14年高考真题——理科数学(上海卷)

14年 高考 地理事物空间分布特征语文高考下定义高考日语答题卡模板高考688高频词汇高考文言文120个实词 真题——理科数学(上海卷) 2014年普通高等学校招生全国统一考试(上海)卷 数学(理科) 一(填空题:共14小题，每小题4分，共56分。 2 1(函数的最小正周期是______________。 yx,,12cos2，， 1,,zi,，12i 2(若复数，其中是虚数单位，则______________。 zz，,,,,z,, 22xy2 3(若抛物线的焦点与椭圆的右焦点重合，则该抛物线的准线方，,1ypx,295 程为_______________。 ,xxa,，，, 4(设，若，则的取值范围是_______________。 f24,fx,a，，，，,2xxa,，，,, 22 5(若实数满足，则的最小值为______________。 xy,xy,1xy，2 6(若圆锥的侧面积是底面积的3倍，则其母线与底面夹角的大小为____________(结 果用反三角函数 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 示)。 CC,,,3cos4sin1,, 7(已知曲线的极坐标方程为，则与极轴的交点到极点的，， 距离为___________。 aaaa,，，，lim？a 8(设无穷等比数列的公比为q，若，则q,________。 ，，,,134nn,,n 21,32fx,0 9(若fxxx,,，则满足的的取值范围为________________。 x，，，， 10(为强化安全意识，某商场拟在未来的连续10天中随机选择3天进行紧急疏散演练，则选择的3天恰好为连续3天的概率是______________(结果用最简分数表示)。 22ab,0ab，,abab,,, 11(已知互异的实数满足，集合，则________。 ab,,,,, sin3cosxxa，,0,2,xxx,, 12(设常数使方程在闭区间上恰有三个解，则a,,123xxx，，,___________。 123 E,,4.2 13(某游戏的得分为，随机变量表示小白玩该游戏的得分。若，1,2,3,4,5,，，则小白得5分的概率至少为__________。 2Clx,6Cxy,,,4Am,0 14(已知曲线:，直线:。若对于点，存在上的点，， ,,,,,,,,, lPmQ和上的点，使得，则的取值范围为________________。 APAQ，,0 二(选择题:共4小题，每小题5分，共20分。 attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined ab，,4a,2b,215(设，则“”是“且”的( ) abR,, (A)充分条件 (B)必要条件 (C)充分必要条件 (D)既非充分又非必要条件 16(如图，四个棱长为1的正方体排成一个正四棱柱， 是一条侧棱，是底面上其余的八个ABPi,1,2,,8？，，i ,,,,,,,, 点，则的不同值的个数为( ) ABAPi,,1,2,,8？，，i (A)1 (B)2 (C)4 (D)8 k17(已知与是直线(Pab,Pab,ykx,，1，，，，111222 axby，,1,11为常数)上两个不同的点，则关于和的方程组的解的情况是( ) yx,axby，,122, (A)无论如何，总是无解 (B)无论如何，总有唯一解 kPP,,kPP,,1212 (C)存在，使之恰有两解 (D)存在，使之有无穷多解 kPP,,kPP,,1212 2,xax,,0，，，，,fx,，若f0是fx的最小值，则的取值范围是18(设a，，，，，，,1xax，，,0，，,x, ,1,2,1,01,20,2( ) (A) (B) (C) (D) ,,,,,,,,三(解答题(本大题共5题，满分74分) P319((本题满分12分)底面边长为2的正三棱锥 PABC,，其表面展开图是三角形PPP，如图，求123 AC V,PPP的各边长及此三棱锥的体积。 123 x2，aPP21Ba,0fx, 20((6分+8分)设常数，函数。，，x2,a ,1yfx,yfx,，，，，a,4a?若，求函数的反函数;?根据的不同取值，讨论函数yfx,，，的奇偶性，并说明理由。 D 21((6分+8分)如图，某公司要在AB,两地连线 CCDACD上的定点处建造广告牌，其中为顶端，长βαABCBA35米，AB,长80米，设点在同一水平面上，从C CDCDBD,,,,2,和看的仰角分别为和。?设计中是铅垂方向，若要求，问的长attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 2014年高考真题理科数学(解析版) 上海卷 0.01CD至多为多少(结果精确到米),?施工完成后，与铅垂方向有偏差，现在实测得 00CD0.01，，求的长(结果精确到米), ,,38.12,,18.45 l 22((3分+5分+8分)在平面直角坐标系中，对于直线:和点axbyc，，,0xOy PxyPxy,,,,,，，，，axbycaxbyc，记。若，则称点被，，，，，，，，P,P,,0111222112212 lllCC直线分割。若曲线与直线没有公共点，且曲线上存在点被直线分割，则称直P,P12 AB1,2,1,0,lC线为曲线的一条分割线。?求证:点被直线分割;?若，，，，x，y,1,0 22Q0,2，，k直线是曲线的分割线，求实数的取值范围;?动点到点的My,kxx,4y,1 距离与到轴的距离之积为1，设点M的轨迹为E，求证:通过原点的直线中，有且仅有y 一条直线是E的分割线。 1，aaanN,,,23((3 分+7分+8分)已知数列a满足，。 a,13,,，，nnnn11，3 a?若，，，求的取值范围;?若是公比为等比数列，qa,2ax,a,9x,,n234 1，SSSnN,,,，若，求的取值范围;?若qSaaa,，，，？3，，nnn1nn12，3 kk成等差数列，且，求正整数的最大值，以及取aaa,,,？aaa，，，,？100012k12k 最大值时相应数列aaa,,,？的公差。 12k 2014年普通高校招生全国统考数学试卷上海卷解答 ,1151,x,,2arccos,,,222一(1(;2(6;3(;4(;5(;6(;7(;8(;，,3322 0.2,10,12,311573,9(;10(;11(;12(;13(;14( ，，,,二(BABD 0，,ABC60PBP,,，,，,，ABPBAPCBP 19(解:由题共线，因，，故11212 000,PPP，,，,，,ABPBAPCBP60，,P60，,，,PP60，因此。同理。