2016年5月福州市普通高中毕业班综合测试文科数学试题(word 版含(5)

π

又|OA| 4cos 2，

3

所以|AB| |OA| |OB| 1． ········································································ 10分 （24）选修4 5：不等式选讲

2016年5月7日福州高三质检文科数学含答案

本小题考查绝对值不等式的解法与性质、不等式的证明等基础知识，考查运算求解能力、推理论证能力，考查分类与整合思想、化归与转化思想等．满分10分． 解：（Ⅰ）由|x 3| 2x 1得， x 3, x 3,

或 ·································································· 2分

(x 3) 2x 1,x 3 2x 1, 解得x 2． 依题意m 2． ·························································································· 5分

11 11

（Ⅱ）因为x t x x t x t t ，

tt tt

1

当且仅当 x t x 0时取等号， ···························································· 7分

t

1

因为关于x的方程|x t| |x | 2（t 0）有实数根，

t

1

所以t 2． ························································································ 8分

t

另一方面，t 所以t

1

…2， t

1

2， ························································································ 9分 t

所以t 1或t 1． ·················································································· 10分