江蘇省南通市如東縣部分學(xué)校2023-2024學(xué)年七年級(jí)下學(xué)期期中考試數(shù)學(xué)試卷

七年級(jí)數(shù)學(xué)期中試題第2頁(yè)（共6頁(yè)）七年級(jí)數(shù)學(xué)期中試題第1頁(yè)（共6頁(yè)）2023-2024學(xué)年度第二學(xué)期期中學(xué)情調(diào)研七年級(jí)數(shù)學(xué)試題（總分150分，考試時(shí)間120分鐘）一．選擇題（本大題共10小題，每小題3分，共30分．在每小題給出的四個(gè)選項(xiàng)中，恰有一項(xiàng)是符合題目要求的，請(qǐng)將正確選項(xiàng)的字母代號(hào)填涂在答題卡相應(yīng)位置上）1.64的平方根是A.±8 B.±4 C.8 D.42.下列各數(shù)中，無(wú)理數(shù)是A.25 B.8 C.2273.下列調(diào)查中，適宜采用全面調(diào)查方式的是A.了解全國(guó)中學(xué)生的視力情況B.調(diào)查某批次日光燈的使用壽命C.調(diào)查市場(chǎng)上礦泉水的質(zhì)量情況D.調(diào)查機(jī)場(chǎng)乘坐飛機(jī)的旅客是否攜帶了違禁物品4.在平面直角坐標(biāo)系中，點(diǎn)P(m，?4?mA.第一象限 B.第二象限 C.第三象限 D.第四象限已知a，b是兩個(gè)連續(xù)整數(shù)，a<3?3<b，則a+b的值是

2 B.3 C.4 D.5若x>y，則下列不等式中一定成立的是

A.x2>y2 B.?3x>?3y C.x7.不等式組x?1＞04?2x≥0的解集在數(shù)軸上表示為

A. B.C. D.8.若關(guān)于x，y的方程組3x?4y=8mx+(2m?1)y=7的解也是二元一次方程x+2y=1A.152 B.132 9.《孫子算經(jīng)》是中國(guó)古代重要的數(shù)學(xué)著作，成書(shū)大約在一千五百年前，其中一道題，原文是：“今三人共車，兩車空；二人共車，九人步．問(wèn)人與車各幾何？”意思是：現(xiàn)有若干人和車，若每輛車乘坐3人，則空余兩輛車；若每輛車乘坐2人，則有9人步行．問(wèn)人與車各多少？設(shè)有x人，y輛車，可列方程組為

