20259150150一、閱讀（72（一）閱讀Ⅰ（5小題，19分答：答：答：答：所謂濕干肥瘠，皆是過(guò)分而言。因?yàn)檫^(guò)干如經(jīng)發(fā)覺(jué)，可以立刻澆灌而使之濕，過(guò)濕則不能立刻使下列對(duì)原文相關(guān)內(nèi)容的理解和分析，正確的一項(xiàng)是（下列對(duì)原文相關(guān)內(nèi)容的分析和評(píng)價(jià)，不正確的一項(xiàng)是（ ①的地方。栽 ②。栽植 ③，過(guò)淺又容易發(fā)生倒伏。最后將土填滿，用腳踩實(shí)后再澆透（二）閱讀Ⅱ（4小題，16分 關(guān)于文本一中方寶慶這個(gè)人物，下列說(shuō)法不正確的一項(xiàng)是()（三）閱讀Ⅲ（522使我終歲不食葵。鄰人女奔，隨人亡，其家倩吾兄行追之。逢霖水出，溺流而死，令吾終身無(wú)兄。兄”之言，[注]春秋末期，宗周王室動(dòng)蕩，晉強(qiáng)鄭弱。子大叔為鄭國(guó)正卿，范獻(xiàn)子為晉國(guó)大臣。ABCDEFGH所避乎！下列對(duì)材料中加點(diǎn)的詞語(yǔ)及相關(guān)內(nèi)容的解說(shuō)，不正確的一項(xiàng)是（下列對(duì)材料有關(guān)內(nèi)容的概述，不正確的一項(xiàng)是（（四）閱讀Ⅳ（2，9下列對(duì)這首詩(shī)的理解和賞析，不正確的一項(xiàng)是（（五）名篇名句默寫(xiě)（1，6 5小題，18展宏‘兔’(圖)”；電視廣告里，則有“默默無(wú)‘蚊’(聞)的奉獻(xiàn)”(蚊香廣告)等有趣的說(shuō) 的意思不明確，使人()。所以，使用諧音雙關(guān)，要注意語(yǔ)言格調(diào)高雅和信息傳遞有效，避免出現(xiàn)上下列填入文中橫線處的句子，銜接最恰當(dāng)?shù)囊豁?xiàng)是()填入文中第四段括號(hào)內(nèi)的詞語(yǔ)，不恰當(dāng)?shù)囊豁?xiàng)是()A.莫名其 B.無(wú)所適 C.大惑不 D.一頭霧800

20259150150一、閱讀（72（一）閱讀Ⅰ（5小題，19分答：答：答：答：所謂濕干肥瘠，皆是過(guò)分而言。因?yàn)檫^(guò)干如經(jīng)發(fā)覺(jué)，可以立刻澆灌而使之濕，過(guò)濕則不能立刻使下列對(duì)原文相關(guān)內(nèi)容的理解和分析，正確的一項(xiàng)是（下列對(duì)原文相關(guān)內(nèi)容的分析和評(píng)價(jià)，不正確的一項(xiàng)是（ ①的地方。栽 ②。栽植 ③，過(guò)淺又容易發(fā)生倒伏。最后將土填滿，用腳踩實(shí)后再澆透【答案】1. 2.3 4.示例一【1A問(wèn)三、問(wèn)十三問(wèn)十四【2【3【4【5（二）閱讀Ⅱ（4小題，16分 關(guān)于文本一中方寶慶這個(gè)人物，下列說(shuō)法不正確的一項(xiàng)是() 7.①《鼓書(shū)藝人》的創(chuàng)作源自作者抗戰(zhàn)時(shí)期的親身經(jīng)歷；②文本一的場(chǎng)景再現(xiàn)了作者在戰(zhàn)爭(zhēng)中感受到的人【6行，兩岸有高山峭崖，當(dāng)太陽(yáng)被峭崖遮擋時(shí)就比較陰冷，再加上江上的寒風(fēng)，乘客們冷得打戰(zhàn)；而隨著船的前行，太陽(yáng)又間或從山間或巖石縫里露出來(lái)，江面上水汽大，陽(yáng)光射入，容易在江面上投下彩虹，這些第九段又寫(xiě)“人們不是煩惱，就是生氣，悲傷”，這些都表明他們的心情并未因陽(yáng)光和彩虹而變得積極樂(lè)D他不愿意離開(kāi)武漢，因?yàn)橛小霸诖髸r(shí)代分擔(dān)一部分的工作”的強(qiáng)烈意愿，待在武漢，正是“勇氣與力量”的表現(xiàn)；而后來(lái)武漢戰(zhàn)局吃緊，“遷移之議既成”，老舍無(wú)法繼續(xù)在武漢從事“文協(xié)”相關(guān)工作，這才乘船去往大后方。他為抗戰(zhàn)工作的意愿并未發(fā)生變化。所以，他在思想和認(rèn)識(shí)上并沒(méi)有發(fā)生“重大轉(zhuǎn)變”，【7【8【9（三）閱讀Ⅲ（522使我終歲不食葵。鄰人女奔，隨人亡，其家倩吾兄行追之。逢霖水出，溺流而死，令吾終身無(wú)兄。[注]春秋末期，宗周王室動(dòng)蕩，晉強(qiáng)鄭弱。子大叔為鄭國(guó)正卿，范獻(xiàn)子為晉國(guó)大臣。ABCDEFGH所避乎！下列對(duì)材料中加點(diǎn)的詞語(yǔ)及相關(guān)內(nèi)容的解說(shuō)，不正確的一項(xiàng)是（下列對(duì)材料有關(guān)內(nèi)容的概述，不正確的一項(xiàng)是（【答案】1011. 12.【10B處斷開(kāi)；D處斷開(kāi)；F處斷開(kāi)。【12【13【14（四）閱讀Ⅳ（2，9下列對(duì)這首詩(shī)的理解和賞析，不正確的一項(xiàng)是（【答案】15.D 【15【16（五）名篇名句默寫(xiě)（1，6 【答案】①(是故)弟子不必不如師②.師不必賢于弟子③.兩情若是久長(zhǎng)時(shí)④.又豈在朝朝暮暮⑤.水面清圓⑥.一一風(fēng)荷舉（江南可采蓮，蓮葉何田田/惟有綠荷紅菡萏，卷舒開(kāi)合任天5小題，18展宏‘兔’(圖)”；電視廣告里，則有“默默無(wú)‘蚊’(聞)的奉獻(xiàn)”(蚊香廣告)等有趣的說(shuō) 的意思不明確，使人()。所以，使用諧音雙關(guān)，要注意語(yǔ)言格調(diào)高雅和信息傳遞有效，避免出現(xiàn)上下列填入文中橫線處的句子，銜接最恰當(dāng)?shù)囊豁?xiàng)是()填入文中第四段括號(hào)內(nèi)的詞語(yǔ)，不恰當(dāng)?shù)囊豁?xiàng)是()A.莫名其 B.無(wú)所適 C.大惑不 D.一頭霧.19. 20.【18【19AB；D。【20【21【228002025年普通高等學(xué)校招生全國(guó)統(tǒng)一考試（1卷2B鉛筆將試卷類(lèi)型和考生號(hào)填涂在答題卡相應(yīng)位置上。2B鉛筆把答題卡上對(duì)應(yīng)的題目選項(xiàng)的答案信息點(diǎn)涂黑：如需改(15i)i的虛部為（

