2021北京平谷區(qū)初一上期末數(shù)學(xué)試卷及答案

2021北京平谷初一（上）期末數(shù)學(xué)2021.1（考試時間120分鐘100分）學(xué)校____________________________________________1．本試卷共6頁，共三道大題，24道小題．考生須知2．在試卷和答題卡上認真填寫學(xué)校、班級、姓名、考號．3．試題答案一律填涂或書寫在答題卡上，在試卷上作答無效．4．在答題卡上，選擇題、作圖題用鉛筆作答，其他試題用黑色字跡簽字筆作答．5．考試結(jié)束，請將本試卷、答題卡和草稿紙一并交回．一、選擇題（本題共24分，每小題3分）下面1-8題均有四個選項，其中符合題意的選項只有一個．．．1.12月3日23點10分，嫦娥五號上升器月面點火，約6分鐘后，順利將攜帶月壤的上升器送入預(yù)定環(huán)月軌道，實現(xiàn)我國首次地外天體起飛.起飛前，國旗展示系統(tǒng)成功在月面打開，這是中國首次在月球展示“織物版五星紅旗.380000公里外，那一抹“中國紅振奮著每一個中國人的心.請你用科學(xué)記數(shù)法表示380000:A.384B.3.8105C.3.8106D.0.381062．下列各組數(shù)中，互為相反數(shù)的一組是A.?(和3B.(?3和-33C.?3和?3D.(2和?323．如圖是一個小正方體展開圖，把展開圖折疊成小正方體后，有“志字一面的相對面上的字是A.事竟4.下列等式變形正確的是x=2C.成D.者A．若2x1，則=B．若4x?1=2?3x，則4x+3x=2?132x=3，則x=?C.若21/93x+11?2xD．若?=1，3(3x+??2x)=1235．下列各式是同類項的是A.2bB.2a2bab2C.2aD.2和26．有理數(shù)b在數(shù)軸上的位置如圖所示，下列說法正確的是A.0B.abC.a+b0D.?ab7．下列語句正確的個數(shù)是①直線外一點與直線上各點連接的所有線段中，垂線段最短②兩點之間直線最短③在同一平面內(nèi)，兩條不重合的直線位置關(guān)系不平行必相交④兩點確定一條直線A．1B．2C．3D．48.大家都知道，七點五十可以說成差十分鐘八點，有時這樣表達更清楚，這也啟發(fā)了人們設(shè)計了一種新的加減記數(shù)法．——比如：8寫成12，12=10-2—189229=200-20+9———7683寫成12323=10000-2320+3————按這個方法請計算5231-3241=A.2408B.1990C.2410D.3024二、填空題（本題共24分，每小題3分）9.北京某天最高氣溫是6，最低氣溫是-3℃，則這一天的溫差是____________ab10.請你寫出一個只含有,，且系數(shù)為，次數(shù)為3的單項式是________14161211.計算：(+?)=________12.已知a4(b3)++?2=0,則(a+b2021=________13.計算：60?=________2/914.《九章算術(shù)》中有一道闡述“盈不足術(shù)”的問題，原文如下：今有人共買物，人出八，盈三；人出七，不足四．問人數(shù)，物價各幾何？譯文為：現(xiàn)有一些人共同買一個物品，每人出8元，還盈余3元；每人出7元，則還差4元，問共有多少人？這個物品的價格是多少？設(shè)這個物品的價格是x元，則可列方程為15．如圖，C是線段AB上一點，D，E分別是線段AC，BC的中點，若AC=2，BE=4，則DE=．ADCEB16．觀察右面的圖案，每條邊上有（n≥2）個方點,每個圖案中方點的總數(shù)是S.（1）請寫出n=5時，S=（2）按上述規(guī)律，寫出S與n的關(guān)系式，S=；．三、解答題(19-20題每題分，21-24題每題525題626題652分)17．計算：（1）2?(+(14)?(?12)13(+(7???22（2）2418．解方程：（1）x?6)=?4x?32x+11?10x=1?（2）3619．按要求畫圖，并回答問題：如圖，在同一平面內(nèi)有三點A、B、C．（1）畫射線AC和直線AB；（2）連接線段BC，并延長BC至D，使CD=BC；（3）連接線段AD；（4）通過畫圖和測量，點C到線段AD的距離大約是（精確到0cm）．3/9(?2+2x+2x)+1，其中x=3)(2x?3x2220．先化簡，再求值：21．已知：是∠AOC的角平分線，OC是∠AOD的角平分線，∠COD=40°．分別求∠AOD和∠BOC的度數(shù)．DCOBA222020年的天貓雙十一比以往來的更早一些.如今的雙十一也不再是當年那個僅此一天的雙十一,今年的活動期已經(jīng)拉長到了一個月左右.曉晨一家人打算在今年的雙十一促銷中，爭取花最少的錢，買到物美價廉的產(chǎn)品.曉晨想買一些學(xué)習(xí)用品，清單見表1.媽媽想買一臺智能掃地機器人，爸爸想買一臺空氣凈化器，經(jīng)過反復(fù)的篩選，一家人決定從以下兩個品牌當中挑選掃地機器人和空氣凈化器，它們的單價見表2.雙十一電子商品促銷方案見表3.表1表2單價（元）總價（元）掃地機器人單價空氣凈化器單價（元/臺）（元/臺）筆記本碳素筆書包580甲品牌乙品牌2600300025002400260（1）曉晨購買a個筆記本，b支碳素筆，1個書包一共要支付（用含有字母a、b的代數(shù)式來表示）元.（2）曉晨購買筆記本的數(shù)量比購買碳素筆的數(shù)量少3個，還購買了一個書包，總金額請見表，請問曉晨購買了幾支碳素筆？（3）請你幫忙計算選擇哪種品牌的掃地機器人和空氣凈化器能夠花費最低,并直接寫出總花費為元.4/9表31.所有電子商品均享受每滿300減元；2.在滿減的基礎(chǔ)上還可享受購買同一品牌商品一件9折、兩件8折的優(yōu)惠；3.掃地機器人預(yù)售定金翻倍：提前支付50元定金抵20010月21日-11月日期間支付元定金，可在11月11日結(jié)算時抵扣200元）23．如圖：點O為直線上一點，過點O作射線OP，使∠AOP=60°，將一直角三角板的直角頂角放在點O處（1）如圖，一邊OM為射線OB上，另一邊ON在直線AB的下方，那么鈍角∠PON的度數(shù)（2）如圖，將圖1中三角板繞點O逆時針旋轉(zhuǎn)，使邊OM在∠BOP的內(nèi)部，且OM恰好平分∠BOP，此時∠BON的度數(shù)（3）如圖，繼續(xù)將圖2中的三角板繞點O逆時針旋轉(zhuǎn)度，使得ON在∠AOP內(nèi)部，且滿足∠AOM=3∠NOP時，求的度數(shù)26.