当前位置:首页 > 八年级 > 数学试卷

【324343】2024八年级数学下学期期中测试模拟卷(第1~5章)(含解析)(新版)浙教版

时间:2025-01-15 21:59:12 作者: 字数:26008字


 <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/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> 期中测试模拟卷

考试范围:八年级下第15章 考试时间:120分钟 总分:120

一、选择题(每题3分,共30分)

1.下列等式正确的是(  )

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/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/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/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/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 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/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>

【分析】直接利用二次根式的性质以及立方根的定义分析得出答案.

【解答】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/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/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> ,故此选项符合题意;

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/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> 根号下是负数无意义,故此选项不合题意;

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/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> 无法化简,故此选项不合题意;

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/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/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> ,故此选项不合题意;

故选:A

2.下列几种名车标志中,是中心对称图形的有(  )

 <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/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>

A1 B2 C3 D4

【分析】根据中心对称图形的概念判断.把一个图形绕某一点旋转180°,如果旋转后的图形能够与原来的图形重合,那么这个图形就叫做中心对称图形.

【解答】解:左起第一、三、四共3个标志都能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以是中心对称图形,

第二个标志不能找到这样的一个点,使图形绕某一点旋转180°后与原来的图形重合,所以不是中心对称图形,

故选:C

3.用配方法解方程x2﹣4x﹣50时,配方结果正确的是(  )

A.(x﹣221 B.(x﹣22=﹣1 C.(x﹣229 D.(x﹣22=﹣9

【分析】方程移项后,利用完全平方公式配方得到结果,即可作出判断.

【解答】解:方程移项得:x2﹣4x5

配方得:x2﹣4x+49,即(x﹣229

故选:C

4.为了参加市中学生篮球赛,某校一支篮球队购买了10双运动鞋,尺码如表,则这10双运动鞋尺码的众数和中位数分别为(  )

尺码(  )

25

25.5

26

26.5

27

购买量(双)

1

2

3

2

2

A25.5cm26cmB26cm25.5cm C25.5cm25.5cmD26cm26cm

【分析】众数是一组数据中出现次数最多的数据,注意众数可以不止一个;找中位数要把数据按从小到大的顺序排列,位于最中间的一个数或两个数的平均数为中位数.

【解答】解:数据26出现了3次最多,这组数据的众数是26

10个数据,从小到大排列此数据处在第56位的数都为26,故中位数是26

故选:D

5.一元二次方程x2﹣4x+40的根的情况为(  )

A.没有实数根 B.只有一个实数根

C.两个相等的实数根 D.两个不相等实数根

【分析】先计算根的判别式,然后利用根的判别式的意义判断方程根的情况.

【解答】解:∵Δ=(﹣42﹣4×40

方程有两个相等的实数根.

故选:C

6.某经济技术开发区今年一月份工业产值达50亿元,且一月份、二月份、三月份的产值共为180亿元,问二、三月平均每月的增长率是多少?设平均每月的增长率为x,根据题意可列方程(  )

A501+x2180 B50+501+x2180

C501+x+501+x2180 D50+501+x+501+x2180

【分析】增长率问题,一般用增长后的量=增长前的量×1+增长率),本题可先用x表示出二月份的产值,再根据题意表示出三月份的产值,然后将三个月的产值相加,即可列出方程.

【解答】解:二月份的产值为:501+x)(亿元),

三月份的产值为:501+x)(1+x)=501+x2(亿元),

故第一季度总产值为:50+501+x+501+x2180

故选:D

7.用反证法证明命题“四边形中至少有一个角是钝角或直角”,应首先假设这个四边形中(  )

A.没有一个角是锐角 B.每一个角都是钝角或直角

C.至少有一个角是钝角或直角 D.所有角都是锐角

【分析】反证法的步骤中,第一步是假设结论不成立,反面成立.

【解答】解:用反证法证明“四边形中至少有一个角是钝角或直角”时第一步应假设:四边形中所有角都是锐角.

故选:D

8.如图,P是▱ABCD内一点,且SPAB6SPAD2,则阴影部分的面积为(  ) <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/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>

A4 B4.5 C5 D.无法计算

【分析】根据图形得出SPAB+SPCDSADC,求出SADCSPCDSPAB,求出SPACSPABSPAD,代入求出即可.