若點(diǎn)(a,0)(a0)是函數(shù)y2tanxπ的圖象的一個(gè)對(duì)稱(chēng)中心，則a的最小值為

設(shè)f(x)是定義在R上且周期為2的偶函數(shù)，當(dāng)2x3時(shí)，f(x)52x，則f3

若圓x2(y2)2r2(r0)上到直線y 若實(shí)數(shù)x，y，z滿足2log2x3log3y5log5z，則x，y，z的大小關(guān)系不可能是 xy

xz

yx

yz361860 AD C．CC1∥平面 D．AD∥設(shè)拋物線Cy26xFFCA、BFAB的直線交lx3 A．|AD||AF

B．|AE||AB

C．|AB|

D．|AE||BE|已知△ABC的面積為1，若cos2Acos2Bcos2C2,cosAcosBsinC1，則 sinCsin2Asin2

AB C．sinAsinB

D．AC2BC23515若直線y2x5是曲線yexxa的切線，則a 學(xué)期望E(X) 57715.（13）1000附2

n(ad(ab)(cd)(ac)(bd16．（15分）設(shè)數(shù)列a滿足a3，an1an n n(n設(shè)

f(x)axax2

axmf(2 17．（15分）PABCDPAABCDBCADABAD PABPAAB

2,AD

31BC2，P，B，C，D證明：OABCD18．（17分）設(shè)橢圓C:

2 2

PyRAPARAP3P(mnR的坐標(biāo)（m，n表示O為坐標(biāo)原點(diǎn)，QCOROP3倍，求|PQ|19．（17分）f(x5cosxcos5xf(x在0π 2025年普通高等學(xué)校招生全國(guó)統(tǒng)一考試（1卷在答題卡上.2B鉛筆將試卷類(lèi)型和考生號(hào)填涂在答題卡相應(yīng)位置上.2B鉛筆把答題卡上對(duì)應(yīng)的題目選項(xiàng)的答案信息點(diǎn)涂黑：如需

C. D.【詳解】因?yàn)?5iii5i25i1，2.設(shè)全集U AB.C.D.

D.aba2b2c2b

7aa2b2c2a27a28a2，則c22a即ec 若點(diǎn)(a,0)(a0)是函數(shù)y2tanxπ的圖象的一個(gè)對(duì)稱(chēng)中心，則a的最小值為 A. B.

y2tan(xπxπkπkZ π 即y2tan(x3)的對(duì)稱(chēng)中心是 2,0,kZ aπkπkZ a0k0aπa設(shè)f(x)是定義在R上且周期為2的偶函數(shù)，當(dāng)2x3時(shí)，f(x)52x，則f3

f(xf(x),f(x2)f(xxR于是f(3)f()f(11)52111 帆船賽中，運(yùn)員可借助力計(jì)測(cè)定速的大小方向，出的結(jié)果航海學(xué)中為視風(fēng)風(fēng)，視風(fēng)風(fēng)速對(duì)應(yīng)的向量，是真風(fēng)風(fēng)速對(duì)應(yīng)的向量與船行風(fēng)速對(duì)應(yīng)的向量之和，其中船行風(fēng)速對(duì)應(yīng)的向量與船速對(duì)的量小等向反.圖1出部風(fēng)等級(jí)稱(chēng)風(fēng)大的應(yīng)系.知帆運(yùn)員在時(shí)測(cè)的風(fēng)速應(yīng)向與速應(yīng)向如圖速大和量大相同A.輕 B.微 C.和 D.勁得出真風(fēng)風(fēng)速的大小，即可由圖1得出結(jié)論.2222n1

x2y2)2r2(r0)y

3x212r A. C.(3,

D.(0,

x2y22r2r0E02r3203320321

3x2的距離為：d 2r1時(shí)，圓x2y22r2r0上有且僅有一個(gè)點(diǎn)（A點(diǎn)）到直線y 3x2的距離等于1；當(dāng)r3時(shí)，圓x2y22r2r0上有且僅有三個(gè)點(diǎn)（B,C,D點(diǎn)）到直線y 3x2的距離等于1；當(dāng)則r的取值范圍為1,3時(shí)，圓x2y22r2r0上有且僅有兩個(gè)點(diǎn)到直線y 若實(shí)數(shù)x，y，z滿足2log2x3log3y5log5z，則x，y，z的大小關(guān)系不可能是 xyC.yx

xzD.yz【分析】法一：設(shè)2log2x3log3y5log5zm，對(duì)mxyz，即可得出大小關(guān)系，2log2x3log3y5log5zmm2x1y311z531xyz，A m5x8y9z1yxz，Cm8x2664y35243z53125yzx，D有可能；2log2x3log3y5log5zmx2m2y3m3zy2x2y3x3y5x5y2x2y3x3y5x5的圖象與xm的交點(diǎn)縱坐標(biāo)，如圖所示：易知，隨著mxyzyxzyzxzyx，3618分.要求.60分 A.ADC.CC1BCAD//ADABCAA1ADA1AAD0因?yàn)閂ABCDBCADBC，則CDAD A1CADA1AADCDADA1AAD

