山东省淄博市中考数学试卷参考答案及解析.docx

初中学业水平考试数学试题参考答案第PAGE8页（共5页）

数学试题参考答案及评分标准

一选择题：本大题共12个小题,每小题5分，共60分。

题目

1

2

3

4

5

6

7

8

9

10

11

12

题号

A

D

C

D

B

A

C

C

D

B

A

B

二填空题：本大题共5个小题，每小题4分，共20分。

13a≥514x（x+3）（x—3）15（1，3）16—217（—2024，2024）

三解答题：本大题共7个小题，共70分。

18（本题满分8分）

解：整理方程组得，·········································2分

①×2—②得—7y=7，

y=1，····································································4分

把y=1代入①得x—2=3，

解得x=5，································································6分

∴方程组的解为··················································8分

19（本题满分8分）

证明：∵△ABC是等腰三角形，

∴∠EBC＝∠DCB，·······················································2分

在△EBC与△DCB中，

∴BE=CD，BC=CB

∴△EBC≌△DCB(SAS)，··················································6分

∴BD＝CE······························································8分

20（本题满分10分）

解：（1）将点A(1，2)代入y=，得m=2，

∴双曲线的表达式为：y＝，···············································1分

把A（1，2）和B（4，0）代入y＝kx+b得：

y＝，解得：，·········································3分

∴直线的表达式为：y＝x+；·········································4分

（2）联立，解得，或，·························5分

∵点A的坐标为（1，2），

∴点B的坐标为（3，），···············································6分

∵S△AOB=S△AOB—S△AOB=OC·—OC·

=×4×2—×4×

=，

∴△AOB的面积为；···················································8分

（3）1m3····························································10分

21（本题满分10分）

解：（1）12099························································4分

（2）如图：

··············8分

（3）把“礼仪”“陶艺”“园艺”“厨艺”及“编程”等五门校本课程分别记为ABCDE，画树状图如下：

共有25种等可能的结果，其中小刚和小强两人恰好选到同一门课程的结果有5种，

∴小刚和小强两人恰好选到同—门课程的概率P=

············································10分

22（本题满分10分）

解：小明能运用以上数据，得到综合楼的高度，理由如下：

作EG⊥AB，垂足为G，作AH⊥CD，垂足为H，如图：

22题

22题答案图

····················2分

由题意知，EG=BF=40米，EF=BG=1288米，∠HAE=16°=∠AEG=16°，∠CAH=9°，

在Rt△AEG中，

tan∠AEG=，

∴tan16°=，即0287≈，············································4分

∴AG=40×0287=1148（米），

∴AB=AG+BG=1148+1288=2436（米），····································6分

∴HD=AB=2436米，

在Rt△ACH中，AH=BD=BF＋FD=80米，

tan∠CAH=，

∴tan