(x) = 3x² - 6x, donc f'(1) = 3 - 6 = -3. Attention, la question demande le coefficient directeur, mais l'option B correspond à f(1) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26721,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) est égal à :","option_a":"A. 4\/5","option_b":"B. 3\/4","option_c":"C. 5\/3","option_d":"D. 2\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, cos(θ) = √(1 - sin²(θ)) = √(1 - 9\/25) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26722,"question":"La dérivée de la fonction f(x) = cos(2x) est f'(x) = -2sin(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = -sin(2x) * 2 = -2sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26723,"question":"Quelle est la valeur de tan(π\/3) ?","option_a":"A. 1","option_b":"B. √3","option_c":"C. 1\/√3","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"tan(π\/3) = sin(π\/3)\/cos(π\/3) = (√3\/2)\/(1\/2) = √3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26724,"question":"Soit un cube d'arête 4 cm. Quel est son volume ?","option_a":"A. 16 cm³","option_b":"B. 64 cm³","option_c":"C. 32 cm³","option_d":"D. 12 cm³","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le volume d'un cube est donné par V = arête³ = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26725,"question":"La fonction f(x) = x² + 1 est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 2x est négative pour x \u003C 0, donc la fonction est décroissante sur ]-∞, 0[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26726,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"A. 3e^(3x)","option_b":"B. e^(3x)","option_c":"C. 3x e^(3x)","option_d":"D. e^(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation des fonctions exponentielles, f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26727,"question":"Dans un repère orthonormé, la distance entre les points A(1, 2) et B(4, 6) est :","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. √29","option_e":"","option_f":"","bonne_reponse":"B","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. L'option B correspond à la somme des coordonnées.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]