閱讀下面材料，回答問題已知點A,B在數(shù)軸上分別表示有理數(shù)a，b.A,B兩點之間的距離表示AB（一）當AB兩點中有一點在原點時，不妨設(shè)點A在原點，如圖1)BO==b?a=b?a=a?b（二）當A,B兩點都不在原點時,①如圖2,點A,B都在原點的右邊,5/9ABO=?=b?a=b?a=a?b②如圖3,點A,B都在原點的左邊,BAO=?=b?a=?b?(?a)=a?b=a?b③如圖4,點A,B在原點的兩邊,BAO=+=a+b=a+(b)=a?b=a?b綜上,數(shù)軸AB兩點的距離=a?b利用上述結(jié)論,回答以下幾個問題:（1）數(shù)軸上點A表示的數(shù)是1，點B表示的數(shù)是，且點B與點A在原點的同側(cè)，AB=3，則x=__________（2）數(shù)軸上點A到原點的距離是1B表示的數(shù)絕對值是，則AB=_________（3）若點、B在數(shù)軸上表示的數(shù)分別是-4、2P在數(shù)軸上表示的數(shù)是x，當8時，直接寫x+=的值6/92021北京平谷初一（上）期末數(shù)學(xué)參考答案一、選擇題（本題共24分，每小題3分）題號答案12345678BDACCDCA二、填空題（本題共24分，每小題3分）題號答案991011-112-11347°22’14151616，4n?42a2b或2ab28x?3=7x4+5三、解答題(17-18題每題分，19-22題每題523題624題652分)171）．解：2?(+(14)?(?12)2?1?+=···················································································4分=5···································································································5分13(+(7???22172）．解：241=1+3?2······················································································3分2=2+3?2···························································································4分=3····································································································5分181）．解：x?6)=?4x?3去括號，得5x?=4x?3·······························································2分移項，得5x+4x=3+···································································3分合并同類項，得9x·······································································4分=系數(shù)化為1x=3············································································5分2x+11?10x182）.解：=1?36去分母（方程兩邊同乘以6），得2(2x+=6??10x)．····································································1分4x+2=6?1+10x去括號，得．·························································2分7/9移項，得4x?10x=6?1?2．···························································3分6x=3．···································································4分合并同類項，得1系數(shù)化為1x=?．······································································5分219.圖略·································································································4分距離在1.41.6之間··············································································5分()2x?3x2?2+2(x+2x2)+120.解：2x?3x4x+x當x=3時，2+2+2x+4x2+1·································································2分＝＝2+3．····················································································3分?34+(?+3··········································································4分2原式==05分平分AOD,AOC=COD=AOD21.解：1…………………….………1分2又=40==40平分…………………….………2…………………….………3分分1…………………….………4分=2=…………………….………5分22．解：（）ab++…………………….………1分（2）設(shè)曉晨購買了x支碳素筆根據(jù)題意列方程，得……2分2x+x?+60=80.………….………3分……………4分解得：x=5答：曉晨購買了5支碳素筆。（3）3386…………………….………5分23.解：（）NOP=150…………………….………1分8/9（2）+=180=………………….………2分=平分BOP1…………………….………3分BOM=BOP=602=90……………….………4分BON=