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【324325】2024八年级数学下学期期末模拟测试卷(含解析)(新版)浙教版

时间:2025-01-15 21:57:16 作者: 字数:15222字
简介:



 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 期末模拟测试卷01

一、选择题(本大题共10小题,每小题3分,共30分。在每小题所给出的四个选项中,恰有一项是符合题目要求的,请将正确选项前的字母代号填涂在答题卡相应位置上)

1.下列设计的图案中,是中心对称图形但不是轴对称图形的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:A、是轴对称图形,也是中心对称图形,不符合题意;

B、是轴对称图形,也是中心对称图形,不符合题意;

C、不是轴对称图形,是中心对称图形,符合题意;

D、是轴对称图形,也是中心对称图形,不符合题意.

答案:C

2.下列根式中,属于最简二次根式的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ,被开方数含分母,故本选项不符合题意;

B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 被开方数不含分母;被开方数不含能开得尽方的因数或因式,故本选项符合题意;

C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 4,被开方数含能开得尽方的因数,故本选项不符合题意;

D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ,被开方数含能开得尽方的因数,故本选项不符合题意;

答案:B

3.某校八年级甲、乙两班举行电脑汉字输入速度比赛,两个班参加比赛的学生每分钟输入汉字的个数经统计和计算后结果如表:

班级

参加人数

中位数

方差

平均字数

55

149

191

135

55

151

110

135

有一位同学根据上表得出如下结论:

甲、乙两班学生的平均水平相同;

乙班优秀的人数比甲班优秀的人数多(每分钟输入汉字达150个以上为优秀);

甲班学生比赛成绩的波动比乙班学生比赛成绩的波动大.

上述结论正确的是(  )

A.①②③ B.①② C.①③ D.②③

解:①甲、乙两班学生的平均水平相同,说法正确;

乙班优秀的人数比甲班优秀的人数多(每分钟输入汉字达150个以上为优秀),说法正确;

甲班学生比赛成绩的波动比乙班学生比赛成绩的波动大,说法正确;

答案:A

4.在ABCD中,对角线ACBD交于点O.若BD6,则OD的长是(  )

A3 B4 C5 D6

解:如图,

四边形ABCD是平行四边形,

ODOB <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> BD

BD6

OD3

答案:A

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

5.用反证法证明命题“一个三角形中不能有两个角是钝角”,应先假设这个三角形中(  )

A.有两个角是直角

B.有两个角是钝角

C.有两个角是锐角

D.一个角是钝角,一个角是直角

解:用反证法证明命题“一个三角形中不能有两个角是钝角”,

应先假设这个三角形有两个角是钝角,

答案:B

6.如图,四边形ABCD中,∠A90°AB8AD6,点MN分别为线段BCAB上的动点(含端点,但点M不与点B重合),点EF分别为DMMN的中点,则EF长度的最大值为(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

A8 B6 C4 D5

解:如图,连接DN

DEEMFNFM

EF <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> DN

当点N与点B重合时,DN的值最大即EF最大,

Rt△ABD中,∵∠A90°AD6AB8

BD <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 10

EF的最大值 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> BD5

答案:D

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

7.如图,某学校有一块长35米、宽20米的长方形试验田,为了便于管理,现要在中间开辟一横两纵三条等宽的小道,要使种植面积为600平方米.设小道的宽为x米,根据题意可列方程为(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

A.(35﹣x)(20﹣2x)=600

B35×20﹣35x﹣20x+2x2600

C.(35﹣2x)(20﹣x)=600

D35x+2×20x﹣2x2600

解:若设小道的宽为x米,则剩余部分可合成长(35﹣2x)米,宽(20﹣x)米的长方形,

依题意得:(35﹣2x)(20﹣x)=600

答案:C

8.已知点Aam),Ba﹣1n),C(﹣23)在反比例函数y <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 的图象上.若a1,则mn的大小关系是(  )

Amn Bmn

Cmn Dmn的大小不确定

解:将点C(﹣23)代入反比例函数y <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 中得:k=﹣6

k0

在该反比例函数图象的每个象限内,yx的增大而增大,

又∵a1

aa﹣10

mn

答案:B

9.若一元二次方程3x2+4x+m0有一个实数解x=﹣1,则m的取值是(  )

Am4 Bm1 Cm=﹣4 Dm <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:∵一元二次方程3x2+4x+m0有一个实数解x=﹣1

(﹣12+4×(﹣1+m0

解得 m1

答案:B

10.关于抛物线yx2ax﹣1,下列说法:①图象与x轴一定有两个交点;②顶点在直线y2x上时,y有最小值﹣2;③xa时,yx的增大而增大;④与双曲线 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 可能有3个交点,其中正确的说法有(  )

A1 B2 C3 D4

解:∵抛物线yx2ax﹣1

Δ=(﹣a2﹣4×1×(﹣1)=a2+40

图象与x轴一定有两个交点,故①正确;

yx2ax﹣1=(x <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 1

顶点坐标为( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 1),

顶点在直线y2x上时,

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 12• <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解得a=﹣2

此时y有最小值﹣2,故②正确;

顶点为( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 1),开口向上,

x <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 时,yx的增大而增大,故③错误;

根据题意得 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

此方程组可能有3个解,

抛物线yx2ax﹣1与双曲线 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 可能有3个交点,故④正确.