CDAD

0ADA1CABCABCAA1BC，BCAA1DBAA1AA1DCC1AA1D，所以CC1AA1DC正確；DABCA1B1C1A1B1AB，ADA1B1ADABADABA矛盾，AD//A1B1D錯(cuò)誤；D000,A

3,0,0,A1

AAD300A1C31hADA1CA BCBC020,CC100hAA100hADAAD→xyz

3,0,0 AA1nhz則–––→ ，得xz0，

y

ADn3xBC020→CCn0

0ADABD設(shè)拋物線Cy26xFFCA、BFAB的直線交lx3 A.|AD||AF B.|AE||ABC.|AB| D.|AE||BE|三角形相似證得AEB90C，利用直線的反設(shè)法（法一）與正設(shè)法（法二），聯(lián)立直線AB與拋物線方程，結(jié)合韋達(dá)定理與焦點(diǎn)弦公式可判斷C；利用利用三角形相似證得AE2AFAB BFABA，對(duì)于拋物線C:y26xp3x3F30 ADAF|AD||AF|A正確；BB作準(zhǔn)線lP，ADlEFAB，則ADEAFE90，又|AD||AF||AE||AE|，所以VADE@VAFE，所以AEDAEF，同理BEPBEF又AEDAEFBEPBEF180

90，即AEB90AB為ABE的斜邊，則|AE||AB|B錯(cuò)誤；CAB的斜率不為0，ABxmy3AxyBxyxmy

聯(lián)立y2

2y26my90易知0y1y26my1y29xmy3xmy3 所以|AB|xxpmy

336m266 m0CD，在Rt△ABE與RtAEFBAEEAF所以RtABERtAEF

AE2

AFAB同理 BFABAFBFx3x3my3my 2 m2yy3myy99m218m299m211 AB6m266m21AE2BE2BFAFAB29m2136m212 AEBE3m2126m2118m21218D正確.A，對(duì)于拋物線C:y26xp3x3F30 ADAF|AD||AF|A正確；BB作準(zhǔn)線lP，ADlEFAB，則ADEAFE90，又|AD||AF||AE||AE|，所以VADE@VAFE，所以AEDAEF，同理BEPBEF又AEDAEFBEPBEF180AB為ABE的斜邊，則|AE||AB|B錯(cuò)誤；CAB的斜率不存在時(shí)，AB2p6；ABABykx3 2 kxy kx聯(lián)立 2，消去y，得k2x23k26xk20 y2易知0xx36xx9

k1k1k1k1k

1 xx 4x 11k1k

6 632

16 k2|AB|6CD，在Rt△ABE與RtAEFBAEEAF所以RtABERtAEF

AE2

AFAB同理 BFAB當(dāng)直線AB的斜率不存在時(shí)，AB6，AFBF AB3 所以AE BFAFAB23362，即AEBE18 當(dāng)直線AB的斜率存在時(shí)， 611 k2 AFBFx3x3xx3xx 2 1 933691 k2 k2 1 1 所以AE BFAF 9 36 AE

1k2

1k2

121822 AEBE18D正確.已知VABC1，若cos2Acos2B2sinC2cosAcosBsinC

A.sinCsin2Asin2 B.ABC.sinAsinB

D.AC2BC2【分析】對(duì)cos2Acos2B2sinC2AAB的大小，亦可使用正余弦定理討論解決，結(jié)合正弦函數(shù)的單調(diào)性可推出CcosAcosBsinC1AB取值，最后利用三角形面積求出三邊長(zhǎng)，即可判斷每個(gè)選項(xiàng)

，然后利用【詳解】cos2Acos2B2sinC2，由二倍角公式，12sin2A12sin2B2sinC2sinCsin2Asin2B，A選項(xiàng)正確；sinAB)sinπCsinC，展開(kāi)可得sinAcosBsinBcosAsin2Asin2B，即sinA(sinAcosB)sinB(sinBcosA)0，ABπ，則sinAcosBsinBcosAABπAπBsinAcosB，同理sinBcosA 又sinA0sinB0，于是sinA(sinAcosBsinB(sinBcosA0ABπABπ，類(lèi)似可推導(dǎo)出sinA(sinAcosBsinB(sinBcosA)0ABπ不成立 ABπ，即Cπ sinCsin2Asin2B時(shí)，由C(0π，則sinC(0,1，于是1sinCsin2Asin2Bsin2C，a2b2c2cosC0，則C(0π (0,)，則AB，注意到cosAcosBsinC，則cosAcosB0 于是cosA0cosB0（兩者同負(fù)會(huì)有兩個(gè)鈍角，不成立）AB0π 2 ABπAπBAπB都是銳角，則sinAsinπBcosB0

于是sinCsin2Asin2Bcos2Bsin2B1，這和sinC1相矛盾，故C0,π)不成立，則Cπ 由cosAcosBsinC1cosAcosBABπ，則cosBsinA，即sinAcosA1 則sin2A1，同理sin2B1AB是銳角，則2A2B(0π AB2Aπ2B5πA

