2024年江苏省南京市建邺区中考数学一模试题

2023-2024学年第二学期练习（一）

数学试卷参考答案及评分标准

说明：本评分标准每题给出了一种或几种解法供参考．如果考生的解法与本解答不同，参照本评分标准的精神给分．

一、选择题（本大题共6小题，每小题2分，共12分）

二、填空题（本大题共10小题，每小题2分，共20分）

7．x ≠－1

8．2 9．2×10－8 10．－5 11．8 12．⎩⎨⎧x ＋y=352x ＋4y=94 13．V ≥0.6 14． 2 15．（ 3 2， 9 2） 16． 3 2

3 三、解答题（本大题共11小题，共88分）

17．（本题7分）

解：

a 2－

b 2ab ÷(1－ b a ) ＝(a ＋b )(a －b )ab · a a －b

················································································ 3分 ＝ a ＋b b

································································································· 5分 把a ＝－2，b ＝1代入得“

a ＋

b b ＝ －2＋1 1

＝－1 ··············································································· 7分 18．（本题7分）

解：解不等式①，得x ≥－1． ·········································································· 2分 解不等式②，得x ＜2． ··················································································· 4分

···································································· 6分

所以，不等式组的解集是－1≤x ＜2． ································································ 7分

19．（本题7分）

（1）解：x 2－4x －5＝0

(x ＋1)(x －5)＝0 ······················································································· 3分 x ＋1＝0或x －5＝0

所以x 1＝－1，x 2＝5． ·············································································· 5分

（2）x 1＝2023，x 2＝2029． ············································································· 7分 题号

1 2 3 4 5 6 答案 A C D B B A

0 1 2 3 -3 -2 -1

20．（本题8分）

解：（1）1.9 ·································································································· 2分

（2）① ······································································································· 4分

（3）1990至2020年我国老年人口数量不断增长；从2000至2020年，全国人口增长较

慢是导致老年人口比重快速上升的原因之一． ··············································· 8分 说明：第（3）问答案不唯一，每条结论2分，共4分；

如果只是描述某年的数据，只得1分；

21．（本题8分）

解：（1）13． ································································································· 2分

（2）将一等奖区域记为A ，二等奖区域平均划分为两个区域，分别记为B ，C ．小丽转两次转盘的结果有：（A ，A ）、（A ，B ）、（A ，C ）、（B ，A ）、（B ，B ）、（B ，C ）、（C ，A ）、（C ，

B ），（

C ，C ）共有9种结果，它们出现的可能性相同．满足两次一等奖（记为事件M ）的

结果有1种，即（A ，A ），所以P （M ）＝19

． ···················································· 8分 说明：第（2）问共6分，其中

（1）枚举、树状图、表格过程正确且所有结果罗列完整得3分；

分子1分，分母和等可能性得1分，结果1分；

（2）无过程仅有正确结果只得1分；

（3））结果正确但没有列出所有结果或没有说明等可能性扣1分;

（4）若枚举过程中枚举不全但其中有正确结果（只要有一个对的）得1分。

22．（本题8分）

（1）连接OA ,OB ,OD

∵ AB 是⊙O 的切线，OB 是半径，

∴ OB ⊥AB ．

∴ ∠OBA ＝90°．

∵ 四边形ABCD 是菱形，

∴ AD ＝AB ．

∵ OA ＝OA ，OD ＝OB ，AD ＝AB ，

∴ △AOD ≌△AOB （SSS ）．

∴ ∠ODA ＝∠OBA ＝90°．

∴ OD ⊥AD ．

又∵OD 是半径，

∴ AD 是⊙O 的切线． ·················································································· 4分 （第22题） A B C

D E F O