七年级(上)期末数学试卷(含答案)

1、第一学期期末考试七年级数学试卷2018.1试卷满分：100 分，考试时间：100 分钟一、选择题（本题共 30 分，每小题 3 分）下面各题均有四个选项，其中只有一个是符合题意的1据中新社2017 年 10 月 8 日报道，2017年我国粮食总产量达到736 000 000吨，将736 000 000用科学记数法表示为（）.（A） 736 ´ 10 6（B） 73.6 

2、0; 10 7（C） 7.36 ´ 10 8（D） 0.736 ´1092. 如图所示，将两个圆柱体紧靠在一起，从上面看这两个立体图形，得到的平面图形是（）.4.  下列各式进行的变形中，不正确的是（   ）.（A）（B）（C）（D）3. 下列运算中，正确的是（）.（A） (-2)2 = -4（B） -22 = 4（C） 32 = 6（D

3、） (-3)3 = -27（A）若 3a =2b，则 3a +2 =2b +2（B）若 3a =2b，则 3a -5 =2b- 5（C）若 3a =2b，则 9a=4b（D）若 3a =2b，则5若 ( x - 1)2 + 2 y + 1 = 0 ，则 x+y 

4、;的值为（）.a  b=2  32               2          （D） -（A）12        （B） -1      &#

5、160;        3（C）32转门的三片旋转翼把空间等分成三个部分，下图是从上面俯视旋转门的平面图，两片旋6. 在一些商场、饭店或写字楼中，常常能看到一种三翼式旋转门在圆柱体的空间內旋转. 旋转翼之间的角度是（）.1（A）100°（B）120°（C）135°（D）150°7. 实数 a，b，c，d 在数轴上对应点的位置如图所示，正确的结论是8.  如图，在下列各关系式中，不正确的是（ 

6、60; ）.（A）a > c（B）b +c > 0（C）|a|d|（D）-bd（A） AD - CD=AB + BC（B） AC- BC=AD -DB（C） AC- BC=AC + BD（D） AD -AC=BD -BC9. 某礼品包装商店提供了多种款式的包装纸片，将它们沿实线折叠（图案在包装纸片的外部，内部无图案），再用透明胶条粘合，就折成了正方体包装盒，小明用购

7、买的纸片制作的包装盒如右图所示，在下列四种款式的纸片中，小明所选的款式的是（）.（A）（B）（C）（D）.“10.九章算术是中国古代数学专著，九章算术方程篇中有这样一道题： 今有善行者”行一百步，不善行者行六十步，今不善行者先行一百步，善行者追之，问几何步及之？这是一道行程问题，意思是说：走路快的人走100步的时候，走路慢的才走了60步；走路2慢的人先走100步，然后走路快的人去追赶，问走路快的人要走多少步才能追上走路慢的人？ 如果走路慢的人先走100步，设走路快的人要走 x 步才能追上走路慢的人，那么，下面所列方程正确的是（）.（A）（C）x 

8、; x - 100                    x   x - 100（B）=                   &#

9、160;            =60   100                    100    60x  x + 100   

10、60;                x   x - 100（D）=                           

11、;     =60   100                    100    60二、填空题（本题共 20 分，第 1114 题每小题 3 分，第 1518 题每小题 2 分

12、）11已知 x= 2 是关于 x 的方程 3x + a = 8 的解，则 a =12一个有理数 x 满足: x0 且 x < 2 ，写出一个满足条件的有理数 x 的值: x=13在一面墙上用一根钉子钉木条时，木条总是来回晃动；用两根钉子钉木条时， 条就会固定不动，用数学知识解释这两种生活现象为14已知 x2 + 

13、2 x = 2 ，则多项式 2 x 2 + 4 x - 3 的值为15已知一个角的补角比这个角的一半多 30°，设这个角的度数为 x°，则列出的方程是：16右图是一所住宅的建筑平面图（图中长度单位：m），这所住宅的建筑面积为m 2. 17如图，点A，O，B在同一条直线上，射线OD平分BOC，射线OE在AOC的内部，且DOE=90°，写出图中所有互为余角的角：18如图，一艘货轮位于 O&#

14、160;地，发现灯塔 A 在它的正北方向上，这艘货轮沿正东方向航行，到达 B 地，此时发现灯塔 A 在它的北偏西 60°的方向上(1) 在图中用直尺、量角器画出 B 地的位置；3(2) 连接 AB，若货轮位于 O 地时，货轮与灯塔 A 相距 1.5 千米，通过测量图中 AB 的长度，计算出货轮到达 B 地时与灯塔 A 的实际距离约为千米（精确到&#

15、160;0.1 千米）20  (-   ) ´ (-   ) ¸ (-2   )三、计算题（本题共 16 分，每小题 4 分）19 (-21) - (-9) + (-8) - (-12)解：311424解：4  - (-25) ´21 25 

16、;´ 3解：1 12 + 25 ´ (- 4 )22 ( -2) 3 ´ 0.25 - 4 ¸ ( -   )2 -    - 401328解：四、解答题（本题共 20 分，每小题 5 分）423先化简，再求值：3( x 2

17、60;- xy ) - 2( x 2 - y 2 ) + 3xy ，其中 x = -1 ， y = 3 解：2 +  x - 23  = 4 24解方程x + 1解：ì x + 2 y = 5，25解方程组&#

18、160;íî3x - y = 1.解：26已知 AB=10，点C 在射线 AB 上， 且BC = 1 AB ，D 为 AC 的中点25（1）依题意，画出图形；（2）直接写出线段BD 的长解：（1）依题意，画图如下：（2）线段BD 的长为五、解答题（本题共 13 分，第 27 题 6 分，第 28 题 7

