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2025年中考模拟考试试题（二）
数学参考答案及评分意见
一、选择题（每小题 3分，共 30分）
1.A 2.B 3. D 4.A 5.D 6. C 7.B 8. C 9.D 10.B
二、填空题（每小题 3分，共 15分）
11. y x2 1（答案不唯一） 12. m<1 13. 14. 2 21
6
15. 3 2 10 ，3 2 10 .
三、解答题（本大题共 8个小题，满分 75分）
16．（1）（2025-π）0- 2- 8 1 （ ）-1
2
1 2 2 2 2 ············································································ 2分
1 2 2 2 2 ············································································ 4分
5 2 2 ·················································································· 5分
1 4 a 2
（2） a 2 a2 4 a2 4a 4
1 4 a 2
a 2 a 2 (a 2) (a 2)2 ·············································· 2分 （ ）
a 2 (a 2)2
····························································· 4分
(a 2)(a 2) (a 2)
a 2
·················································································· 5分
a 2
17.（1）64.5，44，条形统计图如图： ························································· 3分
（2）男生的成绩好.因为男生女生成绩的平均数相同，男生成绩的中位数与众数都高于
女生. （注：答案不唯一，解释合理即可） ········································6分
3 144 100% 40% 400 22（ ） ＝ ， × ＋350×40%＝316（人）.························ 8分
360 50
答：成绩为 A等级的考生人数是 316人··············································9分
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1 C 4 2 y k18．（ ）把点 （ ， ）代入 ，得 k 4 2 8．………………………………2分
x
8
∴反比例函数的解析式是 y ．…………………………………………………3分
x
（2）如图
………………………………………………………………………………… 7分
（3）6. ……………………………………………………………………………9分
19.（1）如图.
......................................................................4分
（2）证明：由（1），得 ∠DAM=∠C.
∵ AD∥BC，
∴ ∠DAM=∠AMB.
∴ ∠AMB=∠C.
∴ AM∥DC.
∴ 四边形 AMCD是平行四边形. ······················································ 6分
∴ AD=MC.
∵ BC=2AD，
∴ BC=2MC.
∵ BC=BM+MC，
∴ BM=MC=AD.
∴ 四边形ABMD是平行四边形.························································· 8分
∵ AB=AD,
∴ □ABMD是菱形.········································································9分
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20. 解：由题意得，MN＝2，BC＝3.5，DM＝EN=FC=1.5，
∴BF=BC－FC=2
在 Rt△BDF中，∠BDF=14°，tan∠BDF= BF .........3分
DF
DF BF 2＝ 8 .
tan BDF 0.25
∴EF＝8－2＝6.......................................................................5分
在 Rt△AEF中，∠AEF=53°，tan∠AEF= AF
EF
∴ AF EF tan53 6 1.33 7.98 , ·······················································7分
∴AB＝AF－BF＝7.98－2＝5.98≈6··························································8分
答：文王雕像 AB的高度约为 6 m. ························································9分
21．（1）设每个足球的价格是 x元，则每个排球的价格是（x-30）元，依题意得
1600 1000
············································ 1分
x x 30
解得 x =80. ····································································· 2分
经检验，x=80是原分式方程的解且符合题意. ········································3分
∴x-30=50.
答：每个足球的价格是 80元，每个排球的价格是 50元． ·························4分
（2）设购进足球 m个，则购进排球（120-m）个，购买总费用是 w元，依题意得
1
m≥ (120-m)． ············································ 5分
3
解得 m≥30. ······················································································ 6分
w=80m+50 (120-m)=30m+6000. ···························································7分
∵30>0，∴w随 m的增大而增大，当 m=30时，w取得最小值 6900元.
此时，120-30=90. ············································································· 8分
答：当购买足球 30个，排球 90个时，总费用最少，最少总费用为 6900元. ···9分
22. v（1） 0 ·····························································································3分
12
2 t v0 s 75（ ）由题意得，当 时，
12 8
∴ 6 v
2
0 v v0 75
12 0

12 8
∴ v . 即刹车前小型汽车的行驶速度为 15 m/s ······································ 6分0 15
（3）超速（注：若没写出结果，但后续说理正确，不扣分）·························· 7分
理由如下：
由题意得 6 32 3v0 12
解得 v0 22
∵ 22 m/s=79.2 km/h>60 km/h
∴该车超速·····················································································10分
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23 3．解：（1） ·················································································· 2分
2
（2）AE=BC.（注：若没写出结果，但后续说理正确，不扣分）········· 3分
理由如下：
如图 2，∵ ∠ADB＝∠ABC＝90°，∠A＝45°，
∴ ∠ABD＝45°．
∴ ∠CBD＝45°．
∴ ∠A＝∠CBD，AD＝BD．....................................4分
∵ CD⊥DE，
∴ ∠CDE＝90°．
∵ ∠BDC+∠BDE＝90°，∠ADE+∠BDE＝90°，
∴ ∠ADE＝∠BDC．
∴ △ADE≌△BDC．
∴ AE＝BC．··········································································· 5分
（3）如图 3，∵ ∠ADB=∠CDE＝90°，
∴ ∠ADE=∠BDC.
又∵∠A=∠CBD，
∴ △BDC∽△ADE.......................................7分 E
BD BC
∴ tan .
AD AE 图 3
BC m
∴ AE .
tan tan
∴ BE AB AE n m .························································ 8分
tan
（4） 4 2或 2 2 .············································································· 10分
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