答案:C

二、填空题(本大题共6小题,每小题4分,共24分。不需写出解答过程,请将答案直接填写在答题卡相应位置上)

11.二次根式 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 有意义,则x的取值范围是  x≤3 

解:二次根式 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 有意义,则9﹣3x≥0

x的取值范围是x≤3

答案:x≤3

12.如果一个多边形的外角和是它内角和的3倍,那么这个多边形是 八 边形.

解:设这个多边形是n边形,

根据题意得,(n﹣2)•180°3×360°

解得n8

答案:八.

13.如图,∠MON90°,矩形ABCD的顶点AB分别在OMON上,当点B在射线ON上运动时,点A随之在射线OM上运动(点A不与点O重合),矩形ABCD的形状保持不变,其中AB3BC1,若OD的长为整数,则OD的长可以为 32 

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:如图,取AB的中点E,连接OEDEOD

ODOE+DE

ODE三点共线时,点D到点O的距离最大,

此时,∵AB3BC1

OEAE <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> AB <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

DE <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

OD的最大值为: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

OD的长为整数,则OD的长可以为32

答案:32

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

14.某单位定期对员工按照专业能力、工作业绩、考勤情况三方面进行考核(每项满分100分),三者权重之比为352.小明经过考核后三项务数分别为90分,86分、83分,则小明的最后得分为 86.6 分.

解:小明的最后得分:

90 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 86 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 83 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 27+43+16.686.6(分),

答案:86.6

15.若关于x的一元二次方程(m﹣2x2+x+m2﹣40的一个根为0,则m值是  ﹣2 

解:根据题意,得

x0满足关于x的一元二次方程(m﹣2x2+x+m2﹣40

m2﹣40

解得,m±2

又∵二次项系数m﹣2≠0,即m≠2

m=﹣2

答案:﹣2

16.如图ABCD中,O为对角线交点,DP平分∠ADCCP平分∠BCDAB6AD10,则OP 2 

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:延长DPBCQ,如图所示:

四边形ABCD是平行四边形,

OBODCDAB6BCAD10ADBC

∴∠ADC+∠BCD180°,∠ADP=∠CQD

DP平分∠ADCCP平分∠BCD

∴∠ADP=∠CDQ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ADC,∠DCP=∠QCP <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> BCD

∴∠CQD=∠CDQ

CQCD6

BQBCCQ4

∵∠CDQ+∠DCP <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> (∠ADC+∠BCD <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 180°90°

CPDQ

DPQP

OBOD

OP是△BDQ的中位线,

OP <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> BQ2

答案:2

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

三、解答题(本大题共7小题,共66分。请在答题卡指定区域内作答,解答时应写出文字说明、证明过程或演算步骤)

17.(1)计算:2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

2)解方程:x2﹣2x﹣30

解:(1)原式=2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

2)∵x2﹣2x﹣30

x﹣3)(x+1)=0

x﹣30x+10

解得x13x2=﹣1

18.某射击队教练为了了解队员训练情况,从队员中选取甲、乙两名队员进行射击测试,相同条件下各射靶5次,成绩统计如下:

1)根据上述信息可知:甲命中环数的众数是  8 环;

2)通过计算说明甲、乙两人的成绩谁比较稳定.

3)如果乙再射击1次,命中8环,那么乙射击成绩的方差会  变小 .(填“变大”、“变小”或“不变”)

命中环数

6

7

8

9

10

甲命中相应环数的次数

0

1

3

1

0

乙命中相应环数的次数

2

0

0

2

1

解:(1)在甲命中环数中,8出现的次数最多,

甲命中环数的众数是8(环),

答案:8



2)甲的平均数是:(7+8+8+8+9÷58

则甲的方差是:S2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> [7﹣82+38﹣82+9﹣82]0.4

乙的平均数是:(6+6+9+9+10÷58

则乙的方差是:S2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> [2×6﹣82+2×9﹣82+10﹣82]2.8

S2S2

所以甲的成绩比较稳定;



3)如果乙再射击1次,命中8环,平均数不变,根据方差公式可得乙的射击成绩的方差变小.

答案:变小.

19.如图,在矩形OABC中,A30),C02),FAB上的一个动点,F不与AB重合,过点F的反比例函数y <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 的图象与BC边交于点E

1)当FAB的中点时,求该函数的解析式及△EFA的面积;

2)当△EFA的面积为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 时,求F点的坐标.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:(1)∵点FAB的中点,A30),C02),

F31),AF1

k3×13

y <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

E <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>2),

BE <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

SAEF <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 1 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

2)设点F3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ),则AF <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

E的纵坐标为2

E <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>2),

BE3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

SAEF <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解得:k14k22

F13 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ),F23 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ).

