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北京市西城区 2023—2024 学年度第二学期期末试卷
七年级数学答案及评分参考 2024.7
一、选择题（共 16 分，每题 2 分）
题号 1 2 3 4 5 6 7 8
答案 B B A D B D C C
二、填空题（共 16 分，每题 2 分）
3 3 x 1,
9. . 10. . 11.答案不唯一，如

3 2 y 3.
12. 如果两个角是对顶角，那么这两个角相等 13. 8. 14.（3，6）.
15. 90°＋α. 16. 3，n≥3.
三、解答题（共 68 分，第 17 题 8 分，第 18 题 11 分，第 19-21 题，每题 9 分，第 22 题 5
分，第 23 题 9 分，第 24 题 8 分）
17.（1）计算： 3 8 3 4 2 3 .
解：＝ 2 3 2 2 3 ································································································ 3 分
＝- 3 . ·················································································································· 4 分
2
（2）解：由 (x 1) 16，
可得 x 1 4 或 x 1 4，
所以 x 5或 x 3. ··························································································· 8 分
2x 3y 3， ①
18.（1）
4x y 4 . ②
解：①×2-②，得-5y＝10.
y＝-2. ···················································································· 3 分
3
将 y＝-2 代入①中，得 x . ·············································································· 4 分
2
3
x ，
所以，这个方程组的解是 2 ··········································································· 5 分
y 2 .
3x 2≥ x， ①