π,B5π 由兩角和差的正弦公式可知

πsin5π

6 2

6 2

6，C 由兩角和的正切公式可得，tan5π2 BCtAC2

3tAB

6t

31423423

(2 3)t2，則t2

，則t

于是AB 2)t ，B選項(xiàng)正確，由勾股定理可知，AC2BC22，D選項(xiàng)錯(cuò)誤3515分若直線y2x5是曲線yexxa的切線，則a yexxayex1，y2x52，yex12，即ex1x0x0y2x5y2055，所以切點(diǎn)坐標(biāo)為(05)，因?yàn)榍悬c(diǎn)(05yexxa所以5e00a，即51aa4yexxayexy2x5yexxa的切點(diǎn)為x0y0ex01則y2x

，解得a4 yex0x n項(xiàng)和的定【詳解】法一：設(shè)該等比數(shù)列為anSnnS44S868，設(shè)anq，q1S44a14a11S88a1868q1

a1q4 1

1q81

68

1q81

1 1 即 1則1q417q2，所以該等比數(shù)列公比為2.法二：設(shè)該等比數(shù)列為anSnnS44S868，設(shè)anq，S4a1a2a3a44S8a1a2a3a4a5a6a7aaaaaq4aq4aq4a aaaa1q468 41q468，則1q417q2，所以該等比數(shù)列公比為2.法三：設(shè)該等比數(shù)列為anSnnS44S868，設(shè)anq，SSaaaaaaa

q468464 S4a1a2a3a44S8S4q46416q2 所以該等比數(shù)列公比為2數(shù)學(xué)期望E(X) 25EXXiEXi，進(jìn)X1、2、3，總的選取可能數(shù)為53125，X15PX151 X2：恰好兩種不同球被取出（即一球出現(xiàn)兩次，另一球出現(xiàn)一次），54種方式，3X2的可能情況有54360PX2

12 X3X3的可能情有況54360PX3

12 1521231261 Xi

XXi EXEXiEXi5EXi 由題意可知，球i4

4 由于抽取獨(dú)立，三次均未取出球i的概率為PX0

因此球iPX116461EXi

EX5EX5

577分.解答應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟

n(ad(ab)(cd)(ac)(bdPx2?k（2）根據(jù)獨(dú)立性檢驗(yàn)的基本思想,求出2,然后與小概率值0.001對(duì)應(yīng)的臨界值10.8281200人中有180p1809 2 10002020780180 根據(jù)表中數(shù)據(jù)可得，2 765.62510.828800200800200

x0.001根據(jù)小概率值0.001的2H0不成立，即認(rèn)為超聲波檢查結(jié)果與患該病有關(guān)，該推斷犯錯(cuò)誤的概率不超過(guò)0.001.設(shè)數(shù)列a滿足a3，an1an n(n f(xaxax2

axmf(2)（2）f273m 【分析】（1）根據(jù)題目所給條件an1an n nn1在數(shù)列a中，a3，an1an n nnn1an1nan1，即n1an1nan2由題意及（1）nN*

31n1

12fxaxax2axm fx3x2x212xm，fx34xm2 m fx34xm2x1x0 1∴fx 1

x1xm11

m2 1 212m1 m22m∴f2 1212m11

m22m

m221 3m72 PABCDPAABCDBCADABADPABPADPAAB 2AD 3BC2PBCD在同一個(gè)球面上，設(shè)該球面的球心為O（ii）2【分析】（1）APABAPADABPAD中，得出點(diǎn)O坐標(biāo)，進(jìn)而得出點(diǎn)OOPOBOCODAC的長(zhǎng)，過(guò)點(diǎn)OACBC的延長(zhǎng)線為C1AC1PC1，利用勾股定理求1詳解】PABCDPAABCDABAD∴APAB，APADAPPADADPADAPADAABPADPABPAD2PABCDAPABAPADABADBCADPAAB AD1 ∴A0,0,0,B

2,0,0,C

2,2,0,D0,1

3,0,P0, PBCDOPOBOCODxAy∴A0,0,B

2,0,C

2,2,D0,1

3∴線段CDF233 13 313 33直線CD的垂直平分線EF斜率：k23

6∴直線CD的方程：y336 x2， 2即y6

2

3 2 當(dāng)y1時(shí)，16 x233，解得：x0， 2 ∴O021202120200 2212OB00 2212202OC00113OD解得：OPOBOCOD ∴點(diǎn)OABCD上.PBCD在△BCD中，到三角形三點(diǎn)距離相等的點(diǎn)是該三角形的外心，BC和CD的垂直平分線，如下圖所示，OEAB ，BECE

1BC1，ODADAOBO

12122 ∴O1DBO1CO1在RtAOP中，APAD，AP AP2AP2AO

22∴PO1BO1CO1O22∴點(diǎn)O1PBCD所在球的球心O，此時(shí)點(diǎn)OADADABCD，∴點(diǎn)OABCD上 AC2,2,0,PO0,1,2，021021222200122 AC由幾何知識(shí)得，PO ABAD，BC∥AD∴ABBC在RtVABC中，AB ，BC2，由勾股定理得222過(guò)點(diǎn)OACBC的延長(zhǎng)線為C1AC1PC1則OC1AC ，直線AC與直線PO所成角即為△POC1中POC1或其補(bǔ)角PAABCDAC1ABCDPAAC1A∴PAAC1在RtABC1中，AB ，BC1BCCC1213，由勾股定理得

22222222

PA2ACPA2ACPC2PO2OC22POOCcosPOC cosPOC1ACPOcosPOC13設(shè)橢圓C:

