上期期中高一数学答案

河南省实验中学20232024学年上期期中试卷答案（高一）一、单选题（共8小题）14BCCA58AABD二、多选题（共4小题）9.ABC10.ABC11.AC12.ABD三、填空题（共4小题）13.314.﹣ex+2x+115.[-3，3]16.四．解答题（共6小题）17．解：（1）原式=(=327+27-21=3+27﹣21＝9（2）原式＝lg52+lg2•lg50+（lg2）2﹣eln8＝2lg5+lg2（1+lg5）+（lg2）2﹣8＝2lg5+lg2+lg2•lg5+（lg2）2﹣8＝2lg5+lg2+lg2（lg5+lg2）﹣8＝2（lg5+lg2）﹣8＝﹣6．················································（10分）18．解：（1）当m＝﹣1时，A＝{x|﹣3≤x≤1}，集合B＝{x|﹣1＜x≤2}，所以∁UB＝{x|x＞2或x≤﹣1}，···········································（2分）所以①A∪B＝{x|﹣3≤x≤2}；············································（4分）②A∩（∁UB）＝{x|﹣3≤x≤﹣1}；········································（6分）（2）若A∩B＝∅，当A＝∅时，2m﹣1＞m+2，即m＞3，······································（8分）当A≠∅时，2m解得m≤﹣3或32＜m≤3，··········································综上，m的范围为{m|m≤﹣3或m＞32}．··································（19.解：（1）∵f(x)=(3m2-2m)解得m＝1或m=-13，又∵幂函数在（0，+∞）上单调递增，∴m-12＞0，得m＝1（2）由第一问得f(x)=x12，在[1所以f（x）的值域为[1，2]，即集合A＝{x|1≤x≤2}，·······················（6分）而g（x）＝﹣3x+t在[1，4]上递减，所以g（x）的值域为[t﹣81，t﹣3]，即B＝{x|t﹣81≤x≤t﹣3}，··············································（8分）由命题q是命题p的必要不充分条件可得A⫋B，···························（10分）所以t-3≥2t-81≤1，解得5即t的取值范围为[5，82]．··············································（12分）20．解：（1）由f（x+y）＝f（x）+f（y），令x＝y＝0得f（0）＝f（0）+f（0），∴f（0）＝0．·························································（2分）（2）f（x）是奇函数，证明：f（x）定义为R，关于原点对称·································（3分）由f（x+y）＝f（x）+f（y），令y＝﹣x，得f（x﹣x）＝f（x）+f（﹣x），即f（x）+f（﹣x）＝f（0）＝0，f（﹣x）＝﹣f（x），所以f（x）是奇函数．······························（6分）（3）任取x1，x2∈R，x1＜x2，x2﹣x1＞0，·······························（7分）由f（x+y）＝f（x）+f（y）知f（x+y）﹣f（x）=f（y）f（x1）﹣f（x2）＝f（x1﹣x2）＝﹣f（x2﹣x1），···························（8分）由于x2﹣x1＞0，所以f（x2﹣x1）＜0，所以f（x1）﹣f（x2）＝﹣f（x2﹣x1）＞0，即f（x1）＞f（x2），所以f（x）是减函数，·················································（9分）f（6）＝f（3+3）＝f（3）+f（3）＝﹣8，································（10分）所以不等式f（t﹣1）+f（t）＜﹣8即f（t﹣1+t）＜f（6），所以2t﹣1＞6，t＞7所以不等式f（t﹣1）+f（t）＜﹣8的解集为（72，+∞）．····················（1221．解：（1）由题意得W（x）＝800x﹣R（x）﹣250，∵R（x）=10∴当0＜x＜40时，R（x）＝10x2+200x+1000，则W（x）＝800x﹣（10x2+200x+1000）﹣250＝﹣10x2+600x﹣1250，·········（2分）当x≥40时，R（x）＝701x+10000x则W（x）＝800x﹣（801x+10000x-8450）﹣250＝﹣x-10000综上所述，W（x）=-10x2+600x-1250，（2）由（1）得W（x）=-10则当0＜x＜40时，W（x）＝﹣10x2+600x﹣1250＝﹣10（x﹣30）2+7750，二次函数W（x）的图象开口向下，且对称轴为直线x＝30，∴W（x）max＝W（30）＝7750，·········································（8分）当x≥40时，W（x）＝﹣x-10000x又x+10000x≥2x⋅10000x=200，当且仅当∴W（x）＝﹣x-10000x+8200≤﹣200+8200＝8000，···················∵8000＞7750，∴2023年产量为100（千部）时，企业所获利润最大，最大利润是8000万元．··（12分）22．解：（1）∵f（x）为R上的奇函数，∴f（0）＝0，可得b＝1················································（1分）又∵f（﹣1）＝﹣f（1）∴1-2-12-1+a=-1-22+a经检验当a＝1且b＝1时，f（x）=1-满足f（﹣x）＝﹣f（x）是奇函数．·······································（3分）故a＝1，b＝1·························································（4分）（2）由（1）得f（x）=1-2x任取实数x1、x2，且x1＜x2················································（5分）则f（x1）﹣f（x2）=22x1∵x1＜x2，可得2x1∴f（x1）﹣f（x2）＞0，即f（x1）＞f（x2），······························（7分）∴函数f（x）在（﹣∞，+∞）上为减函数；·······························（8分）（3）根据（1）（2）知，函数f（x）是奇函数且在（﹣∞，+∞）上为减函数．∴不等式f（t2﹣2t）+f（2t2﹣k）＜0恒成立，即