19、60;分）27 列方程或方程组解应用题为了备战学校体育节的乒乓球比赛活动，某班计划买 5 副乒乓球拍和若干盒乒乓球（多于 5 盒） 该班体育委员发现在学校附近有甲、乙两家商店都在出售相同品牌的乒乓球拍和乒乓球，乒乓球拍每副售价 100 元，乒乓球每盒售价 25 元经过体育委员的洽谈，甲商店给出每买一副乒乓球拍送一盒乒乓球的优惠；乙商店给出乒乓球拍和乒乓球全部九折的优惠（1）若这个班计划购买 6 盒乒乓球，则在甲商店付款元，在乙商店付款元；（2）当这个班购买多少盒乒乓球时，在甲

20、、乙两家商店付款相同？28.如图，A，O，B 三点在同一直线上，BOD 与BOC 互补.6（1）试判断AOC 与BOD 之间有怎样的数量关系，写出你的结论，并加以证明；（2）OM 平分AOC，ON 平分AOD， 依题意，将备用图补全； 若MON=40°，求BOD 的度数.解：（1）答：AOC 与BOD 之间的数量关系为：；理由如下：（2）补全图形；备用图北京市西城区 2017 2018 学年度第一学期期末试卷七年级数学参考答案及评分标准

21、2018.17答案    2   答案不唯一，2  x + 30答案       x2 + 2x + 18      1 和3, 2 和3,424   ·········

22、··················································

23、··················· 2 分429   ·························&

24、#183;·················································&

25、#183;·· 3 分6   · ·······································

26、3;·············································· 4 分一、选择题（本题

27、共 30 分，每小题 3 分）题号12345678910答案CADCABDCDB二、填空题（本题共 20 分，第 1114 题每小题 3 分，第 1518 题每小题 2 分）题号1112131415经过一点有无数条直线，180 - x = 1如：-1两点确定一条直线1题号161718作图位置正确 1 分1 和4,2 和4 互为余角3.0 千米2 分

28、三、计算题（本题共 16 分，每小题 4 分）19 (-21)- (-9) + (-8) - (-12)解： (-21)- (-9) + (-8) - (-12)= -21 + 9 - 8 + 12 · ···········&#

29、183;·················································&#

30、183;········· 1 分= -29 + 21··································

31、;················································· 

32、;3 分= -8 · ············································

33、············································· 4 分31120 (-

34、60;) ´ (- ) ¸ (-2 )424311解： (- ) ´ (- ) ¸ (-2 )4243 19=- ´ ¸3 14=- ´ ´=- 14  - (-25) ´21 25 ´ 31 12 

35、+ 25 ´ (- 4 )4  - (-25) ´解： 25 ´ 31 12 + 25 ´ (- 4 )22 ( -2) 3 ´ 0.25 - 4 ¸ ( -   )2 -   &

36、#160;- 40解： ( -2) 3 ´ 0.25 - 4 ¸ ( -   )2 -    - 40= 25 ´ 3 + 25 ´ 1 - 25 ´ 1· ·····&

37、#183;·················································&

38、#183;·· 1 分424= 25 ´ ( 3 + 1 - 1 ) ·······························

39、3;······································ 2 分424=25········&#

40、183;·················································&#

41、183;········································ 4 分1328132882 +  x - 

42、;23  = 4  î  y = 2.    ··································

43、83;·············· 5 分13= -8 ´ 0.25 - 4 ¸ ( - ) - 40 · ··············&#

44、183;··········································· 1 分481= -8 ´

45、 0.25 - 4 ¸ (- ) - 40 ······································

46、························ 2 分8= -2 + 4 ´ 8 - 40 ·············

47、··················································

48、············ 3 分= -10 ·································

49、··················································

50、···· 4 分四、解答题（本题共 21 分，2325 题每小题 5 分，第 26 题 6 分）23 3( x 2 - xy ) - 2( x 2 - y 2 ) + 3xy ，其中 x = -1 ， y = 

51、3 解： 3( x 2 - xy ) - 2( x 2 - y 2 ) + xy= 3x 2 - 3xy - 2 x 2 + 2 y 2 + 3xy ···········

52、;··············································· 2 分=&#

53、160;x 2 + 2 y 2 ··········································&#

54、183;······································· 3 分当 x = -1 ， y =

55、0;3 时，原式= (-1)2 + 2 ´ 32 · ·····································&

56、#183;······························· 4 分=19···············&#

57、183;·················································&#

58、183;················ 5 分24解方程x + 1)x (解： 去分母，得3 (x + 1+2 -=2 ) 2· ··············

59、···························· 1 分x444435去括号，得3x + 3+ 2 - =2 ··········&

60、#183;···································· 2 分移项，得3x + 2x = 2 + -  

61、3;·················································

62、0;3 分合并同类项，得5x = 2 ···········································

63、83;············ 4 分系数化 1，得 x = 5  ···························

64、3;···································· 5 分ì x + 2 y = 5， 25 í

65、;î3x - y = 1.解：由得 x = 5 - 2 y ···································

66、··························· 1 分把代入，得 3(5- 2 y) - y = 1 ··········

67、······································ 2 分解这个方程，得 y = 2  ···

68、··················································

69、········· 3 分把 y = 2 代入，得 x = 1  ····························

70、;···························· 4 分ì x = 1，所以，这个方程组的解为 í26解：（1）依题意，画图如下：9ADCBADBC图 1图 2····&

71、#183;·················································&

72、#183;································· 4 分（2）15 或 5· ········

73、3;·················································

74、3;····· 6 分五、解答题（本题共 13 分，第 27 题 6 分，第 28 题 7 分）27（1）525 ，585； · ·····················

75、3;·················································

76、3;···· 2 分（2）解：设这个班购买 x ( x>5 ) 盒乒乓球时，在甲、乙两家商店付款相同··································································&#