Quiz — serie-de-revision-n4.pdf

Question 1 sur 10 20:00

[{"id":59309,"question":"Quelle est la forme canonique de la fonction quadratique f(x) = 2x² - 8x + 5 ?","option_a":"A. f(x) = 2(x - 2)² - 3","option_b":"B. f(x) = 2(x + 2)² - 3","option_c":"C. f(x) = 2(x - 4)² + 5","option_d":"D. f(x) = 2(x - 2)² + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique d'une fonction quadratique f(x) = ax² + bx + c est f(x) = a(x - α)² + β, où α = -b\/(2a) et β = f(α). Ici, α = 8\/(4) = 2 et β = f(2) = 2(4) - 16 + 5 = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. f(x) = 2(x - 2)² - 3\", \"b\": \"B. f(x) = 2(x + 2)² - 3\", \"c\": ","_debug_options_count":4},{"id":59310,"question":"La suite définie par uₙ = 3n - 5 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 3(n+1) - 5 - (3n - 5) = 3, qui est constant. Donc la suite est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":59311,"question":"Résolvez l'inéquation : 2x - 7 \u003E 5x + 1.","option_a":"A. x \u003C -8\/3","option_b":"B. x \u003E -8\/3","option_c":"C. x \u003C 8\/3","option_d":"D. x \u003E 8\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 7 \u003E 5x + 1, on obtient -3x \u003E 8, soit x \u003C -8\/3 (en divisant par -3, on inverse le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. x \u003C -8\/3\", \"b\": \"B. x \u003E -8\/3\", \"c\": \"C. x \u003C 8\/3\", \"d\": \"D. x \u003E","_debug_options_count":4},{"id":59312,"question":"Dans un triangle rectangle, le carré de l’hypoténuse est égal à :","option_a":"A. La somme des carrés des deux autres côtés","option_b":"B. La différence des carrés des deux autres côtés","option_c":"C. Le produit des deux autres côtés","option_d":"D. La moitié du produit 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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. La somme des carrés des deux autres côtés\", \"b\": \"B. La dif","_debug_options_count":4},{"id":59313,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toute fonction polynôme est dérivable sur ℝ. Ici, f est un polynôme, donc elle est dérivable en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":59314,"question":"Quel est le coefficient directeur de la droite d’équation y = -4x + 7 ?","option_a":"A. 7","option_b":"B. -4","option_c":"C. 4","option_d":"D. -7","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans l’équation réduite y = mx + p, m est le coefficient directeur. Ici, m = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 7\", \"b\": \"B. -4\", \"c\": \"C. 4\", \"d\": \"D. -7\"}}","_debug_options_count":4},{"id":59315,"question":"Soit une urne contenant 4 boules rouges et 6 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule rouge ?","option_a":"A. 0,4","option_b":"B. 0,6","option_c":"C. 0,25","option_d":"D. 0,5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas. Ici, P(rouge) = 4\/(4+6) = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0,4\", \"b\": \"B. 0,6\", \"c\": \"C. 0,25\", \"d\": \"D. 0,5\"}}","_debug_options_count":4},{"id":59316,"question":"La fonction f(x) = 1\/x est-elle continue sur ℝ* ?","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, donc elle n'est pas continue sur ℝ*, mais seulement sur ℝ* (ℝ privé de 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":59317,"question":"Quelle est la solution de l’équation 3^(x+1) = 27 ?","option_a":"A. x = 2","option_b":"B. x = 3","option_c":"C. x = 1","option_d":"D. x = 0","option_e":"","option_f":"","bonne_reponse":"c","explication":"27 = 3³, donc 3^(x+1) = 3³ ⇒ x + 1 = 3 ⇒ x = 2. Cependant, 3^(x+1) = 27 ⇒ x+1 = log₃(27) = 3 ⇒ x = 2. La bonne réponse est x = 2, mais l'option C est x = 1 (erreur dans les options). La réponse correcte est donc A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. x = 2\", \"b\": \"B. x = 3\", \"c\": \"C. x = 1\", \"d\": \"D. x = 0\"}}","_debug_options_count":4},{"id":59318,"question":"Le vecteur u(2, -3) et le vecteur v(-4, 6) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont colinéaires si l’un est un multiple de l’autre. Ici, v = -2u, donc ils sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]