【解答】解:∵SPAB+SPCD <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/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> S平行四边形ABCDSADC

SADCSPCDSPAB

SPACSACDSPCDSPAD

SPABSPAD

6﹣2

4

故选A

9.如图,在菱形ABCD中,AB6cm,∠ADC120°,点EF同时由AC两点出发,分别沿ABCB方向向点B匀速移动,点E的速度为1cm/s,点F的速度为2cm/s,经过t秒△DEF为等边三角形,则t的值为(  )

 <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/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>

A1 B1.3 C1.5 D2

【分析】延长ABM,使BMAE,连FM,然后证明△DAE≌△EMF,再证明△BMF是等边三角形,可得BFAE,然后根据题意可得AEtCF2t,再根据BCCF+BF6列方程求解即可.

【解答】解:延长ABM,使BMAE,连FM

 <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/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>

四边形ABCD是菱形,∠ADC120°

ABAD,∠A60°

∴∠AED+∠ADE120°

BMAE

ADME

∵△DEF为等边三角形,

∴∠DEF60°

∴∠MEF+∠AED120°

∴∠MEF=∠ADE

在△ADE和△MEF

 <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/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>

∴△DAE≌△EMFSAS),

AEMF,∠M=∠A60°

又∵BMAE

∴△BMF是等边三角形,

BFAE

AEtCF2t

BCCF+BF3t

BC6

t2

故选D

10.如图,已知一个矩形纸片OACB,将该纸片放置在平面直角坐标系中,点A100),点B06),点PBC边上的动点,将△OBP沿OP折叠得到△OPD,连接CDAD.则下列结论中:①当∠BOP45°时,四边形OBPD为正方形;②当∠BOP30°时,△OAD的面积为15;③当ODAD时,BP2.其中结论正确的有(  )

 <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/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>

A0 B1 C2 D3

【分析】①由矩形的性质得到∠OBC90°,根据折叠的性质得到OBOD,∠PDO=∠OBP90°,∠BOP=∠DOP,推出四边形OBPD是矩形,根据正方形的判定定理即可得到四边形OBPD为正方形;故①正确;

DDHOAH,得到OA10OB6,根据直角三角形的性质得到DH3,根据三角形的面积公式得到△OAD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/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> OADH <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/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> ×3×1015,故②正确;

根据已知条件推出PDA三点共线,根据平行线的性质得到∠OPB=∠POA,等量代换得到∠OPA=∠POA,求得APOA10,根据勾股定理得到BPBCCP10﹣82,故③正确.

【解答】解:①∵四边形OACB是矩形,

∴∠OBC90°

将△OBP沿OP折叠得到△OPD

OBOD,∠PDO=∠OBP90°,∠BOP=∠DOP

∵∠BOP45°

∴∠DOP=∠BOP45°

∴∠BOD90°

∴∠BOD=∠OBP=∠ODP90°

四边形OBPD是矩形,

OBOD

四边形OBPD为正方形;故①正确;

DDHOAH

 <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/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>

A100),点B06),

OA10OB6

ODOB6,∠BOP=∠DOP30°

∴∠DOA30°

DH <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/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> OD3

∴△OAD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/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> OADH <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/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> ×3×1015,故②正确;

③∵ODAD

∴∠ADO90°

∵∠ODP=∠OBP90°

∴∠ADP180°

PDA三点共线,

OACB

∴∠OPB=∠POA

∵∠OPB=∠OPD

∴∠OPA=∠POA

APOA10

AC6

CP <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/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> 8

BPBCCP10﹣82,故③正确;

故选:D

二、填空题(每题4分,共24分)

11.若一个正多边形的内角和是其外角和的3倍,则该多边形每个外角的度数为    

【分析】先由多边形的内角和和外角和的关系判断出多边形的边数,即可得到结论.

【解答】解:设多边形的边数为n

因为正多边形内角和为(n﹣2)•180°,正多边形外角和为360°

根据题意得:(n﹣2)•180°360°×3

解得:n8

这个正多边形的每个外角= <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/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> 45°

故答案为:45°

12.已知,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/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/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,则2xy的值是    

【分析】根据二次根式有意义的条件列不等式组求解,确定xy的值,然后代入求值.

【解答】解:由题意可得 <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/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:x4

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/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/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=﹣2

2xy8+210

故答案为:10

13.若x1x2,⋯,x99个数的平均数 <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/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> ,方差S22,则x1x2,⋯,x9 <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/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个数的平均数是    ,方差是    

【分析】由于若x1x2,…,x99个数的平均数 <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/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> ,那么x1x2,…,x9 <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/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个数的平均数为[10×9+10]÷1010,而原来的方差S22,平均数没有改变,由此即可求出新数据的方差.

