2024年北京燕山區(qū)七年級(jí)初一（上）期中數(shù)學(xué)試題（含答案）

第1頁(yè)/共1頁(yè)數(shù)學(xué)2024年11月學(xué)校_________________班級(jí)________姓名________學(xué)號(hào)________考生須知1．本試卷共4頁(yè)，共三道大題，26道小題，滿分100分?？荚嚂r(shí)間100分鐘。2．在試卷和答題卡上準(zhǔn)確填寫學(xué)校名稱、班級(jí)、姓名和學(xué)號(hào)。3．試題答案一律填涂或書寫在答題卡上，在試卷上作答無(wú)效。4．2B5．考試結(jié)束，請(qǐng)將本試卷和答題卡一并交回。一、選擇題(共20分，每題2分)第110題均有四個(gè)選項(xiàng)，符合題意的選項(xiàng)只有一個(gè)．1．的相反數(shù)是A． B． C． D．2．下表是幾種液體在標(biāo)準(zhǔn)大氣壓下的沸點(diǎn)：液體名稱液態(tài)氧液態(tài)氫液態(tài)氮液態(tài)氦沸點(diǎn)/℃－183－252.78－196－268.9則沸點(diǎn)最低的液體是A．液態(tài)氧 B．液態(tài)氫 C．液態(tài)氮 D．液態(tài)氦3．據(jù)統(tǒng)計(jì)，今年“十·一”小長(zhǎng)假期間，近70000人次游覽了園博園“京彩燈會(huì)”．將70000用科學(xué)記數(shù)法表示應(yīng)為A． B． C． D．4．有理數(shù)a，b，c在數(shù)軸上的對(duì)應(yīng)點(diǎn)的位置如圖所示，則下列式子中正確的是A． B．C． D．5．已知是方程的解，則的值是A．－3 B．－1 C．1 D．36．下列運(yùn)算中，正確的是A． B．C． D．7．如果，那么根據(jù)等式的性質(zhì)，下列變形不正確的是A． B．C． D．8．下面四個(gè)式子中，不能表示圖中陰影部分面積的是A． B．C． D．9．我國(guó)古代典籍《莊子·天下篇》中有這樣一句話：“一尺之棰，日取其半，萬(wàn)世不竭”．現(xiàn)有一根長(zhǎng)為1尺的木桿，第1次截取其長(zhǎng)度的一半，第2次截取其第1次剩下長(zhǎng)度的一半，第3次截取其第2次剩下長(zhǎng)度的一半，…，則第99次截取后，木桿剩下的長(zhǎng)度為A．尺 B．尺 C．尺 D．尺10．右圖是某月的月歷，現(xiàn)用“”圖形在月歷中框出5個(gè)數(shù)，它們的和為55．不改變“”圖形的大小，將“”圖形在該月歷上移動(dòng)，所得5個(gè)數(shù)的和可能是A．40 B．88C．107 D．110二、填空題(共16分，每題2分)11．用四舍五入法對(duì)1.654取近似數(shù)(精確到十分位)是．12．比較大小：(填“＜”，“＞”或“＝”)．13．計(jì)算：，＝．14．請(qǐng)寫出一個(gè)與為同類項(xiàng)的整式：．15．一臺(tái)電腦原價(jià)為a元，降價(jià)20％后，又降低m元，現(xiàn)售價(jià)為元．16．已知，則代數(shù)式的值為．17．觀察下列代數(shù)式：，，，，，…，按照上述規(guī)律，第2024個(gè)代數(shù)式是，第個(gè)代數(shù)式是．18．計(jì)算機(jī)將信息轉(zhuǎn)換成二進(jìn)制數(shù)處理的，二進(jìn)制即"逢2進(jìn)1"，如（1101)2表示二進(jìn)制數(shù)，將它轉(zhuǎn)換成十進(jìn)制形式是1×23+1×22+0×21+1×20=13，那么將二進(jìn)制數(shù)（10111)2轉(zhuǎn)換成十進(jìn)制是，將十進(jìn)制數(shù)21轉(zhuǎn)換成二進(jìn)制是．三、解答題(共64分，第19題16分，每小題4分；第20-21題，每題10分，每小題5分；第22-23題，每題5分；第24-26題，每題6分)19．計(jì)算：(1)；(2)；(3)；(4)．20．化簡(jiǎn)：(1)；(2)．21．解方程：(1)；(2)．22．已知，，求代數(shù)式的值．23．如圖，數(shù)軸上點(diǎn)A表示的數(shù)為a，點(diǎn)B表示的數(shù)為b，點(diǎn)C表示的數(shù)為c，其中b是最大的負(fù)整數(shù)，c是最小的正整數(shù).(1)b＝，c＝；(2)用“＜”將a，，－c，c連接起來(lái)；(3)點(diǎn)P為數(shù)軸上一動(dòng)點(diǎn)，則的最小值為．24．隨著人們生活水平的提高，家用轎車越來(lái)越多地進(jìn)入家庭．小明家買了一輛小轎車，他記錄了連續(xù)7天中每天行駛的路程(如下表，單位：km)，以50km為標(biāo)準(zhǔn)，多于50km的記為“＋”，不足50km的記為“－”，剛好50km的記為“0”．第一天第二天第三天第四天第五天第六天第七天－8－11－140－16＋38＋18(1)這七天中，行程最多的一天比行程最少的一天多行駛了多少千米？(2)請(qǐng)求出這七天中平均每天行駛多少千米；(3)若行駛100km需用汽油6L，汽油價(jià)為8.2元/L，請(qǐng)估計(jì)小明家一個(gè)月(按30天計(jì)算)的汽油費(fèi)用是多少元？(結(jié)果保留整數(shù))25．為迎接新生，某中學(xué)計(jì)劃添置100張課桌和把椅子．現(xiàn)經(jīng)調(diào)查發(fā)現(xiàn)，某家具廠的每張課桌定價(jià)為200元，每把椅子定價(jià)為80元，而廠方在開(kāi)展促銷活動(dòng)期間，向客戶提供了兩種優(yōu)惠方案：方案一：每買一張課桌就贈(zèng)送一把椅子．方案二：課桌和椅子都按定價(jià)的80％付款．(1)用含的代數(shù)式分別表示方案一與方案二各需付款多少元？(2)當(dāng)時(shí)，通過(guò)計(jì)算說(shuō)明該中學(xué)選擇哪種方案更省錢．26．