20.中考临近,某商家抓住商机,准备了一批考试专用笔及文具袋.去年五月份.笔的售价比文具袋的售价少2元,笔和文具袋的销售量都为100,结果笔与文具袋的总销售额为1400元.

1)求去年五月份笔和文具袋的售价;

2)受市场影响,该商家估计今年五月份购买笔的人会减少,于是降低了笔的售价,结果发现五月份笔的销售量有提升.经统计发现与去年五月份相比文具袋的售价每降价1元,文具袋的销售量就增加10件,同时笔的销售量就增加20件,且笔的售价不变.如果今年五月份笔和文具盒的总销售额比去年五月份的笔和文具盒的总销售额多90元,求今年五月份文具袋的售价.

解:(1)设去年五月份笔的售价为x元,文具袋的售价为y元,

依题意,得: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解得: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

答:去年五月份笔的售价为6元,文具袋的售价为8元.

2)设今年五月份文具袋的售价为m元,则文具袋的销售量为[100+108﹣m]件,笔的销售量为[100+208﹣m]件,

依题意,得:m[100+108﹣m]+6[100+208﹣m]1400+90

整理,得:m2﹣6m﹣70

解得:m1=﹣1m27

答:今年五月份文具袋的售价为7元.

21.如图,ABACCDAB,点EAC上一点,且∠ABE=∠CAD,延长BEAD于点F

1)求证:△ABE≌△CAD

2)如果∠ABC65°,∠ABE25°,求∠D的度数.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

1)证明:∵CDAB

∴∠BAE=∠ACD

∵∠ABE=∠CADABAC

∴△ABE≌△CADASA);

2)解:∵ABAC

∴∠ABC=∠ACB65°

∴∠BAC180°﹣∠ABC﹣∠ACB180°﹣65°﹣65°50°

又∵∠ABE=∠CAD25°

∴∠BAD=∠BAC+∠CAD50°+25°75°

ABCD

∴∠D180°﹣∠BAD180°﹣75°105°

22.如图,直线y13x﹣5与反比例函数 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 的图象交于点A2m)、Bn,﹣6)两点,连接OAOB

1)求mnk的值;

2)求△AOB的面积;

3)直接写出y1y2x的取值范围.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

解:(1)∵A2m)在直线y3x﹣5上,

m3×2﹣51

A21),

Bn,﹣6)在直线y3x﹣5上,

∴﹣63n﹣5

解得:n <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ,﹣6),

反比例函数y <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 的图象过点B

k﹣1 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> (﹣6),

解得:k3



2)设直线y3x﹣5分别与x轴、y轴交于CD

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

y0时,3x﹣50x <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

OC <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

x0时,y=﹣5

OD5

∴△AOB的面积SSBOD+SCOD+SAOC <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 5 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 5 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 1 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

3)∵A21),B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> ,﹣6),

由图象可知,当y1y2时,x <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 0x2

23.矩形ABCD的边长AB18cm,点EBC上,把△ABE沿AE折叠,使点B落在CD边的点F处,∠BAE30°

1)如图1,求DF的长度;

2)如图2,点N从点F出发沿FD以每秒1cm的速度向点D运动,同时点P从点A出发沿AF以每秒2cm的速度向点F运动,运动时间为t秒(0t9),过点PPMAD,于点M

请证明在NP运动的过程中,四边形FNMP是平行四边形;

连接NP,当t为何值时,△MNP为直角三角形?

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

1)解:∵四边形ABCD是矩形,

∴∠D=∠BAD=∠B90°

由折叠的性质得:AFAB18cm,∠FAE=∠BAE30°

∴∠DAF90°﹣30°﹣30°30°

DF <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> AF9cm);

2)①证明:由题意得:FNtcmPA2tcm

PF=(18﹣2tcm

PMADFDAD

PMFD,∠PMA90°

由(1)得:∠DAF30°

PM <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> PAtcm),

FNPM

四边形FNMP是平行四边形;

解:分三种情况:

a、当∠MPN90°时,PMPN,如图2所示:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

PMADADCD

PNADPNCD

∴∠FPN=∠DAF30°,∠PNF90°

FN <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> PF

t <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 18﹣2t),

解得:t <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

b、当∠PMN90°时,点NM重合,不能构成△MNP

c、当∠PNM90°时,如图3所示:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

PPHFNH

则四边形PHDM是矩形,∠PHF=∠PHD90°PHAD

PHDM,∠HPF=∠DAF30°

FH <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> PF=(9﹣tcm

NDDFFN=(9﹣tcm

FNND

∵∠D=∠PHF90°PHMD

∴△DMN≌△HPFSAS),

MNPF=(18﹣2tcm,∠DMN=∠HPF30°

∴∠NMP90°﹣30°60°

∴∠MPN90°﹣60°30°

PM2MN=(36﹣4tcm

PMtcm

36﹣4tt

解得:t <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a>

综上所述,当t <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 秒或 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/8/" title="模拟" class="c1" target="_blank">模拟</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> 秒时,△MNP为直角三角形.



1