【解答】解:∵若x1x2,…,x99个数的平均数 <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/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>

x1x2,…,x9 <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/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个数的平均数为[10×9+10]÷1010

而原来的数据的方差为S22

 <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/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

x1﹣102+…+x9﹣10218

x1x2,…,x9 <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/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个数的方差是

 <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/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/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> 1.8

故答案为:101.8

14.已知关于x的一元二次方程x22m+1x+m2﹣10有实数根ab,则代数式a2ab+b2的最小值为   

【分析】由韦达定理得出abm的关系式、由一元二次方程的根与判别式的关系得出m的取值范围,再对代数式a2ab+b2配方并将a+bab整体代入化简,然后再配方,结合m的取值范围可得出答案.

【解答】解:∵关于x的一元二次方程x22m+1x+m2﹣10有实数根ab

a+b2m+1abm2﹣1,△≥0

Δ[﹣2m+1]2﹣4×1×m2﹣1

4m2+4m+1﹣4m2+4

4m+5≥0

m≥﹣ <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/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>

a2ab+b2

=(a+b2﹣3ab

=(2m+12﹣3m2﹣1

4m2+4m+1﹣3m2+3

m2+4m+4

=(m+22

a2ab+b2的最小值为: <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/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/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>

故答案为: <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/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>

15.如图,在▱ABCD中,∠ABC、∠BCD的平分线BECF分别与AD相交于点EFBECF相交于点G,若AB6BC10CF4,则BE的长为

 <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/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>

【分析】根据平行四边形两组对边分别平行可得∠ABC+∠BCD180°,再根据角平分线的性质可得∠EBC+∠FCB90°,可得BECF;过AAMFC,交BCM,交BEO,证明△ABE是等腰三角形,进而得到BOEO,再利用勾股定理计算出EO的长,进而可得答案.

【解答】解:∵四边形ABCD是平行四边形,

ABCD

∴∠ABC+∠BCD180°

∵∠ABC、∠BCD的平分线BECF分别与AD相交于点EF

∴∠EBC+∠FCB <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/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> ABC+ <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/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> DCB90°

EBFC

∴∠FGB90°

AAMFC,交BCM,交BEO,如图所示:

AMFC

∴∠AOB=∠FGB90°

BE平分∠ABC

∴∠ABE=∠EBC

ADBC

∴∠AEB=∠CBE

∴∠ABE=∠AEB

ABAE6

AOBE

BOEO

在△AOE和△MOB中,

 <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/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>

∴△AOE≌△MOBASA),

AOMO

AFCMAMFC

四边形AMCF是平行四边形,

AMFC4

AO2

EO <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/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/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 <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/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>

BE8 <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/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/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>

16.综合实践课上,小聪用一张长方形纸ABCD对不同折法下的折痕进行了探究,已知AB12,∠CAB30°,点EF分别在ABCD上,且AE5

1)把长方形纸片沿着直线EF翻折,使点A的对应点A恰好落在对角线AC上,点D的对应点为D,如图①,则折痕EF长为    

2)在EFAD上取点GH,沿着直线GH继续翻折,使点E与点F重合,如图②,则折痕GH长为    

 <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/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>

【分析】(1)过点FFMABM,则四边形ADFM是矩形,证明△FME∽△ABC,可以求出ME4EF8即可;

2)连接FNEN,设AHx,根据GH垂直平分线段EF,可得HFHE,根据勾股定理可得DF2+DH2AE2+AH2,列出方程12+4 <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/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> x252+x2,解方程求出x,可得结论.

【解答】解:(1)如图,过点FFMABM,则四边形ADFM是矩形,

 <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/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>

四边形ADFM是矩形,

ADFMBCBFAM

四边形ABCD是矩形,

∴∠B=∠D90°

AB12,∠CAB30°

BC <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/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> AB4 <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/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>

AC2BC8 <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/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>

ADFMBC4 <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/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>

∵∠MFE+∠AEN90°,∠BAC+∠AEN90°

∴∠MFE=∠BAC

∵∠FME=∠B90°

∴△FME∽△ABC

 <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/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/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/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/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/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/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>

ME4EF8

故答案为:8

2)如图,连接FHEH,设ACEFN

 <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/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>

ME4EF8

DFAMAEME5﹣41

AHx

GH垂直平分线段EF

HFHE

AEAE5DFDF1DHAD′﹣AH4 <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/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> x

根据勾股定理,得:

DF2+DH2AE2+AH2

12+4 <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/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> x252+x2

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/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>

HE <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/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/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/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>

EF8

EG <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/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> EF4

GH <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/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/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/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>

故答案为: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/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(共8题,共66分)

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/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.(6分)计算

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/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

【分析】(1)先利用二次根式的乘法和除法法则运算,然后化简即可;

2)先利用二次根式的乘法和除法法则运算,然后化简后合并即可.