21(ab02

PyRAPARAP3P(mnR的坐標(biāo)（m，n表示OMOR的斜率為直線OP3倍，求|PM|

x22 n2m2n2

m2n

m2n12

2 P的軌跡為圓（除去兩點(diǎn)），再根據(jù)點(diǎn)與圓的最值求法結(jié)合三角換元或者直接1a2a2由題可知,A0,b,Ba,0，所以ec2 ，解得a29,b21,c282

x2

c2a2 n1，故y01n1，且mx0

xy因?yàn)锳0,1，xy

3m2n m2n

n2m2即1mx0m3x0m2n12y0m2n12 n2m2n2所以點(diǎn)R的坐標(biāo)為 m2n m2n12 法二：設(shè)ARAP,0，則ARAP3m2n123，所

3n m2n

m2n

m2n

2 n2m2n2點(diǎn)R的坐標(biāo)為 m2n m2n12 kOR

n2m2n2m2n12 m2n12

n2m2

n,由 3n

n2m2

m2n28n20,即

n

18m0

PMmaxMN的距離加上半徑,M3cossin,所以MN23cos2sin429cos2sin28cos2181sin28sin28sin 1 8sin

2727,當(dāng)且僅當(dāng)sin時(shí)取等號(hào)所以

33

2

MN2x2 4299y2y28 168y28

8

2727

時(shí)取等號(hào)故

33

2f(x5cosxcos5xfx在0π 先考慮t0π時(shí)b的范圍，對(duì)于t0π時(shí)，可利用（2）中的結(jié)論結(jié)合特值法求得b

可得b的最小值；或者先根據(jù)函數(shù)解析特征得b0，再結(jié)合特值法可得b

11fx5sinx5sin5x10cos3xsin2xx0π2x0π，故sin2x0 當(dāng)0xπcos3x0fx0πxπcos3x0fx0 fx在0π上為增函數(shù)，在ππ 6 64 故fx在0,π上的最大值為fπ5cosπcos5π 4

6 2：我們有cos5xcosx4xcosxcos4xsinxsin4xcosx2cos22x1sinx2sin2xcoscosx8cos4x8cos2x14cosxcos2xsin28cos5x8cos3xcosx4cosx2cos2x11cos216cos5x20cos3x5cosx.fx5cosxcos5x5cosx16cos5x20cos3x5cosx20cos3x16cos54cos3x54cos2x4cosx354cosx24cosx3

52cos

52cos32cosxcosxcosx153 2cosx153 2cosx3 15151515 cosxcosxcosx

2cosx35 332 ，同時(shí)又有fπ5cosπcos5π 故fx在0,π上的最大值為 ，在R上的最大值也是 4 21：由余弦函數(shù)的性質(zhì)得cosxcos的解為2kπ2kπ2πkZ，若任意2kπ2kπ+2πkZ與aa交集為空，a2kπ2πa2kπ2πakZ2k1πa2kπak

a1k

a

2π31h(x5cosxcos5xth(x2π5cosx2πcos5x10π+thx當(dāng)tπh(x)5cosxcos5xπ6cosx6，當(dāng)t0h(x5cosxcos5xh(x)5sinx5sin5x5cos3xsin2xx02πh(x0

ππ5π 7π3π11π,, ,π, x6 x)))33,))0,)h(0)h(2π4

π

11π)

)33,h(π)4

h( 取5π，則cosy3xyt,xyt, 55 66故5cosx

綜上b

xπt0使得等號(hào)成立綜上，bmin 2gtx5cosxcos5xttgtx5cosxcos5xtbxtgtxgtxπbgtxbx恒成立，這直接得到b0tπmgxb bgtπ5costπcost5π5costπcostπ6costπ6cost 6 6 6 6 6 6 bgtπ5costπcost5π5costπcostπ6costπ

πt66 66 6 66 66 66 6cosm3 bgtπ5costπcost5π5costπcostπ6costπ

πt62 62 2 62 62 62 6cosm3

cosmcosmπ,cosmπb 再結(jié)合cos2x2cosx1， 2π

2π

b 就得到cos2m,cos2m3,cos2m3均不超過(guò)21 6 33假設(shè)b

，則b1 11 故cos2mcos2m2πcos2m2π11 3 3 2 但這是不可能的，因?yàn)槿齻€(gè)角2m2m2π2m2π x1所以假設(shè)不成立，這意味著b ②另一方面，若b3 ，則由（1）中已經(jīng)證明fx3 知存在t0，使得5cosxcos5xt5cosxcos5xfx b從而b

綜合上述兩個(gè)方面，可知b的最小值是332025（I）150分,120分鐘。第一部分聽(tīng)力（共兩節(jié),30分）第二部分閱讀（共兩節(jié),50分第一節(jié)（15小題;2.5分,37.5分,Thegreeningofplanes,trainsandMovinggoodsandpeoplearoundtheworldisresponsibleforalargepartofglobalCO2emissios

