Quiz : Maîtrisez les bases de l'algèbre en 1ère année secondaire

Question 1 sur 10 10:00

[{"id":45616,"question":"Quelle est la solution de l'équation 3x + 5 = 2x - 1 ?","option_a":"x = -6","option_b":"x = 6","option_c":"x = -4","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Soustraire 2x des deux côtés : x + 5 = -1. Puis soustraire 5 : x = -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45617,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La solution est x \u003E 4 (ajouter 3 : 2x \u003E 8, puis diviser par 2 : x \u003E 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45618,"question":"Quel est le développement de (x + 2)(x - 3) ?","option_a":"x² - x - 6","option_b":"x² + x - 6","option_c":"x² - 5x - 6","option_d":"x² - x + 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Utiliser la distributivité : x*x + x*(-3) + 2*x + 2*(-3) = x² - 3x + 2x - 6 = x² - x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45619,"question":"La factorisation de x² - 9 est :","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"x(x - 9)","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une identité remarquable : a² - b² = (a - b)(a + b). Ici, a = x et b = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45620,"question":"L'équation x² = 16 a pour solutions :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Vrai. Les solutions sont x = 4 et x = -4 (car 4² = 16 et (-4)² = 16).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45621,"question":"Quel est le résultat de 2(x + 3) - 4x ?","option_a":"-2x + 6","option_b":"2x + 6","option_c":"-2x - 6","option_d":"6x - 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développer : 2x + 6 - 4x = -2x + 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45622,"question":"L'inéquation 5 - x ≤ 2x + 1 a pour solution :","option_a":"x ≥ 4\/3","option_b":"x ≤ 4\/3","option_c":"x ≥ 3\/4","option_d":"x ≤ 3\/4","option_e":"","option_f":"","bonne_reponse":"B","explication":"Ajouter x des deux côtés : 5 ≤ 3x + 1. Puis soustraire 1 : 4 ≤ 3x. Diviser par 3 : x ≥ 4\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45623,"question":"La factorisation de x² + 6x + 9 est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Vrai. C'est un carré parfait : (x + 3)² = x² + 6x + 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45624,"question":"Quel est le résultat de (3x - 2)(x + 4) ?","option_a":"3x² + 10x - 8","option_b":"3x² + 14x - 8","option_c":"3x² - 10x - 8","option_d":"3x² + 10x + 8","option_e":"","option_f":"","bonne_reponse":"B","explication":"Développer : 3x*x + 3x*4 - 2*x - 2*4 = 3x² + 12x - 2x - 8 = 3x² + 10x - 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45625,"question":"L'équation 4x + 1 = 2(2x + 0,5) a :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Vrai. L'équation est toujours vraie (4x + 1 = 4x + 1), donc elle a une infinité de solutions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]