【解答】解:(1)原式= <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/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/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/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/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/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/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/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/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/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)原式= <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/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/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/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﹣ <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/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/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+ <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/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.(6分)用适当的方法解下列方程:

1x2﹣2x﹣20;(2)(x+1)(x+2)=2x+4

【分析】(1)将常数项移到方程的右边,两边都加上一次项系数一半的平方配成完全平方式后,再开方即可得;

2)先移项,再将左边利用提公因式法因式分解,继而可得两个关于x的一元一次方程,分别求解即可得出答案.

【解答】解:(1)∵x2﹣2x﹣20

x2﹣2x2

x2﹣2x+12+1,即(x﹣123

x﹣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/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>

x11+ <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/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> x21﹣ <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/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)∵(x+1)(x+2)=2x+4

x+1)(x+2)﹣2x+2)=0

则(x+2)(x﹣1)=0

x+20x﹣10

解得x1=﹣2x21

19.(6分)如图所示,已知△ABC的三个顶点的坐标分别为A(﹣23),B(﹣60),C(﹣10).

1)直接写出点B关于点A对称的点的坐标    

2)将△ABC绕坐标原点O逆时针旋转90°,画出图形,直接写出点B的对应点的坐标    

3)请直接写出:以ABCD为顶点的平行四边形的第四个顶点D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/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>

【分析】(1)根据中心对称的概念求解即可;

2)将三个顶点分别绕坐标原点O逆时针旋转90°得到其对应点,再首尾顺次连接即可;

3)根据平行四边形的概念作图即可.

【解答】解:(1)如图所示,点P即为点B关于点A的对称点,坐标为(26),

 <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/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>

故答案为:(26);

2)如图所示,△ABC即为所求,点B的对应点的坐标为(0,﹣6),

故答案为:(0,﹣6);

3)如图所示,点D即为所求,其坐标为(﹣73)或(33)或(﹣5,﹣3),

故答案为:(﹣73)或(33)或(﹣5,﹣3).


20.(8分)某工厂第一车间有工人20人,每人日均加工螺杆数统计如图.

 <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/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>

请根据以上提供的信息解答下列问题:

1)该车间工人日均生产螺杆数的平均数、中位数和众数分别是多少?

2)若要从平均数、中位数、众数中选一个作为该车间工人日生产定额,超额部分给予奖励.为鼓励大多数工人,你认为选哪个统计量比较合适,请说明理由.

【分析】(1)根据中位数、众数及平均数的计算公式进行解答即可;

2)根据(1)求出的中位数、众数及平均数,然后找到一个大多数人能达到的统计量即可.

【解答】解:(1)该车间工人日均生产螺杆数的平均数为(10×2+12×7+14×6+16×5÷2013.4(个),

某工厂第一车间有20个工人,把这些数从小到大排列,中位数是第1011个数的平均数,

则中位数为 <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/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(个).

日加工螺杆数为12个的有7名工人,

所以众数为12个;


2)为鼓励大多数工人,选众数比较合适.

21.(8分)已知:BD是△ABC的角平分线,点EAB边上,BEBC,过点EEFAC,交BD于点F,连接CFDE

1)如图1,求证:四边形CDEF是菱形;

2)如图2,当∠DEF90°ACBC时,在不添加任何辅助线的情况下,请直接写出图2中度数为∠ABD的度数2倍的角.

 <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/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>

【分析】(1)直接由SAS得出△BDE≌△BDC,得出DEDC,∠BDE=∠BDC.再由SAS证明△BFE≌△BFC,得出EFCF.由EFAC得出∠EFD=∠BDC,从而∠EFD=∠BDE,根据等角对等边得出DEEF,从而DEEFCFDC,由菱形的判定可知四边形CDEF是菱形;

2)如图2,利用正方形的性质可得∠DFE45°,然后证明∠FEB=∠CBE2∠FBE即可.