Thehardestsectortodecarbonizeisaviation.long-termoptionforsustainablefuelforplanesistomakehydrocarbonsfromrecycledair.Batteriesareenergy-efficientandelectriccarscanplugintoexistingsystemsandservices.Newsolid-statebatterieswillThehardestsectortodecarbonizeisaviation.long-termoptionforsustainablefuelforplanesistomakehydrocarbonsfromrecycledair.Batteriesareenergy-efficientandelectriccarscanplugintoexistingsystemsandservices.Newsolid-statebatterieswilltakeacarfartheronasingleSometrainsarealreadyelectrifiedthroughrailsorwires;otherscanbefuelcellsHydrogenfuelcellsareaLiquidammoniaiseasytokeepandtransportbutitishardtoignite（Thefuelsfortransportneedtobenotjustgreen,cheapandpowerful,butalsolightweightandsafeenoughtobecarriedaround.Eachmodeoftransporthasitsspecificfuelneeds.Muchisstilltobesettled,butherearesomeofthesolutionstogetusgoinggreen.madeelectricinprettysimplechoicethanbatteriesfortrucks,makinggreenhydrogenis燃）andrequiresanengineThisenergytransition（變革）isglobal,andtheamountofrenewableenergytheworldwillneedis"alittlebitmind-blowing,"saysmechanicalengineerKeithWipkeattheNationalRenewableEnergyLaboratoryIt'sestimatedthattheglobaldemandforelectricitycouldmorethandoubleby2050Fortunatelyanalysessuggestthatrenewablesareuptothetask."Weneedtospeedupthedevelopmentofgreenenergyanditwillallgetused,"saysWipke.WhatpercentageofglobaltransportemissionsdidroadvehiclesaccountforinA. B. C. D.WhichmodeoftransportcangogreencomparativelyA. B. C. D.WhatdoesWipkesuggestregardingenergyLimitingfuel B.PuttingmoreeffortintoC.Improvingenergy D.MakingelectricitymoreInmyninth-gradewritingclasslastyear,Imetacowboywhosavedhistown,astrictfatherwhodemandedhissonearnstraightA's,andamodern-dayJulietwhodiedofheartbreakafterherparentsrejectedtheloveofheryounglife.Morethanonce,Ifoundmyselfwonderingjusthowmystudents,who'dcreatedthesepeople,knewtheirsubjectssowell.Butthingsweredifferentfortheirfirstessaywhichwasaboutthequestion:"Whyiswritingimportant?"Mostoftheessaysfilledlessthanonepage,andfewcontainedasentencethatcouldbeinterpretedasathesis（論點(diǎn)）statement.Iwasshocked.ThenIrealizedthattheproblemwasthequestionitself.Theycouldhavewrittenpagesonthenecessityofcomputers,butwriting,inandofitself,simplydidn'tstrikethemasimportant.ThiswouldhavetoAsanewunitstartedIaskedeveryonetowriteapersuasivepieceonahealth-relatedtopicoftheirchoice.Thistimetheyfoundtheexercisemuchmoreinteresting.Forthenexttwoassignments,apersonal-narrativeunitfollowedbyacreative-writingworkshop,Ionlyrequiredthatthepiecemeetthespecificationsofitsgenre（體裁）andthatitcontainathesis.TheresultswerestaggeringThestudentstookondiversetopicsandturnedinstories,10to20pageseach,withcharactersthatbroadenedmyviewandtouchedmyheart.Iwalkedintoclassbelievingthatwritingisimportantasameansofcommunication.However,mystudentsdemonstratedsomethingmoreimportanttome.WhenthefinalbellranginJune,Iwalkedawaywithayearbookfullofmessagesaboutwriting'smostpowerfulsignificance—theabilitytoconnectpeople,toputusinanother'sskin,toteachuswhatitmeanstobehuman.WhoarethepeoplementionedatthebeginningofparagraphNinth B.Students'C.Modern D.FictionalWhydidthestudentsperformpoorlyinwritingtheirfirstTheywerenotgivenenough B.TheyhadaverylimitedC.Theymisunderstoodthe D.TheyhadlittleinterestintheWhatdoestheunderlinedword"staggering"inparagraph3A. B. C. D.Whatdoestheauthor'sexperienceTeachingis B.StillwatersrunC.Knowledgeispower. D.Practicemakesperfect.Whilesafetyimprovementsmighthavebeenmadetoourstreetsinrecentyears,transportstudiesalsoshowdeclinesinpedestrian（行人）mobilityespeciallyamongyoungchildrenManyparentssaythere'stoomuchtrafficontheroadsfortheirchildrentowalksafelytoschool,sotheypackthemintothecarinstead.DutchauthorsThaliaVerkadeandMarcoteBr?mmelstroetarebotheredbyfactslikethese.IntheirnewbookMovement:HowtoTakeBackOurStreetsandTransformOurLives,theycallforarethinkofourstreetsandtheroletheyplayinourlives.Lifeoncitystreetsstartedtochangedecadesago.Wholeneighbourhoodsweredestroyedtomakewayfornewroadnetworksandkidshadtoplayelsewhere.SomecommunitiesfoughtbackMostfamouslyaCanadianjournalistwhohadmovedherfamilytoManhattanintheearly1950sledacampaigntostopthedestructionofherlocalpark.Describingheralarmatitsproposedreplacementwithanexpressway,JaneJacobscalledonhermayor（市長(zhǎng)）tochampionNewYorkasadecentplacetolive,andnotjustrushthroughSimilarcampaignsoccurredinAustraliainthelate1960sand1970saswell.Althoughthesecampaignswerewidespread,therealityisthatthemajorityofthewesterncitieswerecompletelyredesignedaroundtheneedsofthemotorcar.Thenumberofcarsonroadshasbeenincreasingrapidly.InAustraliawenowhaveovertwentymillioncarsforjustovertwenty-sixmillionpeople,amongthehighestrateofcarownershipintheworld.Weinvestalotinroadsthathelpusrushthrough,butwefailtoaccountforthetruecosts.Dowereallyrecognisewhatitcostsusasasocietywhenchildrencan'tmovesafelyaroundourcommunities?TheauthorsofMovementhaveitright:it'stimetothinkdifferentlyaboutthatstreetoutsideyourfrontdoor.WhatphenomenondoestheauthorpointoutinparagraphCarsoftengetstuckonthe