宁夏育才中学2019-2020学年高一上学期期中考试数学试题（PDF版）

$$ 宁夏高一期中数学试卷 参考答案及评分标准 一、 选择题(本大题共 12 小题,每小题 5 分,共 60 分) 1.C 2.C 3.B 4.A 5.D 6.D 7.B 8.C 9.B 10.C 11.B 12.B 二､填空题(本大题共 4 小题,每小题 5 分,共 20 分) 13. {x|x≥1 且 x≠5} 14. [−2,3] 15. 2 16. [60,100] 三､解答题(共 70 分) 17.解(1)∵B={x|x>2}; ∴∁UB={x|x≤2}; ∴(∁UB)∪A={x|x≤3};·················································(5 分) (2)∵C∩A=C, ∴C⊆A;·····························································(7 分) ∴ ; ∴1≤a≤2,·························································(9 分) ∴实数 a 的取值范围为[1,2].·········································(10 分) 18.解:(1)g(x)=f(x)+a2x=x2+(5﹣6a+a2)x+a﹣2 为偶函数, 则 5﹣6a+a2=0, 解得 a=1 或 a=5····················································(5 分) (2)∵f(x)对称轴为 ,又(1,2)内是单调函数, ∴ 或 ,············································(8 分) 解得 或 ∴a 的取值范围为 .····························(12 分) 19.解:(1)原式= ;·······(6 分) (2)原式=4+4+2lg5+lg2·(2﹣lg2)+(lg2)2 =8+2(lg2+lg5) =8+2 =10.······························································(12 分) 20. 解:(1) ∵幂函数 f(x)=xa 的图象经过点(2, ), ∴2a= ,····························································(2 分) 解得 a= , ∴幂函数 f(x)=𝑥 1 2=√𝑥(x≥0);·······································(6 分) (2)由(1)知 f(x)在定义域[0,+∞)上单调递增, 则不等式 f(1+a)>f(3﹣a)可化为 , 解得 1<a≤3,························································(10 分) ∴实数 a 的取值范围是(1,3].·········································(12 分) 21.解:(1)由题,得△=(m+3)2+4m>0, 解得 m<﹣9 或 m>﹣1,················································(3 分) ∴m∈(﹣∞,﹣9)∪(﹣1,+∞);······································(4 分) (2)∵m>0,所以对称轴 ,····································(6 分) 当 ,即 m∈(0,1]时,函数在[0,2]上单调递减, 故当 x=2 时,取最小值 2m﹣7;··········································(9 分) 当 ,即 m∈(1,+∞)时,函数在[0,2]上先减后增, 故当时 ,取最小值 .···································(12 分) 22. 解: (1)∵f(x)+f(﹣x)=0 ∴f(﹣x)=﹣f(x),即 f(x)是奇函数.·································(2 分) ∵f(x﹣1)=f(x+1),∴f(x+2)=f(x),即函数 f(x)是周期为 2 的周期函数, ∴f(0)=0,即 b=﹣1.···············································(4