南京市聯(lián)合體2015年中考二模數(shù)學試題及答案(共12頁)

1、精選優(yōu)質文檔-傾情為你奉上2015年中考模擬試卷（二）數(shù) 學化工園雨花棲霞浦口四區(qū)聯(lián)合體注意事項：1本試卷共6頁全卷滿分120分考試時間為120分鐘考生答題全部答在答題卡上，答在本試卷上無效2請認真核對監(jiān)考教師在答題卡上所粘貼條形碼的姓名、考試證號是否與本人相符合，再將自己的姓名、準考證號用0.5毫米黑色墨水簽字筆填寫在答題卡及本試卷上3答選擇題必須用2B鉛筆將答題卡上對應的答案標號涂黑如需改動，請用橡皮擦干凈后，再選涂其他答案答非選擇題必須用0.5毫米黑色墨水簽字筆寫在答題卡上的指定位置，在其他位置答題一律無效4作圖必須用2B鉛筆作答，并請加黑加粗，描寫清楚一、選擇題（本大題共6小題，每小題

2、2分，共12分在每小題所給出的四個選項中，恰有一項是符合題目要求的，請將正確選項前的字母代號填涂在答題卡相應位置上）1的相反數(shù)是 （ ） A. -2B.2 C. -D. 2.下列計算正確的是（ ）A. a3+a4=a7B2a3a4=2a7C（2a4）3=8a7 Da8÷a2=a43.為調查某班學生每天使用零花錢的情況，張華隨機調查了20名同學，結果如下表：每天使用零花錢（單位：元）12345人數(shù)13655則這20名同學每天使用的零花錢的眾數(shù)和中位數(shù)分別是（ ）A. 3，3B. 3，3.5 C. 3.5，3.5D. 3.5，34小張同學的座右銘是“態(tài)度決定一切”，他將這幾個字寫在一個正

3、方體紙盒的每個面上，其平面展開圖如圖所示，那么在該正方體中， 和“一”相對的字是（ ）A. 態(tài) B. 度C. 決D. 切（第6題）BADCEF（第5題）ABCO（第4題）5. 如圖，O是 ABC的外接圓，OBC=42°，則A的度數(shù)是（ ）A. 42° B. 48° C. 52° D. 58°6如圖，在矩形ABCD中，AB3，BC5，以B為圓心BC為半徑畫弧交AD于點E，連接CE，作BFCE，垂足為F，則tanFBC的值為（ ）A. B. C. D. 二、填空題（本大題共10小題，每小題2分，共20分，請在答題卡指定區(qū)域內作答）7代數(shù)式有意義，則

4、 x的取值范圍是 8. 分解因式：a34a 9. 計算2cos30°|1| .10. 反比例函數(shù)y的圖象經(jīng)過點（1，6）和（m，-3），則m .11. 如圖，在菱形ABCD中，AC2，ABC60°，則BD .BOA1CD（第12題）12. 如圖，在O中， AOCD, 130°，劣弧AB的長為3300千米，則O的周長用科學計數(shù)法表示為 千米ABCD（第11題）13.某商品原價100元，連續(xù)兩次漲價后，售價為144元，若平均增長率為x，則x .14直角坐標系中點A坐標為（5，3），B坐標為（1，0），將點A繞點B逆時針旋轉90°得到點C，則點C的坐標為 .(

5、第15題)15二次函數(shù)yax2+bx+c（a0）的圖象如圖所示，根據(jù)圖象可知：方程ax2+bx+ck有兩個不相等的實數(shù)根，則k的取值范圍為 . O(第16題)16.如圖，在半徑為2的O中，兩個頂點重合的內接正四邊形與正六邊形，則陰影部分的面積為 .三、解答題（本大題共11小題，共88分請在答題卡指定區(qū)域內作答，解答時應寫出文字說明、證明過程或演算步驟）17（6分）解方程組 18.（6分）化簡：（x）÷19.（8分）為了備戰(zhàn)初三物理、化學實驗操作考試，某校對初三學生進行了模擬訓練物理、化學各有3個不同的操作實驗題目，物理用番號、代表，化學用字母a、b、c表示測試時每名學生每科只操作一個

