Quiz : Maîtrisez les équations et la géométrie en 2ème année secondaire

Question 1 sur 10 10:00

[{"id":43316,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = 2","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43317,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43318,"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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43319,"question":"Si sin(θ) = 0,5, alors θ = 30° + k×360° (k ∈ ℤ).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(θ) = 0,5 a aussi pour solution θ = 150° + k×360° (k ∈ ℤ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43320,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 ⇒ 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43321,"question":"Le triangle ABC avec AB = 5, BC = 12 et AC = 13 est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"5² + 12² = 25 + 144 = 169 = 13², donc le triangle est rectangle en B (théorème de Pythagore).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43322,"question":"Quelle est la valeur de x dans l'équation 4(x - 2) = 2x + 8 ?","option_a":"x = 6","option_b":"x = 4","option_c":"x = 8","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x - 8 = 2x + 8 ⇒ 2x = 16 ⇒ x = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43323,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2, et comme le coefficient de x² est positif, c'est un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43324,"question":"Quelle est la solution de l'équation |x - 3| = 5 ?","option_a":"x = 8 ou x = -2","option_b":"x = 2 ou x = -8","option_c":"x = 3 ou x = -5","option_d":"x = 5 ou x = -5","option_e":"","option_f":"","bonne_reponse":"A","explication":"|x - 3| = 5 ⇒ x - 3 = 5 ou x - 3 = -5 ⇒ x = 8 ou x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43325,"question":"Le produit de deux nombres impairs est toujours impair.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Soient a = 2k + 1 et b = 2m + 1, alors a×b = 4km + 2k + 2m + 1 = 2(2km + k + m) + 1, donc impair.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]