B.TrafficaccidentsoccurC.Peoplewalklessanddrive D.PedestriansfailtofollowtheWhatweretheCanadianjournalistandothercampaignerstryingtoKeeptheircities B.PromoteculturalC.Helptheneedy D.MakeexpresswaysWhatcanbeinferredaboutthecampaignsinAustraliainthelate1960sandTheyboostedthesalesof B.TheyturnedoutlargelyC.Theywongovernment D.TheyadvocatedbuildingnewWhatcanbeasuitabletitlefortheWhythe B.What'sC.Whereto D.WhotoMicroplasticshavebecomeacommonsourceofpollutionacrosstheEarth—theyhavesettledinthedeepseaandontheHimalayas,stuckinsidevolcanicrocks,filledthestomachsofseabirdsandevenfalleninfreshAntarcticsnow.Theyareevenappearinginsidehumans.Nownewresearchsuggeststhatasimple,cheapmeasuremaysignificantlyreducethelevelofmicroplasticsinwaterfromyourtap（水龍頭）boilingandfiltering（過(guò)濾）itInastudypublishedWednesdayinEnvironmentalScience&TechnologyLetters,researchersfromChinafoundthatboilingtapwaterforjustfiveminutes—thenfilteringitafteritcools-couldremoveatleast80percentofitsmicroplastics.Cruciallythisprocessreliesonthewatercontainingenoughcalciumcarbonate（碳酸鈣）totraptheplastics.Inthestudy,boilinghardwatercontaining300milligramsofcalciumcarbonateledtoanalmost90percentdropinplastics.Butinsampleswithlessthan60milligramsofcalciumcarbonate,boilingreducedthelevelofplasticsbyjust25percentAdditionally,theresearchdidn'tincludealltypesofplastics.Theteamfocusedonlyonthreecommontypes—polystyrene,polyethyleneandpolypropylene—andtheydidn'tstudyotherchemicalspreviouslyfoundinwatersuchasvinylchloride.Still,thefindingsshowapotentialpathforwardforreducingmicroplasticexposure—ataskthat'sbecomingincreasinglydifficult.Evenbottledwater,scientistsfoundearlierthisyear,contains10to1,000timesmoremicroplasticsthanoriginallythought.Scientistsarestilltryingtodeterminehowharmfulmicroplasticsare—butwhattheydoknowhasraisedconcerns.Thenewstudysuggestsboilingtapwatercouldbeatooltolimitintake."Thewaytheydemonstratedhowmicroplasticsweretrappedthroughtheboilingprocesswasnice,"CarolineGauchotte-Lindsay,anenvironmentalengineeroftheUniversityofGlasgowinScotlandwhowasnotinvolvedintheresearch,tellsNewScientist."Weshouldbelookingintoupgradingdrinkingwatertreatmentplantssotheyremovemicroplastics."HowdoestheauthorpresenttheissueinthefirstByquotingan B.BydefiningaC.Bygiving D.ByprovidingWhatdeterminestheeffectivenessoftrappingmicroplasticsinThehardnessof B.ThelengthofcoolingC.Thefrequencyof D.ThetypeofplasticinWhatdoestheauthortrytoillustratebymentioningbottledwaterinparagraphTheimportanceofplastic B.TheseverityofthemicroplasticC.Thedangerinoverusingpure D.ThedifficultyintreatingpollutedWhatisGauchotte-Lindsay'ssuggestionChoiceofnewresearch B.PossibledirectionforfurtherC.Needtoinvolvemore D.Potentialapplicationofthe第二節(jié)（5小題;2.5分,12.5分,AnUnsungNeedabreakbetweenclassesorjustaquickpick-me-upinthemorning?TheCollegeCafehasjustthat,more.36. CatherineMurphy,acafeworkerinagreenshirtandblackhat,makessurethateachcustomergetsexactlywhattheyorder.Shegoesbackandforthbetweenmachinestomakethedrinks.37. Asthecustomergrabsthedrinkfromherhand,shesmilesandsays,"Hello,howisyourday?"Evenwhenthelineisgettinglonger,shedoesn'tletitgetinthewayofhergenuineconversations.Murphygetsupataquartertofiveanddrivesthirtyminuteseverydaytogettoworkontime.38. "IdosobecauseIliketomakecoffeeforthestudents.Iknowtheyneeditinthemorning,"Murphysaid.Beingamotherandwifehashelpedherbecomethewomansheis.Shebelievessheisheretoserve.contagioushavingamuchbetterdaythantheywerehavingbeforeseeingher.JoannaWright,aseniorpoliticalsciencemajor,lovescoffeeandgoestothecafeatleastsixdaysaweek.39. "Catherinealwayshasahugesmileonherface,whichalwaysputsmeinacheerfulmood,"Wrightsaid."Ienjoyworkinginthecafe,"Murphysaid.40. Shehaseveryintentionofstayingandcontinuingdoingwhatsheloves.Thecafeclosesat9pmeveryShehastwochildrenagedeightandSometimesshearrivesearlytoservethestudentsAfterfinishinganorder,shecallsoutthenameontheNotonlydoesthiscafeserveupdrinks,italsoservesupGoingtothecafestartsherdayoffgoodandgetsherreadyforShehasservedherefor17yearsandcan'timagineworkinganywhere第三部分語(yǔ)言運(yùn)用（共兩節(jié),30分第一節(jié)（15小題;1分,15分,OneAugustafternoon,Isatinmykitchenstaringataglassvasethathadn'tseendaylightsincemyMyhusbandandIhadjustsoldourhouseandwewerebusy thebelovedhomeourfamilyhadspent23yearsfillingup.Wehaddecidedonkeyitemsforthe42 weweremovingtointown,donatedwhatwecould,andrentedaplaceto43 