A.x3=y+2x2+9=y B.x3=y?2x10.已知關(guān)于x，y的方程組x?y=1x+y=2a+3中x，y均大于0.若a與正數(shù)b的和為4A.?6<a?b<4 B.?6<a?b≤4C.?5<a?b<3二．填空題（本大題共8小題，第11、12題每小題3分，第13—18題每小題4分，共30分．不需寫(xiě)出解答過(guò)程，請(qǐng)把答案直接填寫(xiě)在答題卡相應(yīng)位置上）11.11的相反數(shù)是▲.12.比較大?。?213.空氣是由多種氣體混合而成的，為例直觀地介紹空氣各成分的百分比，最合適使用的統(tǒng)計(jì)圖是▲(從“條形圖，扇形圖，折線圖和直方圖”中選一個(gè)）14.已知點(diǎn)A坐標(biāo)為(1,2)，點(diǎn)B在第四象限，直線AB//y軸.若線段AB=3，則點(diǎn)B的坐標(biāo)為▲.15.若x+2y+3z=5，4x+3y+2z=10，則x+y+z的值是▲.16.某次知識(shí)競(jìng)賽共有20道題，每一題答對(duì)得10分，答錯(cuò)或不答都扣5分，小明得分要超過(guò)90分，他至少要答對(duì)▲道題.17.對(duì)于實(shí)數(shù)x，我們規(guī)定[x]表示不大于x的最大整數(shù)，例如已知[1.5]=1，[?2.7]=?3.若實(shí)數(shù)a滿足[2?a]+1=0，則實(shí)數(shù)a的取值范圍是18.已知關(guān)于x，y的方程m?2x+m?1y=3m+a，不論m是怎樣的常數(shù)，總有一組解為x=2y=b(其中a，b是常數(shù))三、解答題（本大題共8小題，共90分．請(qǐng)?jiān)诖痤}卡指定區(qū)域內(nèi)作答，解答時(shí)應(yīng)寫(xiě)出文字說(shuō)明、證明過(guò)程或演算步驟）19.(本小題12分)（1）計(jì)算：；（2）解方程組：.七年級(jí)數(shù)學(xué)期中試題第3頁(yè)（共6頁(yè)）(本小題8分)解不等式組，并寫(xiě)出它的所有非負(fù)整數(shù)解.(本小題10分)在等式y(tǒng)=ax2+bx+c中，當(dāng)x=1時(shí)，y=?2；當(dāng)x=?1時(shí)，y=20；當(dāng)x=32與x=13(本小題10分)某校在暑假期間開(kāi)展“心懷感恩，孝敬父母”的實(shí)踐活動(dòng)，并隨機(jī)抽取了部分學(xué)生就暑假“平均每天幫助父母干家務(wù)所用時(shí)長(zhǎng)”進(jìn)行了調(diào)查，列出了下面的頻數(shù)分布表：時(shí)長(zhǎng)(分鐘)0≤t<1010≤t<2020≤t<3030≤t<4040≤t<50頻數(shù)6648m304百分比32n12%(1)在本次隨機(jī)抽取的樣本中，調(diào)查的學(xué)生人數(shù)是______人；(2)如表中，m的值為_(kāi)_____，n的值為_(kāi)_____；(3)如果該校共有學(xué)生3000人，請(qǐng)你估計(jì)該校暑假“平均每天幫助父母干家務(wù)的時(shí)長(zhǎng)不少于30分鐘”的學(xué)生大約有多少人？七年級(jí)數(shù)學(xué)期中試題第4頁(yè)（共6頁(yè)）(本小題10分）閱讀下面材料：

分子、分母都是整式，并且分母中含有未知數(shù)的不等式叫做分式不等式．

小亮在解分式不等式時(shí)，是這樣思考的：

根據(jù)兩數(shù)相除，同號(hào)得正，異號(hào)得負(fù)．原分式不等式可轉(zhuǎn)化為下面兩個(gè)不等式組：

①

或

②

解不等式組①得，

解不等式組②得．

所以原不等式的解集為或．

請(qǐng)你參考小亮思考問(wèn)題的方法，解分式不等式．(本小題12分)用1塊A型鋼板可制成1塊C型鋼板和2塊D型鋼板；用1塊B型鋼板可制成2塊C型鋼板和1塊D型鋼板.(1)若現(xiàn)需18塊C型鋼板和21塊D型鋼板，可恰好用A型鋼板、B型鋼板各多少塊？(2)若A型鋼板和B型鋼板共14塊，且能制成的C型鋼板數(shù)多于D型鋼板數(shù)，求A型鋼板至多有多少塊？七年級(jí)數(shù)學(xué)期中試題第5頁(yè)（共6頁(yè)）(本小題14分)如圖，平面直角坐標(biāo)系xOy中，點(diǎn)A，B坐標(biāo)分別為(a,0)，(0,b)，且a，b滿足(1)a=,(2)若點(diǎn)C(m，n)在線段AB上，m，n滿足m+n=5，點(diǎn)D在y軸負(fù)半軸上，線段CD交x軸于點(diǎn)M，三角形MOD與三角形MAC(3)平移直線AB交x軸于點(diǎn)E，交y軸于點(diǎn)F，點(diǎn)P為直線EF上任意一點(diǎn)，且△PAB面積為15,直接寫(xiě)出OE的長(zhǎng).七年級(jí)數(shù)學(xué)期中試題第6頁(yè)（共6頁(yè)）（本小題14分）對(duì)于平面直角坐標(biāo)系xOy中的點(diǎn)A，給出如下定義：若存在點(diǎn)B(不與點(diǎn)A重合，且直線AB不與坐標(biāo)軸平行或重合)，過(guò)點(diǎn)A作直線m//x軸，過(guò)點(diǎn)B作直線n//y軸，直線m，n相交于點(diǎn)C.當(dāng)線段AC，BC的長(zhǎng)度相等時(shí)，稱點(diǎn)B為點(diǎn)A的等距點(diǎn)，稱三角形ABC的面積為點(diǎn)A的等距面積.例如：如圖，點(diǎn)A(2,1)，點(diǎn)B(5,4)，因?yàn)锳C=BC=3，所以B為點(diǎn)A的等距點(diǎn)，此時(shí)點(diǎn)A的等距面積為92．

