二、解答题（本题共4分）
3．（1）如图1，D是线段BC的中点，三角形ABC的面积与三角形ABD的面积比为 ； （2）如图2，将网格图中的梯形ABCD分成三个三角形，使它们的面积比是1:2:3．
4．设x是有理数，我们规定：x?????x(x?0)?0(x?0)，x???．
?0(x?0)?x(x?0)?例如：3?3，(?2)?0；3?0， (?2)??2．解决如下问题： （1）填空： ()? ， (?1)?? ，x??x?? ； （2）分别用一个含|x|,x的式子表示x，x．
解：（1）()? ， (?1)?? ，x??x?? ； （2）
七年级期末 数学试卷 第6页（共6页）
????12?12?
北京市西城区2014— 2015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 2015.1
一、选择题（本题共30分，每小题3分） 题号 答案 1 A 2 B 3 D 4 C 5 B 6 A 7 D 8 A 9 C 10 D 二、填空题（本题共20分，第11～14题每小题3分，第15～18题每小题2分） 题号 答案 题号 答案 11 12 13 134°30′ 14 7 15 答案不唯一，如：x2y 18 52× 275 = 572 ×25(1分)， （10b+a）×[100a+10（a+b）+b]=[100b+10（a+b）+a]×（10a+b） （1分）． 16 5 1? 4m2?n2 17 2 (1分) 4? （1分）
三、计算题（本题共16分，每小题4分） 19．30?11?(?10)?(?12)
解：30?11?(?10)?(?12)
=30?11?10?12 ···························································································· 1分 =42?21 ········································································································· 3分 =21 ················································································································· 4分
20． (?3)?(?)?(?1)
解：(?3)?(?)?(?1)
5614516455···································································································· 2分 ??3?? 6454=?3?? ····································································································· 3分
65=?2 ················································································································· 4分
1321． [1?(1?0.5?)]?[?10?(?3)2]
解：[1?(1?0.5?)]?[?10?(?3)2]
13=[1?(1??)]?(?10?9) ······················································································ 1分 =(1?)?(?1) ··········································································································· 3分 =? ·························································································································· 4分
16561123七年级期末 数学试卷 第7页（共6页）
22．8?(?1213)??(?2)3?(?8)? 5951213解：8?(?)??(?2)3?(?8)?
5951213=?8???8?8? ···················································································· 2分
5951238=?8(?)? ····························································································· 3分
5598=?24?
91=?23 ············································································································ 4分
9
12四、先化简，再求值（本题5分）
23．2(3ab2?a3b)?3(2ab2?a3b)，其中a??，b?4．
解：2(3ab2?a3b)?3(2ab2?a3b)
=6ab2?2a3b?6ab2?3a3b ·············································································· 2分 =a3b ··············································································································· 3分
当a??，b?4时，
12121 ?? ······································································································· 5分
2原式?(?)3?4 ···························································································· 4分
五、解下列方程或方程组（本题共10分，每小题5分） 24．
4x?13x?1 ?1?63)?6解： 去分母，得 (4x?1?2x(?3．1 ························································ 1分
?x6?．2 ·去括号，得 4x?1?6···························································· 2分 ??2．1 ·移项，得 4x?6x?6································································ 3分
合并同类项，得 10x?9． ······································································· 4分 系数化1，得x?9． ················································································ 5分 10?3x?2y?10，① 25．?
x?y?5.② ?解：由②得 x?5?y．③ ················································································ 1分
把③代入①，得 3(y?5)?2y?10． ··························································· 2分 解得 y??1． ······························································································· 3分 把y??1代入③，得 x?5?(?1)?4． ····················································· 4分
七年级期末 数学试卷 第8页（共6页）
?x?4，所以，原方程组的解为 ? ································································ 5分
y??1.?
六、解答题（本题6分）
26．解：（1）补全图形，如图； ···································· 2分
（2）证明：∵∠A+∠B=90°，∠B+∠BDF=90°， ∴ ∠A =∠BDF (理由： 同角的余角相等 ) ． ·················································································· 4分 又∵ DF平分∠BDE ， ······················· 5分 ∴∠BDF=∠EDF(理由： 角平分线定义 ) ． ·················································································· 6分 ∴∠A=∠EDF．
七、列方程或方程组解应用题（本题6分）
27．解：设甲商品的价格x元，乙商品价格y元． ···················································· 1分
ADEBFC?x?2y?108,?由题意，得? ········································································ 3分 1y?(x?y)?3.?4??x?300,解得? ································································································ 5分
y?96.?答：甲商品的价格为300元， 乙商品的价格为96元． ····························· 6分
八、解答题（本题共8分）
28．解：（1）﹣1，5； ·································································································· 2分
（2） 设点C表示的数为x，由m＜n，可得：点A在点B的左侧．
AB?n?m．
①由AC－AB=2，得AC＞AB．以下分两种情况：
ⅰ) 当点C在点B的右侧时，如图1所示，此时AC= x－m．
∵AC－AB =2， ∴(x－m) －(n－m) =2． 解得x?n?2．
ABC图1
∴点C表示的数为n?2． ····················································· 4分 ⅱ) 当点C在点A的左侧时，如图2所示，此时，AC=m－x．
∵AC－AB=2，
∴（m－x）－（n－m） =2． 解得x?2m?n?2．
∴点C表示的数为2m?n?2．
综上，点C表示的数为n?2，2m?n?2． ························ 6分
CAB图2
七年级期末 数学试卷 第9页（共6页）
②由AD?2AC，可得：点C为线段AD上或点C在点A的左侧． 当动点D在线段AB上时，无论点C在何位置均不合题意； 当动点D在点B的右侧时，以下分三种情况：
ⅰ）当点C在线段BD的延长线上时，点C为线段AD的中点，
当点C在线段BD上时，如图3所示． ∴AD?3n?3m．
ⅱ）当点C在线段AB上时，如图4所示．
∴AD?n?m．
ⅲ）当点C在点A左侧时，不合题意．
综上所述，线段AD的长为3n?3m或n?m． ···························· 8分
ABC图3
D5353ACB图4
D5353北京市西城区2014— 2015学年度第一学期期末试卷
七年级数学附加题参考答案及评分标准 2015.1
一、填空题（本题共7分，第1题5分，第2题2分）
?2?1．??； ··················································································································· 3分
?3??2?················································································································ 5分 ?? ． ·
?3??x?y?32,2．? ·············································································································· 2分
5x?3y.?n5二、解答题（本题共13分，第3题6分，第4题7分）
3．解：（1）2:1； ·········································································································· 3分 （2）答案不唯一，如： D A
B E C ···························································· 6分
1?1?1???4．解：（1）???，??1???1，x?x?x； ················································ 3分
22???（2）当x≥0时，x?x，x?x，
∴x???x?x． 2七年级期末 数学试卷 第10页（共6页）
当x＜0时，x?0， ∴x???x?x． 2综上所述，当x为有理数时，x??当x≥0时， x?0，
?x?x． 2x?x． 2?当x＜0时，x?x，x??x
∴x??∴x??x?x； 2?综上所述，当x为有理数时，x?
x?x． ············································ 7分 2七年级期末 数学试卷 第11页（共6页）