Maîtrisez la fonction carré : QCM et défis mathématiques

Question 1 sur 10 10:00

[{"id":58266,"question":"Quelle est l'image de -3 par la fonction carré ?","option_a":"-9","option_b":"9","option_c":"6","option_d":"0","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction carré associe à chaque nombre son carré. Ainsi, f(-3) = (-3)² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58267,"question":"La fonction carré est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x) pour tout x. Ici, f(-x) = (-x)² = x² = f(x), donc elle est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58268,"question":"Quel est le sens de variation de la fonction carré sur l'intervalle [2, 5] ?","option_a":"Décroissante","option_b":"Croissante","option_c":"Constante","option_d":"Non monotone","option_e":"","option_f":"","bonne_reponse":"B","explication":"Sur [0, +∞[, la fonction carré est croissante. Comme 2 et 5 sont dans cet intervalle, elle y est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58269,"question":"L'équation x² = 16 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² = 16 ⇒ x = 4 ou x = -4. L'équation admet donc deux solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58270,"question":"Quelle est la valeur minimale de la fonction carré sur ℝ ?","option_a":"-∞","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction carré atteint sa valeur minimale en x = 0, où f(0) = 0. Elle n'a pas de maximum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58271,"question":"La courbe de la fonction carré passe-t-elle par le point (1, 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(1) = 1² = 1. Le point (1, 1) appartient donc à la courbe de la fonction carré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58272,"question":"Pour quelles valeurs de x la fonction carré est-elle négative ?","option_a":"x ∈ ℝ","option_b":"x ∈ ]-∞, 0[","option_c":"x ∈ ∅","option_d":"x ∈ [0, +∞[","option_e":"","option_f":"","bonne_reponse":"C","explication":"La fonction carré est toujours positive ou nulle (x² ≥ 0 pour tout x réel). Elle n'est jamais strictement négative.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58273,"question":"Quel est le sommet de la parabole représentant la fonction carré ?","option_a":"(0, 1)","option_b":"(1, 0)","option_c":"(0, 0)","option_d":"(1, 1)","option_e":"","option_f":"","bonne_reponse":"C","explication":"La parabole de la fonction carré a son sommet en (0, 0), point où la fonction atteint son minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58274,"question":"L'inéquation x² ≤ 9 admet-elle des solutions ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² ≤ 9 ⇒ -3 ≤ x ≤ 3. L'inéquation admet donc une infinité de solutions dans l'intervalle [-3, 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58275,"question":"Quelle est la dérivée de la fonction carré ?","option_a":"f'(x) = 2x","option_b":"f'(x) = x","option_c":"f'(x) = 0","option_d":"f'(x) = -2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = x² est f'(x) = 2x, obtenue par la règle de dérivation des fonctions puissances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]