【解答】(1)证明:在△BDE和△BDC中,

 <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/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>

∴△BDE≌△BDCSAS);

DEDC,∠BDE=∠BDC

同理△BFE≌△BFC

EFCF

EFAC

∴∠EFD=∠BDC

∴∠EFD=∠BDE

DEEF

DEEFCFDC

四边形CDEF是菱形;

2)∵四边形CDEF是正方形,

∴∠CDE=∠DEF2∠EFD90°

ACBC

∴∠A=∠CBE

∵∠A+∠AED180°﹣90°90°,∠AED+∠FEB90°

∴∠A=∠FEB=∠CBE2∠EBF

∵∠ABD+∠FEB=∠DFE45°

∴∠ABD15°

∴∠FEB30°

∴∠A=∠ABC=∠FEB30°

∵△BFE≌△BFC

∴∠FEB=∠FCB30°

综上所述,度数为∠ABD的度数2倍的角是∠A,∠ABC,∠FEB,∠FCB


22.(10分)安庆某商场销售一批空气加湿器,平均每天可售出30台,每台可盈利50元,为了扩大销售量,增加盈利,尽快减少库存,商场决定采取适当的降价措施,经调查发现,如果每台每降价1元,商场平均每天可多售出2台.

1)若该商场某天降价了5元,则当天可售出    台,当天共盈利    元.

2)在尽快减少库存的前提下,商场每天要盈利2100元,每台空气加湿器应降价多少元?

3)该商场平均每天盈利能达到2500元吗?如果能,求出此时应降价多少;如果不能,请说明理由.

【分析】(1)利用销售数量=30+2×降低的价格,即可求出当天的销售量,再利用总利润=每台的利润×销售数量,即可求出结论;

2)设每台空气加湿器应降价x元,则每台盈利(50﹣x)元,每天可以售出(30+2x)台,利用总利润=每台的利润×销售数量,即可得出关于x的一元二次方程,解之即可得出x的值,再结合要尽快减少库存,即可确定x的值;

3)设每台空气加湿器应降价y元,则每台盈利(50﹣y)元,每天可以售出(30+2y)台,利用总利润=每台的利润×销售数量,即可得出关于y的一元二次方程,由根的判别式Δ=﹣7750可得出该方程无实数根,进而可得出商场平均每天盈利不能达到2500元.

【解答】解:(130+2×530+1040(台),

50﹣5×4045×401800(元).

故答案为:401800

2)设每台空气加湿器应降价x元,则每台盈利(50﹣x)元,每天可以售出(30+2x)台,

依题意得:(50﹣x)(30+2x)=2100

整理得:x2﹣35x+3000

解得:x115x220

尽快减少库存,

x的值应为20

答:每台空气加湿器应降价20元.

3)不能,理由如下:

设每台空气加湿器应降价y元,则每台盈利(50﹣y)元,每天可以售出(30+2y)台,

依题意得:(50﹣y)(30+2y)=2500

整理得:y2﹣35y+5000

Δ=(﹣352﹣4×1×5001225﹣2000=﹣7750

该方程无实数根,

商场平均每天盈利不能达到2500元.



23.(10分)定义:只有一组对角是直角的四边形叫做损矩形,连接它的两个非直角顶点的线段叫做这个损矩形的直径.如图1,∠ABC=∠ADC90°,四边形ABCD是损矩形,则该损矩形的直径是线段AC.同时我们还发现损矩形中有公共边的两个三角形角的特点:在公共边的同侧的两个角是相等的.如图1中:△ABC和△ABD有公共边AB,在AB同侧有∠ADB和∠ACB,此时∠ADB=∠ACB;再比如△ABC和△BCD有公共边BC,在CB同侧有∠BAC和∠BDC,此时∠BAC=∠BDC

1)请在图1中再找出一对这样的角来:      

2)如图2,△ABC中,∠ABC90°,以AC为一边向外作菱形ACEFD为菱形ACEF对角线的交点,连接BD

四边形ABCD   损矩形(填“是”或“不是”);

BD平分∠ABC时,判断四边形ACEF为何种特殊的四边形?请说明理由;

若∠ACE60°AB4BD5 <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/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> ,求BC的长.

 <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/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>

【分析】(1)以AD为公共边,有∠ABD=∠ACD

2)①由菱形的性质可得∠ABC=∠ADC90°,可得四边形ABCD是损矩形;

由四边形ABCD为损矩形,可得∠ACE2∠ACD90°,可得结论;

由四边形ABCD为损矩形,可得∠ACD=∠ABD30°,由直角三角形的性质和勾股定理可求AD长,AC的长,由勾股定理可求解.

