Maths 3ème année secondaire : Testez vos connaissances en équations et fonctions !

Question 1 sur 10 10:00

[{"id":12578,"question":"Quelle est la solution de l'équation 3x + 5 = 2x - 7 ?","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 soustrayant 2x des deux côtés et en ajoutant 7, on obtient x = -12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12579,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette fonction est une parabole ouverte vers le haut, mais elle peut prendre des valeurs négatives entre ses racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12580,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"7","option_b":"-4","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est le nombre devant x, soit -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12581,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) est égal à :","option_a":"4\/5","option_b":"2\/5","option_c":"5\/3","option_d":"3\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant l'identité sin²(θ) + cos²(θ) = 1, on trouve cos(θ) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12582,"question":"L'inéquation 2x - 5 ≤ 3x + 1 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En simplifiant, on obtient x ≥ -6, donc l'inéquation n'est pas toujours vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12583,"question":"Quelle est la dérivée de la fonction f(x) = 5x³ - 2x² + x - 4 ?","option_a":"15x² - 4x + 1","option_b":"15x² - 4x","option_c":"5x² - 2x + 1","option_d":"15x² - 4x + 1 - 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée est obtenue en appliquant la règle de dérivation terme à terme : 15x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12584,"question":"Dans un cercle de rayon 5 cm, la longueur d'un arc de 60° est :","option_a":"5π\/3 cm","option_b":"10π\/3 cm","option_c":"5π cm","option_d":"10π cm","option_e":"","option_f":"","bonne_reponse":"B","explication":"La longueur de l'arc est donnée par (60\/360) × 2π × 5 = 10π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12585,"question":"L'équation x² + 4x + 4 = 0 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette équation a une solution double x = -2, donc elle est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12586,"question":"Quel est le centre de symétrie de la fonction f(x) = (x - 3)² + 2 ?","option_a":"(3, 2)","option_b":"(2, 3)","option_c":"(-3, 2)","option_d":"(0, 0)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le centre de symétrie est le sommet de la parabole, soit (3, 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12587,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont :","option_a":"égaux","option_b":"opposés","option_c":"inverses","option_d":"nuls","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont des coefficients directeurs égaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]