Quiz Maths : Maîtrisez les exercices types de 4ème année secondaire

Question 1 sur 10 10:00

[{"id":56951,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x + 2x","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":56952,"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 = b² - 4ac = (-4)² - 4*1*4 = 16 - 16 = 0. Une solution double existe, donc les solutions ne sont pas distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56953,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal :","option_a":"À la somme des carrés des deux autres côtés","option_b":"À la différence des carrés des deux autres côtés","option_c":"Au produit des deux autres côtés","option_d":"À la moitié de la somme des deux autres côtés","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56954,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56955,"question":"Résoudre l'inéquation 2x - 3 \u003E 5.","option_a":"x \u003E 4","option_b":"x \u003E 1","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. L'inéquation se résout en isolant x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56956,"question":"La droite d'équation y = 2x + 3 passe-t-elle par le point (1, 5) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x = 1, y = 2*1 + 3 = 5. Le point (1, 5) appartient bien à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56957,"question":"Quelle est la valeur de sin(π\/2) ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/2) = 1, car π\/2 correspond à 90° et sin(90°) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56958,"question":"L'équation 3x + 2 = 0 admet-elle une solution positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"3x + 2 = 0 ⇒ x = -2\/3. La solution est négative, donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56959,"question":"Quelle est l'aire d'un cercle de rayon 3 cm ?","option_a":"9π cm²","option_b":"6π cm²","option_c":"3π cm²","option_d":"18π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un cercle se calcule par la formule A = πr². Ici, A = π*3² = 9π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56960,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² est toujours positive ou nulle (sauf en x = 0 où elle est nulle). La fonction est donc croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]