6、實驗，實驗的題目由學生抽簽確定（1）小張同學對物理的、和化學的b、c實驗準備得較好.請用樹形圖或列表法求他兩科都抽到準備得較好的實驗題目的概率；（2）小明同學對物理的、和化學的a實驗準備得較好.他兩科都抽到準備得較好的實驗題目的概率為 .20. （8分）據(jù)報道，歷經(jīng)一百天的調查研究，南京PM 2.5源解析已經(jīng)通過專家論證各種調查顯示，機動車成為PM 2.5的最大來源，一輛車每行駛20千米平均向大氣里排放0.035千克污染物校環(huán)保志愿小分隊從環(huán)保局了解到南京100天的空氣質量等級情況，并制成統(tǒng)計圖和表：2014年南京市100天空氣質量等級天數(shù)統(tǒng)計圖 空氣質量等級優(yōu)良輕度污染中度污染重度污染嚴重污

7、染天數(shù)（天）10a12825b2014年南京市100天空氣質量等級天數(shù)統(tǒng)計表優(yōu)良輕度重度嚴重10%25%12%8%n°25%中度（1） 表中a ，b ，圖中嚴重污染部分對應的圓心角n °.（2）請你根據(jù)“2014年南京市100天空氣質量等級天數(shù)統(tǒng)計表”計算100天內重度污染和嚴重污染出現(xiàn)的頻率共是多少？（3）小明是社區(qū)環(huán)保志愿者，他和同學們調查了機動車每天的行駛路程，了解到每輛車每天平均出行25千米已知南京市2014年機動車保有量已突破200萬輛，請你通過計算，估計2014年南京市一天中出行的機動車至少要向大氣里排放多少千克污染物？21.（8分）如圖， 在ABCD中，E、F

8、、G、H分別為AB、BC、CD、AD的中點，AF與EH交于點M，F(xiàn)G與CH交于點N.（1）求證：四邊形MFNH為平行四邊形；（2）求證：AMHCNF.ABCDFGEHMN22. （8分）端午節(jié)期間，某食堂根據(jù)職工食用習慣，購進甲、乙兩種粽子260個，其中甲種粽子花費300圓，乙種粽子花費400元，已知甲種粽子單價比乙種粽子單價高20%，乙種粽子的單價是多少元？甲、乙兩種粽子各購買了多少個？23.（8分）如圖，為了測出某塔CD的高度，在塔前的平地上選擇一點A，用測角儀測得塔頂D的仰角為30º，在A、C之間選擇一點B （A、B、C三點在同一直線上），用測角儀測得塔頂D的仰角為75

9、6;，且AB間距離為40m（1）求點B到AD的距離； （2）求塔高CD（結果用根號表示）ABCD（第23題）30°75°24（8分）小林家、小華家、圖書館依次在一條直線上小林、小華兩人同時各自從家沿直線勻速步行到圖書館借閱圖書，已知小林到達圖書館花了20分鐘.設兩人出發(fā)x（分鐘）后，小林離小華家的距離為y（米），y與x的函數(shù)關系如圖所示.（1）小林的速度為 米/分鐘 ，a ，小林家離圖書館的距離為 米；（2）已知小華的步行速度是40米/分鐘，設小華步行時與自己家的距離為y1（米），請在圖中畫出y1（米）與x（分鐘 ）的函數(shù)圖象；（3）小華出發(fā)幾分鐘后兩人在途中相遇？第題（第

10、24題）x（分鐘）y（米）420240Oa25(8分)施工隊要修建一個橫斷面為拋物線的公路隧道，其高度為6米，寬度OM為12米現(xiàn)以O點為原點，OM所在直線為x軸建立直角坐標系（如圖所示）（1）求出這條拋物線的函數(shù)表達式，并寫出自變量x的取值范圍；（2）隧道下的公路是雙向行車道(正中間有一條寬1米的隔離帶)，其中的一條行車道能否行駛寬2.5米、高5米的特種車輛？請通過計算說明；（第25題）26. （10分）如圖，已知ABC，AB=6、AC8，點D是BC邊上一動點，以AD為直徑的O分別交AB、AC于點E、F.（1）如圖若AEFC，求證：BC與O相切；（2）如圖，若BAC90°，BD長為多

