2023 年秋学期九年级期中学情调查数学试卷
参考答案(仅供参考)
一、 选择题（每题 3 分，共 18 分）
题号 1 2 3 4 5 6
答案 D C A C D B
二．填空题（每题 3 分，共 30 分）
7． 8 或-2 8． 86
9． 9 10． -1（任一负数即可）
11． 5 12． 135°
13． = 14． 46°
15． 60 16． 2三．解答题（共 102 分）
17．（1） 不正确，不正确， ·································································· 4
1
（2） 解： 3(2x +1) = (2x +1)2 (2x +1)(2 2x) = 0, x1 = , x2 =1 ················· 10
2
1
18. （1） ······························································································ 3
3
（2）记左下右为 ABC···· 乙 丙 丁 ························ 6
B C 相邻
A
C B 相邻
A C 相对
开始 B
C A 相对
A B 相邻
C
B A 相邻
2
P（丙丁相邻）= ·············································································· 8
3
19. （1）①②；③（答案不唯一）······························································· 2
（2）略···························································································· 8
1
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20. （1）m = 2 ······································································ 3
边长为 1 ······································································ 5
（2）m = 3 ····································································· 7
周长为 6 ···································································· 10
21. （1） 2 ； 2 ··········································································· 2
（2） 2 ； 8 分 ··········································································· 4
（3）不是； ·········································································· 5
七年级的平均分：8.3 分，优秀率 50% ············································ 7
八年级的平均分：8.4 分，优秀率 40% ··········································· 9
8.3＜8.4，但 50%＞40% ·························································· 10
22. ··················· 4
················· 5
················· 9
················· 10
（1）设OB = r,在Rt△AOC中， OA2 + AC2 =OC2
23. ············· 4
482 + (96 r)2 = r2 r = 60
D
AC BD
（2）△AOC~△BOD =
OA OB C 6
当AC = 48,OA = 36时，BD = 80; ······· 8
当BD = 80 35 = 45时，AC = 36,OA = 48 10
AC = 36,点A移动距离：48 36 =12
A O B
24.（1） y =15x + 60 ··················································································· 3
（2） (48 30 2)(15×2+ 60) =1440 ··········································· 6
设降价x元，则(48 30 x)(15x + 60) =1680, 9
（3）x =10或x = 4 ······································ 11
让顾客得到实惠 x =10 12
2
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25.
C
C
F E C
D D
D H
H
A B
O A
O B A
B
O
（1）以 C 为圆心，CD 为半径画弧交 CE 于点 F,连接 BF,BF 即为所求（答案不唯一）· 3
(2) AB时 O的直径 ∠AHB = 90°又 AB=AC HB=HC ························ 4
∠CDB = 90°, HB=HC BC=2DH=4 2 · ··························· 5
在（1）的条件下证CD=CF=2
设AB = AC = x,
AB2 AD2 = BC2 CD2 ····································································· 8
x2 (x 2)2 = (4 2)2 22
x = 8
60 200
（3）S= r2 = ·································································· 12
360 3
4 3
26. （1）AP= 或 ········································································· 4
3 2
（2）
①该准内心 P 为下方圆弧的中点 ························································· 6
② PC = 5 2，PA= 3 10 ······················································· 10
1
③ S ABC = mn （证明仅供参考） ··············································· 14
2
A
A
B C
E
C
O B O
D
P
P
D
3
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【方法一】 【方法二】
过点P作AB、AC的垂线段，垂足为点E、D
过点P作PA的垂线交AC的延长线于点D 证明： EBP DCP（AAS或HL或SAS）
证明： ABP DCP（AAS） 得BE=CD
得AB=DC 证明：正方形AEPD
证明： APD为等腰直角三角形 AB AC
得AP2 + PD2 = AD2 = (AE + BE)(AD CD)
2PA2 = (AB + AC)2 = AE2 CD2
2PA2 = AB2 + 2AB AC + AC2 = AE2 (PC 2 PD2 )
2PA2 = 2PB2 + 2AB AC = 2AE2 PC 2
PA2 PB2 = AB AC = PA2 PC 2
(PA+ PB)(PA PC) = AB AC = (PA+ PB)(PA PC)
1 1
S ABC = mn S
2 ABC
= mn
2
4
{#{QQABbQiEogCAAAIAABgCQwWiCkIQkBGACIoOBBAEMAAAABFABCA=}#}2023年秋学期九年级期中学情调查
数学试卷
(考试时间：120分钟，满分150分）
第一部分选择题（共18分）
一、选择题（本大题共6小题，每小题3分，满分18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，选择正确选项的字母代号涂在答题卡相应的位置上)
1.下列方程是一元二次方程的是
A.x2+y-5=0
B.x(x+3)=x2
D.x(x-1)=0
2.安老师准备在班上开展“法制”“环保”“安全”三场专题教育讲座，若三场讲座随机
安排，则“法制”专题讲座被安排在第一场的概率为
A.G
B
c.
3.甲、乙、丙、丁四人各进行了10次射击测试，他们的平均成绩相同，方差分别是
S2=0.6,S22=1.1,S2=0.9,Sr2=12.则射击成绩最稳定的是
A.甲
B.乙
C.丙
D.丁
4.如图，矩形PAOB内接于扇形ON,顶点P在MN上，且不与M,N重合，当点
P在MN上移动时，矩形PAOB的形状、大小随之变化，则PA+PB的值
A.变大
B.变小
C.不变
D.不能确定
B
(第4题)
(第5题)
(第6题)
5.刘徽在《九章算术注》中首创“割圆术”，利用圆的内接正多边形来确定圆周率，开创
了中国数学发展史上圆周率研究的新纪元，某同学在学习“割圆术“的过程中，作了如
图所示的圆内接正八边形，若圆的半径为1，则这个圆内接正八边形的面积为
A.π
B.2x
C.②
D.2W2
4
九年级数学第1页（共8页）
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6.如图，在Rt△MBC中，∠BAC=90°，AB=AC,已知B,C在线段DE上，
∠DAE=135°且线段BD=9,CE=4,则BC的长为
A.6
B.6W2
C.6.5
D.6N3
第二部分非选择题（共132分)
二、填空题（本大题共有10小题，每小题3分，满分30分，请把答案直接填写在答题卡
相应位置上)
7、方程(x-3)2=25的根为▲
8.小敏同学参加市“书香少年*评选，其中综合荣誉分占40%，现场演讲分占60%，已知
小敏这两项成绩分别为80分和90分，则小敏的最终成绩为▲分.
9,在一个不透明的袋子中装有3个红球和若干个白球.每个球除颜色外其余均相同，若
从袋中随机摸出一个球是红球的概率为牙，则袋中白球的个数为▲
10.若关于x的一元二次方程x2+2x-k+1=0没有实数根，则k的值可以是
▲·（写出一个即可）
11.如图，⊙0是△4BC的外接圆，BC=5,∠BAC=30°，则⊙0的半径长等于▲
12.如图，在正方形网格中，AB、C、DE、F均为格点，则∠BAC的度数为▲°
D
C
B
0
S
.0
A
(第11题)
(第12题)
(第13题)
(第14題)
13.如图，点C是线段AB的黄金分割点，AC>BC，若S表示以AC为一边的正方形
的面积，S2表示长为AB，宽为CB的矩形的面积，则S▲S2·(用
“>”、“=”或“<”填空)
14.如图，四边形ABCD内接于OO,ADBC的延长线相交于点E,AB、DC的延长
线相交于点F,若∠E=52°、∠F=36°，则∠A的度数为▲°，
九年级数学第2页（共8页）
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