閱讀下面方框內(nèi)的材料：一個(gè)含有多個(gè)字母的式子中，任意交換兩個(gè)字母的位置，當(dāng)字母的取值均不相等，且都不為一個(gè)含有多個(gè)字母的式子中，任意交換兩個(gè)字母的位置，當(dāng)字母的取值均不相等，且都不為0時(shí)，式子的值都不變，這樣的式子叫作對(duì)稱式．例如：式子abc中任意兩個(gè)字母交換位置，可得到式子bac，acb，cba，因?yàn)閍bc＝bac＝acb＝cba，所以abc是對(duì)稱式．而式子中的字母a，b交換位置，得到式子，但是，所以不是對(duì)稱式．解答下面的問(wèn)題：(1)下列式子：①；②；③，其中是對(duì)稱式的是(填序號(hào))；(2)寫出一個(gè)系數(shù)為－2，只含有字母a，b且次數(shù)為6的單項(xiàng)式，使該單項(xiàng)式是對(duì)稱式；(3)已知，，求，并判斷所得結(jié)果是否是對(duì)稱式．

一、選擇題（共20分，每題2分）題號(hào)12345678910選項(xiàng)ADBBADCCBD二、填空題（共16分，每題2分）11．1.7；12．>；13．－6，－16；14．（答案不唯一）；15．；16．；17．，；18．23，．三、（共64分，第19題16分，每小題4分；第20-21題，每題10分，每小題5分；第22-23題，每題5分；第24-26題，每題6分）19．計(jì)算(本題滿分16分，每小題4分)解：（1）＝12－3－7········································2分＝2．········································4分（2）＝········································2分＝－(6.5×2×3)＝－39．········································4分（3）＝·········································2分＝－7．········································4分（4）＝········································3分＝＝．·········································4分20．化簡(jiǎn)(本題滿分10分，每小題5分)解：（1）＝··········································2分＝··········································4分＝．···········································5分（2）＝············································2分＝·············································4分＝．·············································5分21．解方程(本題滿分10分，每小題5分)解：（1），·············································2分，·············································3分，·············································4分．·············································5分（2），···············································2分，···············································3分，···············································4分．···············································5分22．(本題滿分5分)解：＝················································2分＝＝··················································4分當(dāng)，時(shí)，原式＝．··················································5分23．(本題滿分5分)解：（1）－1，1；··················································2分（2）；··················································4分（3）．···················································5分24．(本題滿分6分)解：（1）···················································1分＝54km．···················································2分答：行程最多的一天比行程最少的一天多行駛了km．（2）·········································3分＝50＋7÷7＝51km．··············································4分答：這七天中平均每天行駛51km．（3）···············································5分＝752.76≈753元．··············································6分答：小明家一個(gè)月(按30天計(jì)算)的汽油費(fèi)用是元.25．(本題滿分6分)解：（1）方案一：···············································1分＝＝元．·········································