【质检卷】2021年宁德市初中毕业班第二次质量检测数学试卷

∴
BDCE
.
∵∠ABC=90 , D AC
1
∴BD= AC=CD,
2
BDCE
.
(3
)
(6
)
(8
)
,
D
AC
,
19.(
8
)
(−2)(+2)
=
+2
,
2 −4+4
4
4
=(x-2)·
(−2)2
4
=
.
−2
x=3
,
12
=
=12.
3−2
2 −4
:
+2
2 +4
(
-1),
4
x=3.
(2
)
23.(
10
,
“
)
”
.
,
.
,
,
(1)
,
50
:
50
;(
,
0.35~0.45 kg
,
.
0.4 kg)
(2)
,
:
,
:
30
3
x/kg
/(
①
/kg)
/kg
.
0.35≤x<0.55
0.55≤x<0.75
0.75≤x<0.95
26
32
40
,
,
.
;
,
50
②
:
;
,
(1)
8×0.4+12×0.5+15×0.6+7×0.7+8×0.8 29.5
∵4>0,∴y
∴ x=16
:
x
,y
,
,y
=4
224
16+160=224.
.
21.(
8
(1)
)
:
,
BECF,
ABCD
.
E
ABCD
)
(2)
(1)
,
DE, AB=6,AD=8,
DE
.
;(
,
(1)
(1),
BECF
.
(
(4
,
(2)
(3)
)
)
(2)
∵
(1)
(4),
EF BC
ABCD
G,FE
AD
H.
,∴∠ADC=∠BCD=90 ,CD=AB=6,BC=AD=8.
EBD
,
∴BE=ED=BD,∠EBD=60 .
∵AB=AD,
∴AF BD
,
∴EF=BEsin 60 =
AF=EF+EA=
3
3
BE= BD,
2
2
3
BD+CD.
2
)
(2)
:
:AG=
2
1
BD+ CD.
2
2
(1),
AG
EG=CG,
DE,CE.
∵AG⊥CD,AD=AC,
∴DG=CG=EG,
∴∠ECG=∠GEC=∠DEG=∠EDG=45 ,
x=2
Q
2.
y=x2-4x+5, y=10,
(1,2),(5,10).
AB
∴
Q,
y=x2-4x+5, y=2, x=5
x=1
∴
AB
AB
A(1,2),B(5,10)
(5
)
(7
)
(8
)
y=ax+b,
= 2,
ቊ
= 0,
y=2x.
y=2x, y=4,∴ Q
∴PQ=3, S
PAB=S
PAQ+S
1
PBQ=2
A
A'
m=-8, k=24.
m=0,
k=8.
(m+2,-4),
ABC
C'
,k
(m+4,-6),
8
24.
17.(
8
)
:|-1|-
1 -1
16+( ) .
2
=1-4+2
(6
)
=-1.
(8
)
18.(
8
)
,
Rt
ABC ,∠ABC=90 ,
BE∥AC,CE∥BD,BE CE
:
BDCE
E.
.
:∵BE∥AC, CE∥BD,
5.
,
ABC ,∠ACB=90 ,∠ABC
AD=3,
D AB
(
A.1
B.2
C.3
D.4
6.
BD
AC
50
.
,
,
A.
(
B.
AC=5,
)
,
(1)
D.
C.
)
D.
7.
,
,
;
,
,
8
,
,
.
.”
, 3
.
;
7
, 4
:
,
,
(
:“
8x-3=y,
)
A.7x-4=y
B.7x+4=y

C. +4=x
7

D. -4=x
7
,
8.
=
=
=0.59(kg).
50
50
:
(2)①
50
0.59 kg.
50
,
8
P(
(3
8
4
)= = .
50 25
)
50
,
,
(6
)
②
:
0.59
:
(8
50
0.4+12
0.5)
40=239.2+444.8+256=940(
∵940>885,
30=885(
).
26+(15
0.6+7
0.7)
32+8
0.8
).
.
(8×0.4+12×0.5)×26+(15×0.6+7×0.7)×32+8×0.8×40
(1)
,y1-y2=0,
2×1
=k,
(2
1 +2
=2
2
x=2.
,y1=y2,
A,B
)
x=2
(3
,
)
(k,k2-3),∴k=2,
P
y=x2-4x+5,
G
P
-
=k2-3,
G
∴
P
(k,k2-3).
P
∴
,
−2
(2,1).
(4
)
①
P PQ∥y
A,B
y=ax+b,
+ = 2,
ቊ
5 + = 10,
2
(13
)
. (14
)
m=2x-4.
2
y= +3,
2
E
y=2x2-8x+11,
y=2x2-8x+11
(12
)
1
1
∴DG= CD,∠DAG=∠CAG= ∠CAD,
2
2
CD
F.
1
∴∠GAF=∠DAE+∠DAG= ∠BAC=45
2
,
∴∠F=45 ,
∴AG=GF.
Rt
(9
DEF ,sin
∴DF=

sin45
)