（2） x 8 3x
1 . ②
4 4
解：解不等式①，得 x≥1. ······················································································· 6 分
解不等式②，得 x＜3. ······················································································· 8 分
所以这个不等式组的解集是 1≤x＜3，它的整数解是 1，2. ······························· 11 分
北京市西城区 2023—2024 学年度第二学期期末试卷 七年级数学答案及评分参考 第 1 页（共 4 页）
19.解：（1）①画图如图 1； ······································································································· 3 分
图 1 图 2
②＜，垂线段最短. ···························································································· 5 分
（2）证明：∵∠CDF＝∠A，
∴ AB∥HF（同位角相等，两直线平行）（填推理的依据）．
∴∠BDF＝∠ABD（两直线平行，内错角相等）（填推理的依据）．
∵∠BDF＋∠BEG＝180°，
∴∠ABD＋∠BEG＝180°．
∴ BD∥EH．
∴∠BDF＝∠H（两直线平行，同位角相等）（填推理的依据）．
································································································································ 9 分
20. 解：（1）三角形 ABC如图所示， ······················································································· 3 分
在图中分别取点 D（-4，4），E（1，4），F（1，-1）．
S ＝ S S S S
三角形ABC 四边形BFED 三角形BFC 三角形CEA 三角形ADB
5 15
＝ 25 4 11． ····················································································· 5 分
2 2
（2）①（0，-3），（5，-2）；
②答案不唯一，如三角形 ABC 先向右平移 4 个单位长度，再向下平移 2 个单
位长度． ············································································································ 9 分
北京市西城区 2023—2024 学年度第二学期期末试卷 七年级数学答案及评分参考 第 2 页（共 4 页）
21.解：（1）设购进甲种文创产品每件需 x 元，乙种文创产品每件需 y元．
7x 3y 285，
依题意，得 ··················································································· 2 分
2x 6y 210
x 30，
解这个方程组，得
y 25 .
答：购进甲种文创产品每件需 30 元，乙种文创产品每件需 25 元．
···························································································································· 4 分
（2）设购买甲种文创产品 m 件，则购买乙种文创产品（200-m）件．
30m 25(200 m)≤ 5368，
依题意，得 ······························································· 6 分
30m 25(200 m)≥ 5350 .
3
解这个不等式组，得 70 ≤m≤ 73 ． ································································· 7 分
5
因为 m是整数，
所以 m＝70，71，72，73，200-m＝130，129，128，127． ···························· 8 分
答：该商店共有 4 种进货方案．
···························································································································· 9 分
22.解：（1）5，15，50； ············································································································ 3 分
（2）如图所示．
········································ 4 分
20
（3）990 396（名）．
50
答：估计该年级共有 396 名学生获得“阅读达人”称号．
···································································································································· 5 分
23.（1）证明：∵∠AEF 的平分线交 CD 于点 P，
∴ ∠AEP＝∠FEP．
∵ AB∥CD，
∴ ∠AEP＝∠FPE．
∴ ∠FEP=∠FPE． ························································································· 3 分
北京市西城区 2023—2024 学年度第二学期期末试卷 七年级数学答案及评分参考 第 3 页（共 4 页）
（2）①补全图形如图；
∠EGF ＝2∠EHN．
证明：设∠PEG＝α，则∠EGF＝∠AEG＝∠AEP＋α＝∠GEF＋2α．
∵ ∠FEG 的平分线交直线 CD 于点 H，
∴ ∠GEF＝2∠GEH．
∴ ∠EGF＝2∠GEH＋2α．
∵ HN∥PE，
∴ ∠EHN＝∠PEH＝∠GEH＋α．
∴ ∠GEH＝∠EHN-α．
∴ ∠EGF ＝2∠EHN． ············································································ 7 分
②∠EGF＋2∠EHN＝180°． ······················································································· 9 分
24.（1）①（8，-1）； ················································································································ 1 分
②∵ 点 M 在线段 NT 上，且 N（-3，-2），T（1，-2），
∴ 设点 M 的坐标为（x，-2），其中-3≤x≤1．
设点 P 关于点 M 的“2 倍平移点”为 P．
1
∵ P（4，3），
∴ P（4＋2x，-1）， 其中-3≤x≤1．
1
∴ 当 x＝-3 时，4＋2x＝-2，
当 x＝1 时，4＋2x＝6．
∵ 直线 l 上存在点 P 关于点 M 的“2 倍平移点”，
∴ -2≤r≤6． ·········································································································· 6 分
（2）0＜k＜5 或 k＞9． ······································································································ 8 分
四、选做题（共 10 分，第 1 题 4 分，第 2 题 6 分）
25.（1）3； ·································································································································· 1 分
4 8
（2） ，2， ····················································································································· 4 分
3 3
26.（1）4； ·································································································································· 2 分
（2）①2； ······························································································································ 4 分
②-2＜a＜2. ················································································································· 6 分
北京市西城区 2023—2024 学年度第二学期期末试卷 七年级数学答案及评分参考 第 4 页（共 4 页）北京市西城区2023一2024学年度第二学期期末试卷
七年级数学
2024.7
1.
本试卷共6页，共两部分，四道大题，26道小题。其中第一大题至第三大题为
注
必做题，满分100分。第四大题为选做题，满分10分，计入总分，但卷面总分
意
不超过100分。考试时间100分钟。
事
2.
在试卷和答题卡上准确填写学校、班级、姓名和学号
3.
试题答案一律填涂或书写在答题卡上，在试卷上作答无效。
项
4.
在答题卡上，选择题、作图题用2B铅笔作答，其他试题用黑色字迹签字笔作答。
器
如
5.
考试结束，请将考试材料一并交回。
第一部分
选择题
敏
一、
选择题（共16分，每题2分）
第1-8题均有四个选项，符合题意的选项只有一个。
长
1.
下列各组图形或图案中，能将其中一个图形或图案通过平移得到另一个图形或图案的是
R
(①D)
(A)
(B)
(C)
2.
在平面直角坐标系中，下列各点位于第二象限的是
(A)(1,-2)
(B)(-1,2)
(C)(1,2)
(D)(-1,-2)
3.
下列调查中，适合采用全面调查的是
(A)对乘坐飞机的旅客进行安检
(B)调查某批次汽车的抗撞击能力
病
(C)调查某市居民垃圾分类的情况
(D)
调查市场上冷冻食品的质量情况
4,若a(A)a-1(B)-2a>-2b
(C)a+b<2b
(D)a2阳
5.
下列图形中，由AB∥CD,
能得到∠1=∠2的是
D
(A)
B)
(D)
北京市西城区2023一2024学年度第二学期期末试卷七年级数学第1页（共6页）
6.由受学1可以得到用：表示)的代子居
(4)y=3-2
3
(B)y=2x-
1
(C)y=3-
2
(D)y=
2
22
7.下列命题：
①经过直线外一点，有且只有一条直线与这条直线平行
②在同一平面内，过一点有且只有一条直线与已知直线垂直
③两条直线被第三条直线所截，内错角相等
④所有实数都可以用数轴上的点表示
其中真命题的个数是
(B)2
(C)3
(D)4
(A)1
8.右图是某个一元一次不等式的解集在数轴上的表示，
若该不等式恰有两个非负整数解，
则a的取值范围是
(A)2≤a<3
(B)1(C)1≤a<2
(D)0≤a≤1
第二部分
非选择题
二、填空题（共16分，每题2分）
9.
在实数√4,
5,314159,号中，是无理数的是
10.
9的算术平方根是
11.已知二元一次方程x十2y=7,写出该方程的一组正整数解：
12.命题“对项角相等”改写成“如果…，那么…”的形式是
13.一个样本容量为63的样本，最大值是172，最小值是149，取组距为3，则这个样本
可以分成组.
14,平面直角坐标系中，点M(3,1),N(a,a+3),若直线N与y轴平行，则点N的
坐标是
I5.如图，点A,B,C在同一条直线上，ADLAE,且DMBF,
∠CBF=a,则∠CAE=(用含&的代数式表示)，
北京市西城区2023一2024学年度第二学期期末试卷七年级数学第2页（共6页）

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