11、少時，AEF與ABC相似.圖ADBCEFODBOCFAEABC備用 圖27. (10分)已知直角ABC，ACB90°，AC3，BC4，D為AB邊上一動點，沿EF折疊，點C與點D重合，設BD的長度為m.（1）如圖，若折痕EF的兩個端點E、F在直角邊上，則m的范圍為 ;（2）如圖，若m等于2.5，求折痕EF的長度；（3）如圖，若m等于，求折痕EF的長度.DFACDBEFACBACB圖圖圖DEFE2015中考數(shù)學模擬試卷（二）答案一、選擇題（本大題共6小題，每小題2分，共12分）題號123456答案DBBABD二、填空題（本大題共10小題，每小題2分，共20分）7x1 8. a（a2）（a

12、+2） 9. +1 10. 2 11. 2 12.3.96×104 13. （2，4） 14.0.2 15. k2 16. 62三、解答題（本大題共11小題，共88分）17解： ×2得：4x+6y10×3得：9x6y36 +得：13x26解得： x2··························

13、3;·················································

14、3;···························3分把x2代入得y3·····················

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16、·············5分所以方程組的解為···································&#

17、183;·············································6分18.解原式÷··

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19、·························1分×·······················

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21、3;···················2分×·····························&#

22、183;·················································&#

23、183;··················3分×······························

24、··················································

25、···4分-x(x1) ·············································

26、83;·················································

27、83;··············5分x2+x ··································&#

28、183;·················································&#

29、183;···························6分19. （1）畫圖或列表正確···················

30、3;·················································

31、3;·······························4分共有9種等可能結果，期中兩科都滿意的結果有4種··············

32、83;·················································

33、83;·5分P（兩科都滿意）.··············································

34、3;·················································

35、3;········6分（2）·········································

36、;··················································

37、;································8分20. （1）25；20；72°··············

38、··················································

39、······································3分（2）45% ··········

40、83;·················································

41、83;·················································

42、83;5分（3）200×0.035×10000×87500（千克）··········································

43、·································8分21. （1）證明：連接BD，E、F、G、H分別為AB、BC、CD、AD的中點，EH為ABD的中位線，EHBD.同理FGBD.EHFG·····

44、83;·················································

45、83;·················································

46、83;·············2分在ABCD中ADBC，H為AD的中點AHAD，F(xiàn)為BC的中點FCBC，AHFC四邊形AFCH為平行四邊形，AFCH··························

47、3;·················································

48、3;··········································4分又EHFG四邊形MFNH為平行四邊形····&#

49、183;·················································&#

50、183;····································5分（2）四邊形AFCH為平行四邊形FADHCB ·········&

51、#183;·················································&

52、#183;···············································6分EHFG,AMHAFN

53、AFCHAFNCNFAMHCNF···············································&#

54、183;·················································&#

55、183;··········7分又AHCFAMHCNF·····································&

56、#183;·················································&

57、#183;·····················8分22.解：設乙種粽子的單價是x元，則甲種粽子的單價為（1+20%）x元，由題意得， +260，····················

58、··················································

59、·············4分解得：x=2.5，···································&

60、#183;·············································5分經(jīng)檢驗：x=2.5是原分式方程的解，·

61、;··················································

62、;·····································6分（1+20%）x=3，則買甲粽子為： 100個，乙粽子為：160個·······

63、·········································7分答：乙種粽子的單價是2.5元，甲、乙兩種粽子各購買100個、160個···

64、·····································8分23. （1）作BEAD，垂足為E，ABCD（第23題）30°75°E在RtAEB中，sinA， ，BE20··

65、··············3分（2）DBC是ABD的外角ADBDBCA45°，···············4分在RtDEB中，tanEDB ，1，ED20············

66、;·································5分在RtAEB中，cosEAB ， EA20·············

67、·················6分ADED+ EA20+20······························

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69、83;·······7分在RtACD中，sinDAC ， EA10+10············································