2025年广东省深圳市翠园初级中学中考模拟考试数学试卷(含答案)

深圳市2025年中考模拟考试数学学科 参考答案与评分标准 一、选择题 题号 1 2 3 4 5 6 7 8 答案 B A D D C A C B 二、填空题 题号 9 10 11 12 13 答案 13 70 三、解答题 14. 解： ··········································4分（一个知识点1分） ······························································5分 ·················································································6分 15. 解： （1）； ·····················································2分 （2）∵，········································3分 ∴， ·····················································4分 ∴（a﹣1）2＝2，即a2﹣2a+1＝2， ∴a2﹣2a＝1， ·····················································5分 ∴原式＝4（a2﹣2a）﹣2＝4﹣2＝2． ·················································7分 16. 任务1：m=9，n=8 ······································································2分 任务2： A的综合成绩为： ·······························3分 B的综合成绩为： ·······························4分 C的综合成绩为： ·······························5分 ∵86.2>85.8 ∴B机器人的综合成绩最高. ·······················································6分 任务3： ①选择B机器人，因为B机器人得运动能力测试能力比较高. ②选择B机器人，因为B机器人运动能力成绩得方差比较小，说明B机器人得运动能力比较稳定. ③选择A机器人，因为A机器人运动能力测试得众数是9和10，说明较多专业测试员认为A机器人得运动能力很好. (答案不唯一，言之有理即可) ·······················································8分 17. 解： （1）设“哪吒”、“敖丙”两种书签每张的进价分别是x、y元···········1分 由题意知： ······························3分 解得 ······························4分 答：“哪吒”、“敖丙”两种书签每张的进价分别是9、8元. ················5分（2）设购进“哪吒”书签m张，“敖丙”书签（90-x）张 由题意知： 解得 ······························6分 设这批书签全部售出后获利W元，则 ······························7分 ∵2>0， ∴W随m得增大而增大， ∴当m=40时，90-m=50，W有最大值, . 答：当购进“哪吒”书签40张，“敖丙”书签50张时，获得最大利润，最大利润是440元. ······························9分 18.解： 方法1： （1）∵DE⊥AC，DF⊥BC， ∴∠CED=∠CFD=90° ∵∠ACB=90° ∴四边形CEDF是矩形 ····· ... ...