Quiz Mathématiques : Équations, Fonctions et Géométrie — Niveau 4M

Question 1 sur 10 10:00

[{"id":19748,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 ou x = -6","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0. Les solutions sont donc x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19749,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² - 4x + 3 est une parabole ouverte vers le haut avec un sommet en x = 2. Elle est négative entre ses racines (x=1 et x=3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19750,"question":"Quelle est l'équation de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"y = 2x","option_b":"y = 3x - 1","option_c":"y = x + 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (6-2)\/(3-1) = 2. L'équation est donc y = 2x + b. En utilisant A(1,2), on trouve b = 0. D'où y = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19751,"question":"La moyenne d'une série statistique est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La moyenne et la médiane sont égales uniquement si la série est symétrique. Sinon, elles peuvent différer.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19752,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x-3)(x+3)","option_b":"(x-9)(x+1)","option_c":"(x-3)²","option_d":"(x+3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, donc factorisable en (x-3)(x+3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19753,"question":"Le cercle d'équation (x-2)² + (y+1)² = 16 a pour centre :","option_a":"(2, -1)","option_b":"(-2, 1)","option_c":"(2, 1)","option_d":"(-2, -1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation standard d'un cercle est (x-h)² + (y-k)² = r², où (h,k) est le centre. Ici, h=2 et k=-1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19754,"question":"Si f(x) = 3x + 2, alors f(-1) = -5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"f(-1) = 3*(-1) + 2 = -3 + 2 = -1 ≠ -5. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19755,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 5 \u003E 3x + 1 → -5 - 1 \u003E 3x - 2x → -6 \u003E x → x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19756,"question":"La fonction g(x) = -x² + 4x - 3 admet un maximum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction g(x) = -x² + 4x - 3 est une parabole ouverte vers le bas. Son sommet (maximum) est en x = -b\/(2a) = -4\/(2*(-1)) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19757,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces : 3 nombres pairs (2,4,6) et 3 nombres impairs. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]