所以123111223 attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutan 3 / 6 dis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 2223PABC,为正三角形，为正四面体。所以边长为4，。 ,PPPVAB,,123123 x，2444y，44y，xa,4 20(解:?因，故，得，，因fxy,,2,x,log，，2x,24y,1y,1 44x，,1此; yfxxx,,,,,log11或，，，，2x,1 xx,22，，aaxx, ?若为偶函数，则，即，得，fxfxfx,,,a220,,，，，，，，，，xx,22,,aaa,0故，此时为偶函数;若为奇函数，则，即fxfxfxfx,,,，，，，，，，，xx,22，，aa2a,1，得，故，此时为奇函数;当a,,10fxa,，,0,11,:,,，，，，，，xx,22,,aa 时fx为非奇非偶函数。 ，， xx,tan,,tan,,,,,20 21(解:?设CDxm,，则，。因，故,,，，35802 xx1602tan,,020228.28,,,x，代入并整理得，得，,,tantan2,,22356400,x,1tan, CD28.28故的长至多为米; 00DBa,DAb,DCm,?设，，，。则，,,,,ADB180123.43,, 0aAB115sin38.12,a,,85.06，解得，0sinsin,ADB，sin123.43 220CD26.93maa,，,,80160cos18.4526.93，故的长为米。 AB1,2,1,0,1211140，,,,,,,22(解:?将分别代入，得，故xy，,1，，，，，，，，AB1,2,1,0,，，，，点被直线分割; x，y,1,0 ykx,,222140,,k141,,kx ?联立得，依题意该方程无解，故，得，，,22xy,,41, k,,12k,12或; 22222，，xyx，,,21EMxy, ?设xyx，,,2||1，则，故的方程为 ?。，，，，，，，， x,0EPP1,2,1,2,当斜率不存在时，直线，显然与方程?联立无解。又为上两点，，，，，12attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 2014年高考真题理科数学(解析版) 上海卷 x,0x,0且代入，有，故是一条分割线;当斜率存在时，设直线为，,,,,10ykx, 24322432代入方程得。令，则kxkxx，,，,,14410fxkxkxx,，,，,1441，，，，，， 22fk12,,fk,,，12k,2，，。当时，，故f01,,f10,，，，，，，，，，，，， k,2，即在存在实根。故与有公共点;当时，Eff010,fx,00,1ykx,，，，，，，，， ，即在存在实根。故与E有公共点。因此直线ff010,,fx,0,1,0ykx,，，，，，，，， 与曲线始终有公共点，从而不是分割线。综上，所有通过原点的直线中，有且仅Eykx, x,0有一条直线是曲线E的分割线。 112327,,x 23(解:?由题，故。又，故。aaa,,3,,x6aaa,,3234345333 36,,x综上可知; 11n,1,,q3 ?由题，因，故。当时，，aaa,,3Sn,q,1aq,123nn33 n11nq,1SSS,,,，,nn13SSS,,3即成立;当时，，313,,qS,nnn，1nnn，1n3q,133 nn，1nnn，1n，1,320qq,,,1111qqq,,,11q,,即，得，即。因，q,1,,3,,,,3,nnn，131q,3111qqq,,,qq,，,320,, nnnn，1nn，1n,132312220qqqqq,,,,,,,,故。对，令，得qq,，,320，， 2，解得。又当时，故12,,q12,,qq,,30qq,，,320 nnn，1qqqqqqqq,，,,，,,，,,,,323232120成立，因此;当12,,q，，，，，，，， nnnn，1111,q1111,,,qqq,,q1SSS,,3时，，即，得S,,,,,3nnn，1n31,q3111,,,qqq3 nn，1,320qq,,,,nnn，132312qqqq,,,,,,。因，，故 0312,,,qq,,30，，,nn，1qq,，,320,, nnn，1nqqqqqqqq,，,,，,,，,,,,323232120，。故当220q,,，，，，，，，， 11,,q1q,,q2时，不等式恒成立。综上知的取值范围是; 33 dk,1000d,0k,1000?设公差为，显然当，时，是一组符合题意的解。故。maxattempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutan 5 / 6 dis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined 212kd,,,,，，12，,kd，，,k,1000由题，故。当时，,，,,，,11312kdkd，，，，，，,，，3252kd,,,，，,, kkkd,1200022,k，，2可得。又，故，解得d,,,d,,ak,，,1000,i21k,kkk,,1212，，,1i k,1999k，故。所以的最大值为1999，此时公00,,,，k 200021,k差d,,,。 kk,11999，， attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan and pump installation engineering construction and acceptance specification for lifting 6 HG20201-2000 construction installation engineering construction standard 7, HG ... Pressure gauges, using an installed spark arrestor for acetylene cylinders, illegal carrying, using gas cylinders, each operator fined 20 Yuan. Gas bottle without the hot sun exposure measures, responsibilities of team a fine of 50 Yuan. (7) at height and the opening and provisional protective measures have been taken, the responsible unit fined