个人资料整理 仅限参考
七、解答题本题共10分，第30题6分，第31题4分）
30．如图1，已知?AOB?70?．
1）如图2，射线OC 在?AOB的内部，OD 平?AOC,若?BOD?40?，
求?BOC的度数。
2）若?BOD?3?BOC?BOC?45?），且OD 平分?AOC,请你画出图形，
并求?BOC的度数．
B 解1）： O A 图1
B C D O A 图2
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31．阅读下列材料：
一个直角三角形纸片ABC，分别取AB、AC边的中点M、N，连结MN，作?AHM??AHN?90?，沿MN、AH剪开，可将三角形纸片分割成三块,如图1所示。
cdwBAc5s9H 如图2，将三角形纸片①绕AB的中点M旋转至三角形纸片④处，将三角形纸片②绕AC的中点N旋转至三角形纸片⑤处，依此方法操作，可以把一个直角三角形纸片ABC拼接成一个与它面积相等的长方形纸片DBCE.cdwBAc5s9H A A 请你解决下列问题： N N D M ① ② E M ① ② H ① ② H ③1）如图3，一个任意三角形纸片ABC，将其分割后拼接成一个与三角形ABC③ B C B C 面积相等的长方形，在图3中画出分割的实线和拼接的虚线。cdwBAc5s9H ．．．．．．．．．．．．．
图1
2）如图4，一个任意四边形纸片ABCD，将其分割后拼接成一个与原四边形ABCD面积相等的长方形，在图4中画出分割的实线和拼接的虚线．cdwBAc5s9H ．．．．．．．．．．．．．
A
A
D
北京市西城区2011 — 2012学年度第一学期期末试卷北区）
图2
七年级数学参考答案及评分标准A卷）2012.1
一、选择题本题共B 30分，每小题3分） C B C 题号 答案 1 D 2 C 3 图3 C 4 B 5 A 6 D 7 D 8 图4 A 9 B 10 C 二、填空题本题共20分，每小题2分） 11．0.0036 。 12．2x?7。 13．
5。 14．a?1??a。 cdwBAc5s9H 315．18，3每空1分）。 16．26。 17．60。 18．4。 cdwBAc5s9H 19．
23??1。 20．． 22三、解答题本题共16分，每小题4分） 21．解：?13?(?15)?(?27)?10
＝?13?15?27?10 ···································································· 1分 ＝?40?25
＝?15． ····················································································· 4分
22.解：
7145?(?)?(?) 2556755＝?? ··············································································· 2分 25146＝
1． ······················································································· 4分 12 个人资料整理 仅限参考
323.解：(?2)?(?)?91?1 42192＝ (?8)?(?)?? ···································································· 2分
64316＝ ? ······················································································· 3分 ＝?1． ······················································································· 4分 6433224.解：?42?6434?0.83??(4?) 25421641251＝?16???3?
25647＝?16?5?3? ··········································································· 3分 ＝?8．······················································································ 4分
四、先化简，再求值本题4分） 25．解：ab2?17171(6ab?4ab2)?(5ab2?3ab) 2＝ab2?3ab?2ab2?5ab2?3ab ·························································· 2分
＝?6ab2． ··················································································· 3分
1，b?2时， 21原式＝?6??22＝?12． ································································ 4分
2当a?五、解下列方程组）本题共10分，每小题5分） 26．解：去分母方程两边同乘以12），得
4(2x?1)?3(2?5x)?24． ····························································· 1分
去括号，得8x?4?6?15x?24． ····················································· 2分 移项，得 8x?15x?24?4?6．······················································· 3分 合并同类项，得 ?7x?14． ····························································· 4分 系数化为1，得 x??2．
∴ 原方程的解是x??2． ································································ 5分
?3x?2y?28,①
27． ?
② ?x?y?1. 个人资料整理 仅限参考
解法一：由②，得 y?1?x． ③ ······························································· 1分
把③代入①，得3x?2(1?x)?28．
解这个方程，得x?6． ··································································· 3分 把x?6代入③，得 y??5． ···························································· 4分 ∴ 原方程组的解是 ??x?6,?y??5. ······························································ 5分
解法二：2×②，得 2x?2y?2． ③ ··························································· 1分
①＋③，得5x?30．
∴ x?6． ···················································································· 3分 把x?6代入②，得 y??5． ·························································· 4分
x?6, ·∴ 原方程组的解是 ?····························································· 5分 ??y??5.六、列方程解应用题本题共10分，每小题5分）
28．解：设在一个月内，本地累计通话时间为x分钟时，两种计费方式的收费一样．
································································································· 1分 依题意,得 30?0.3x?0.4x． ·························································· 3分 解得 x＝300． ·············································································· 4分 答：在一个月内，本地累计通话时间为300分钟时，两种计费方式的收费一样．
·································································································· 5分
29．解：设动车平均每小时行驶x千M，则快车平均每小时行驶(x?5)千M．
······························································································· 1分
121依题意,得 120?2x?2?(x?5)?1120． ············································· 3分
2解得 x?330．
11····························································· 4分 (x?5)??330?5?170． ·
22答：动车平均每小时行驶330千M，快车平均每小时行驶170千M． ················ 5分 七、解答题本题共10分，第30小题6分，第31题4分） 30． 解：1）∵?AOB?70?，?BOD?40?
∴?AOD??AOB??BOD?70??40??30?． ···························· 1分
B C ∵OD 是?AOC的平分线,
D
O
图1
A
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∴?AOC?2?AOD?60?． ···················· 2分 ∴?BOC??AOB??AOC?10?． ············· 3分 2）设?BOC??，
∵?BOD?3?BOC?3?， 依题意，以下分两种情况：
①当射线OC在?AOB内部时，如图2． ∴?COD??BOD??BOC?2?． ∵OD平分?AOC, ∴?AOC?2?COD?4?．
∴?AOB??AOC??BOC?4????5??70?． ∴??14?．
∴?BOC?14?． ·································································· 4分 ②当射线OC在?AOB外部时，
依题意，此时射线OC靠近射线OB，如图3． ∴?COD??BOC??BOD?4?． ∵OD平分?AOC,
∴?AOC?2?COD?8?，
∴?AOB??AOC??BOC?8????7??70?． ∴??10?． ∴?BOC?10?．
综上所述：?BOC的度数为10?或14?． ·········································· 6分
31．解：
A D ····································································································· 4分
M N G D E
H 阅卷说明：正确画出一个图形得2分．
E A H O
图3
B C
D
O
图2
A
C B
D
A
B C B F C 申明：
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北京市西城区2011—2012学年度第一学期期末试卷（北区）