oursupposedlyimportantobjects.Thatleftahousestill44 withthingsthatwhilenotparticularly45 ,didn'tbelonginalandfill（垃圾填埋場(chǎng)）.Itookapictureofthevaseandposteditonline,for$10.Acoupleofmessagescamein,onewantingadditional ,anotheraskingforapricecut.Asour47 daydrewnear,Isettledonanewprice（$0）andrepostedit.The :"Ihatethisvase.Maybeyouwon't."Inaninstant,awomanracedintomyhouseandlefthappilywiththevase.49 ,Ipostedmore.Mydailypostsandthe50 Ireceivedbecameapreciousrayoflightinthechaosofmyhouse.Eachexchangeprovidedachanceto51 thelandfillandtopleaseanotherpersonImightnototherwisehave52 .Isitinmyapartmenttoday,lovingeachofthe53 thatshareoursmallspace.Itake54 inknowingthat,somewherenearby,someoneis55 somethingthatcouldn'tcomewithus.41.A.painting B.looking C.emptying D.pulling42.A.B.C.D.43.A.B.C.D.44.A.B.C.D.45.A.B.C.D.46.A.B.C.D.47.A.B.C.D.48.A.B.C.D.49.A.B.C.D.50.A.B.C.D.51.A.B.C.D.52.A.B.C.D.53.A.B.C.D.54.A.B.C.D.55.A.B.C.D.第二節(jié)（10小題;1.5分,15分,AnexhibitionattheJiushiArtMuseuminShanghaiisfeaturingartworkinspiredbyGo,orweiqiinChinese, originatedinChinamorethan4,000yearsGoisoneof57. piecesreflectthebasicideasofEasternphilosophy,accordingtoTuNingning,whoisinchargeoftheexhibition."TheexhibitionbringstogetherGoculture,cutting-edgetechnologyandcontemporaryart,"saysTu."We58. （present）theratherabstractGogameandAIinavisualcontext,andinitiatedialogueswithminimalistart,conceptualartandexpressionism.""InaGogame,eachmoveshouldservealong-termgoal.Youtrytoleadtheopponentintoyourtrapandforcethemtofollowyour'59. （guide）'tilltheylose,"explainsWangWei,aGoplayeramongthevisitorstotheexhibition."Theplayers'personalities60. （reveal）duringthegame,andone'sweaknessesareexposedtotheopponent,"sheadds."Adecentwinneralways61. （try）tobeattheopponent62. nomorethanoneortwopointsasagesture（姿態(tài)）ofrespectfortheotherside.”Tusaysthatthebalancebetweentheblackandwhitepieces,thebeautyinthe63. placementofthepieces,64. theenergyflowfollowingeachmoveinspiredartiststocreateoilpaintings,sculptures,65. （digital）generatedpicturesandsilk-screenprintsfortheexhibition.（共兩節(jié),40分第一節(jié)（15分假定你是李華,Jenny提出“Funatmyschool”和“GuesswhoIam”兩Jenny寫(xiě)一封郵件,內(nèi)容包括:DearDearIreallyliketheideaofaddinganewcolumntoourEnglishLi第二節(jié)（25分閱讀下面材料,根據(jù)其內(nèi)容和所給段落開(kāi)頭語(yǔ)續(xù)寫(xiě)兩段,MywifeandIwantedtoshareournewhomewithfamilyandfriendsbyhostingasmallgatheringintheearlysummer.Shehadpreparedlotsofsnacks,whilemyjobwastohavethebackyardinorder.Therewasplentyofspaceforthekidstorunandplay.TherewasjustonethingIhadn'tcountedon:MybrotherchosetobringhisdogToby,a50-poundballoffire.Thoughfriendly,hecouldeasilyknockovermyniece'ssmallboysandmysix-month-oldgranddaughter.So,whenmybrothershowedup,IaskedhimtowatchTobyandkeephimMyplanwasworkingoutjustfine.Tobywasusinguphisenergybyrunningbackandforthinthebackyardandgivingthekidsplentyofroom.Unexpectedly,aftersupper,theweatherchanged.ItstartedtorainandeveryonewentItwasanawkwardmoment.Ididn'twantTobytoberunningaroundinthehouse,andmybrotherwasn'thappywithdrivinghomewithawetdog.Eventually,mybrotherdecidedtoleaveratherthanforcetheissue.Afewdayspassed,andIhadn'theardanythingfrommybrother.Itextedhimandexpressedwishesforhimtocomeoutagain.Hisreplycameasasurprise—ashock,actually:"Notachance."Clearly,hewasunhappyoverthewaywehadparted.Afterall,Ihadlefthimlittlechoice.Well,he'llgetoverit,Ireasoned.Twomonthspassed.MywifesuggestedIgetintouchwithmybrotherbutIresistedthinkingheshouldcallfirst.Howevermyconscience（良心）keptbotheringme.Itriedtoputmyselfinmybrother'sshoes.Hewasfacinghealthissuesandhiswifeofthirty-fiveyearshadpassedawayafewmonthsearlierTobywashisconstantcompanion,theonewhokepthimgoing.IIrealizeditwasmewhowasatWithWiththebiscuitsmywifehadmade,Iarrivedatmybrother's2025年普通高等學(xué)校招生全國(guó)統(tǒng)一考試(I)150分,120第一部分聽(tīng)力(共兩節(jié),30分)第二部分閱讀(共兩節(jié),50分第一節(jié)(15小題;2.5分,37.5分閱讀下列短文,A、B、C、DThegreeningofplanes,trainsandMovinggoodsandpeoplearoundtheworldisresponsibleforalargepartofglobalCO2emissions排放Astheworldracestodecarbonizeeverything,itfacesparticularproblemswithtransportation—whichaccountsforaboutaquarterofourenergy-relatedgreenhousegasemissions.Here’sthebreakdownoftheemissionsin2018fordifferentmodesoftransport.CARS—BatteriesBatteriesareenergy-efficientandelectriccarscanplugintoexistingsystemsandservices.Newsolid-statebatterieswilltakecarfartheronasinglePLANES—SynthetichydrocarbonsThehardestsectortodecarbonizeisaviation.Onelong-termoptionforsustainablefuelforplanesistomakehydrocarbonsfromrecycledThefuelsfortransportneedtoCARS—BatteriesBatteriesareenergy-efficientandelectriccarscanplugintoexistingsystemsandservices.Newsolid-statebatterieswilltakecarfartheronasinglePLANES—SynthetichydrocarbonsThehardestsectortodecarbon