Quiz de révision : Mathématiques 4ème année secondaire

Question 1 sur 10 10:00

[{"id":25208,"question":"Quel est le résultat de l'expression (3x + 2)(x - 5) ?","option_a":"3x² - 13x - 10","option_b":"3x² - 15x + 2x - 10","option_c":"3x² - 13x + 10","option_d":"3x² - 17x - 10","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il faut développer l'expression en utilisant la distributivité : (3x)(x) + (3x)(-5) + 2(x) + 2(-5) = 3x² - 15x + 2x - 10 = 3x² - 13x - 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25209,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction du second degré de la forme ax² + bx + c avec a \u003E 0 admet un minimum en x = -b\/(2a). Ici, a = 1 \u003E 0, donc elle admet un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25210,"question":"Quelle est la solution de l'équation 2x - 7 = 3x + 5 ?","option_a":"x = -12","option_b":"x = 12","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : 2x - 3x = 5 + 7 → -x = 12 → x = -12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25211,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"6 cm","option_d":"4 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : BC² = AB² + AC² = 9 + 16 = 25 → BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25212,"question":"La dérivée de la fonction f(x) = 5x³ - 2x² + x est f'(x) = 15x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée se calcule terme par terme : f'(x) = 15x² - 4x + 1, ce qui correspond bien à l'expression donnée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25213,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0.5","option_b":"√3\/2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La valeur exacte de sin(30°) est 0.5, ce qui correspond à 1\/2 dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25214,"question":"L'équation x² + 2x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 4 - 20 = -16 \u003C 0, donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25215,"question":"Quelle est l'aire d'un disque de rayon 3 cm ?","option_a":"9π cm²","option_b":"6π cm²","option_c":"3π cm²","option_d":"12π cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un disque est donnée par πr². Ici, r = 3 cm, donc A = π × 3² = 9π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25216,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","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 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25217,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 7 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 12","option_d":"x \u003C 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : 3x \u003E 12 → x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]