(1)點(diǎn)A的坐標(biāo)是(0,1)，在點(diǎn)B1(1,0)，B2((2)點(diǎn)A的坐標(biāo)是(3,?①若點(diǎn)A的等距點(diǎn)B的坐標(biāo)是(-1,a)，求點(diǎn)B的坐標(biāo)和此時(shí)點(diǎn)A的等距面積；②若點(diǎn)A的等距面積不小于258，且點(diǎn)A的等距點(diǎn)B在第一象限，寫(xiě)出此時(shí)點(diǎn)B的橫坐標(biāo)t的取值范圍.2023-2024學(xué)年度第二學(xué)期期中學(xué)情調(diào)研七年級(jí)數(shù)學(xué)試題參考答案選擇題題號(hào)12345678910答案ABDABDCBCA二、填空題11.；12.＜；13.扇形圖；14.（1，-1）；15.3；16.13；17.2＜a≤3；18.-5.三、解答題19．（本小題滿分12分）（1）解：原式=·································································3分==··························································································6分（2）解：，得，解得x=6···································································································9分把x=6代入①，得···············································································11分所以原方程組的解是··············································································12分20．（本小題滿分8分）解：解不等式①，得x≤2·······················································································2分解不等式②，得x＞-4·····················································································4分所以不等式組的解集為-4＜x≤2··········································································6分非負(fù)整數(shù)解為：0，1，2.·············································································8分（本小題滿分10分）解：由題意得············································································3分①-②，得2b=-22b=-11····························································································5分由③，得77a=-42ba=6································································································7分把a(bǔ)=6,b=-11代入①，得c=3················································································9分所以，······················································································10分22．（本小題滿分10分）解：（1）200·······································································································2分（2）52,26％······························································································6分（3）510···································································································10分23．（本小題滿分10分）解：原分式不等式可轉(zhuǎn)化為下面兩個(gè)不等式組：①

或

②·····································································4分解不等式組①得··············································································6分解不等式組②得無(wú)解···············································································8分

所以原不等式的解集為·····································································10分24．（本小題滿分12分）解：（1）設(shè)A型鋼板用x塊，B型鋼板用y塊.根據(jù)題意，得，·······································································4分解得：···········································································6分答：A型鋼板用8塊，B型鋼板用5塊.·······························································7分（2）設(shè)A型鋼板用a塊，依題意有···········································································9分解得．································································································11分答：A型鋼板至多6塊．···················································································12分25．（本小題滿分14分）解：（1）4,6，12····························································································4分（2）由m+n=5,得n=5-m，所以點(diǎn)C(m，5-m)因?yàn)镾△AOC+S△BOC=S△AOB所以解得m=2所以n=3所以C(2，3）·····························································································7分設(shè)D（0，y）由S△MOD=S△MAC，得S△BCD=S△AOB所以解得y=-6所以D（0，-6）·············································································