【解答】解:(1)由图1得:△ABD和△ADC有公共边AD,在AD同侧有∠ABD和∠ACD,此时∠ABD=∠ACD

 <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/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>

故答案为:∠ABD,∠ACD(或∠DAC,∠DBC);

2)①∵四边形ACEF是菱形,

AECF

∴∠ABC=∠ADC90°

四边形ABCD是损矩形,

故答案为:是;

四边形ACEF为正方形,理由如下:

证明:∵∠ABC90°BD平分∠ABC

∴∠ABD=∠CBD45°

四边形ABCD为损矩形,

∴∠ACD=∠ABD45°

∴∠ACE2∠ACD90°

四边形ACEF为正方形;

3)过点DDHAB,交BA的延长线于H

 <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/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>

四边形ACEF是菱形,∠ACE60°

ACCE,∠ACF30°AECF

四边形ABCD为损矩形,

∴∠ACD=∠ABD30°

HD <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/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 <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/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> BH <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/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> HD <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/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>

AHBHAB <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/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>

AD <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/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/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>

∵∠ACF30°AECF

AC2 <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/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>

BC <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/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/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 <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/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>

24.(12分)如图,直线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/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> x+11分别交xy轴于AB两点,点D以每秒2个单位的速度从点A出发沿射线AD方向运动,同时点E以每秒1个单位的速度从点B出发沿边BA方向运动,当E到达点A时,点DE同时停止运动,设运动时间为t秒.

1)求点A的坐标及线段AB的长.

2)如图1,当t4 <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/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时,求∠AED的度数.

3)如图2,以DE为对角线作正方形DFEG,在运动过程中,是否存在正方形DFEG的一边恰好落在△ADB的一边上?若存在,请求出所有符合条件的t值;若不存在,请说明理由.

 <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/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>



【分析】(1)由直线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/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> x+11分别交xy轴于AB两点,求点A、点B的坐标,再根据勾股定理求出AB的长;

2)作DKAB于点K,延长DK到点L,使KLDK,连结ALBD,由 <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/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> ABDK <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/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> ADOBSABD,求出DK的长,得到DL的长,可判断△ADL是等边三角形,∠DAK <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/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> DAL30°;再通过计算证明AKEK,可得∠AED=∠DAK,求得∠AED的度数;

3)先证明含30°角的直角三角形的三边的比是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/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> ,再按DFDGOA上、EGEFAB上分类讨论,求出相应的t的值.

【解答】解:(1)当y0时,由﹣ <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/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> x+110得,x11 <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/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> ;当x0时,y11

A11 <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/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> 0),B011),

∵∠AOB90°OA11 <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/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> OB11

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/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> 22.

2)如图1,作DKAB于点K,延长DK到点L,使KLDK,连结ALBD

由题意得,AD2tBEt

t4 <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/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时,AD24 <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/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)=8 <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/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> ﹣4BE4 <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/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/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> ABDK <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/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> ADOBSABD

 <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/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> 22DK <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/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> 8 <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/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> ﹣4×11

解得,DK4 <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/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

DL2DK24 <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/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)=8 <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/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

ADDL

ADALDL

∵△ADL是等边三角形,

∴∠DAL60°

∴∠DAK <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/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> DAL30°

∵∠AKD90°

AK <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/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/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>

EK22﹣4 <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/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/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/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>

AKEK

ADED

∴∠AED=∠DAK30°

3)存在.

如图2,在BO的延长线上取一点H,使OHOB,连结AH

由(2)得,∠OAB30°

AOBH

ABAH

∴∠OAH=∠OAB30°

∴∠BAH60°

∴△BAH是等边三角形;

OBa,则ABBH2a

OA <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/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/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

可得,在直角三角形中,如果有一个角是30°,那么30°角所对的直角边与斜边、另一直角边的比为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/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>

DG边在OA上,如图2,则∠AGE90°

EG <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/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> AE <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/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> 22﹣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/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> 22﹣t+2t <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/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/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> 22﹣t),

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/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>

EF边在AB上,如图3,则∠AFD90°

EFDF <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/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> AD <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/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> 2tt

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/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> 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/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> t

2t+ <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/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> t22

解得,t44﹣22 <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/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>

DF边在OA上,如图4,则∠AFE90°

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/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> EF

EFDFAF+DFAD2t

 <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/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> EF+EF2t

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/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> 1t

AE2EF

22﹣t2 <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/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> 1t

解得,t4 <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/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

EGAB上,如图5,则∠AGD90°

EGDG <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/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> ADtAG <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/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> DG

22﹣t+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/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> t

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/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,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/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> t44﹣22 <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/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> t4 <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/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> +2t <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/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/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/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/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/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/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