F= ,

= 2DE=
AG=GF=DF+DG=
2
BD,
2
(10
)
2
1
BD+ CD.
2
2
(12
)
25.(
1.-2
(
A.2
2.2020
B.-2
,
(GDP)
(
A.0.101 6
1
C.
2
1
D.2
,
,
C.1.016
)
,
1 016 000
.
B.1 016
103
D.1.016
107
)
107
106
1 016 000
“
3.
”
,
.
,
.
(
,
)
4.
A.(a3)2=a6
(
)
B.a6 a2=a3
C.a+2a2=3a3
D.a2·a3=a6
∴n=3-2m,
∴
AB
y=mx-2m+3.
= −2 + 3,
ቊ
= 2 −4 + 5,
E
x2-(4+m)x+2m+2=0,∴x1+x2=4+m.
(x,y),
∵ E AB

x= +2
2

x= +2,
2
m=2x-4
AB
1 +2
,∴x=
= +2.
2
2
y=mx-2m+3,
2
y= +3.
)
(4
)
(6
)
(8
)
20.(
,
8
”
2
)
100
,
80
,
4
,
2
(1)
,
,
3
.
x ,
;(
“
,
y(
x
)
(2)
,
.
)
x
(1)
, y=4x+3
2x+2
(80-x-2x), (2
)
(3
)
(5
)
(6
)
(8
)
y=4x+160.
∴y
x
y=4x+160.
(2)
, 2(80-x-2x)≥4x,
x≤16.
(1)
y=4x+160,
14
2k2-3
(1)
xOy
P
.(
k
)
A(x1,y1),B(x2,y2)(x1<k<x2)
①
G
,
A,B
PCD
G:y=x2-2kx+
,
P.
(2)
②
)
x
2
,
G
x1=1,x2=5
,
:
AB
x1+x2=4
PAB
C,D.
E
,
,y1-y2=0.
;
PAB
.
(1)
4(2 2 −3)−(−2 ) 2
4×1
∴
(2)∵ x1+x2=4
“
”, Δ=
10.
(
A,B,C,D,E,F
(
.
2,
)
A.3- 3
2 3−1
B.
2
3+1
2
13−1
2
C.
),
D.
,
AD,AE,CF,
AD,CF
,
AED=90 ,
CF
G
AE
AE
百度文库G,
GD.
.
GDE=60 .
ED=2,
Rt GED ,GE=EDtan 60 =2 3, AG=EG=2 3, AD= 2 + 2 =
(1)
(2)
,
Rt
D,☉A
DE
:ED=EC;
∠C=30 ,AB=6,
ED
ABC ,∠A=90 ,
.
AC
E.
A
AB
(1)
:
∵ AB=AD,∴∠B=∠ADB.
,
AD,
(1
)
(2
)
∴∠C+∠B=90 ,
(3
)
∴∠EDC=∠C,
(4
)
(5
)
∵DE ☉A
,
∴∠ADE=90 ,
∴∠ADB+∠EDC=180 -∠ADE=90 .
≈31.86(
0.59×50
(10
)
(10
)
/kg).
∵31.86>30,
.
24.(
12
)
,
ABC ,AB=AC,∠BAC=α,
AD,∠DAC<α,
(1)
(1), α=60
①
:
②
AE BD
(2)
EBD,
ABE≌△CBD;
F,
.
α=90
(2),
G.
,
AG,BD,CD
.
A
BD,CD.
,
AF,BD,CD
∴

2
ACE∽△BCD,∴ = = ,
2
∴AE=
2
BD.
2
1
∵EG=CG= CD,AG=AE+EG,
2
AG=
2
1
BD+ CD.
2
2
:AG=
:
2
1
BD+ CD.
2
2
(2),
A AE⊥BD
E,AE
∵AB=AC=AD,
1
1
∴DE= BD,∠DAE=∠BAE= ∠BAD.
2
2
∵AG⊥CD,
A,B,C,D
1
,
.
A
(
A.A
B.B
a,
D
d, d=-2a,
C.C
D.D
)
9.
,
”.
“
“
x2+3x+c=0,
9
C.c=
4
”
y=x2+2x+c
9
c= .
4
”,
)
1
B.c=
4
A.c=1
P “
,
y=x2+2x+c
(
9-4c=0,
P
y=-x ,
4
D.c=
9
= 2 + 2 + ,
ቊ
= −,
,
EF=
10
DGA=α.
,
BC=6 cm,
cm.(
,
,
α=37
,
:sin 37
D
DG
AB CD
, EF=DG. Rt
ADG
EF 10 cm.
EF
3
≈ ,cos
5
AB
37
4
≈ ,tan
5
G,
DG
37
3
≈ )
4
DEFG
,AD=BC=6 cm,

DG=
≈6
sin
5
=10(cm),
3
16.
A BC
,
,
AC
A AG
CD
,
E
ABC
,
AE.
(1)①
∴
ABC
:∵AB=AC,∠BAC=α=60 ,
,
∴AB=BC,∠ABC=60 .
∵
EBD
,
∴BE=BD,∠EBD=60 ,
∴∠ABC=∠EBD,
∴∠ABE=∠CBD,
ABE △CBD.
(4
)
②AF=
3
BD+CD.
2
:∵
∵
(7
ABE≌△CBD,∴AE=CD.
(2,4),
3
1
1+
2
3
3=6.
②
,
P PQ∥y
AB
Q,
C,D
(x1,0),(x2,0),
∵S
PAB=2S
1
PCD,∴2PQ
∴PQ=2,∴ Q
∴
x1,x2
AB
Q(2,3)
(x2-x1)=2
1
2
1
(2,3),
,
AB
(x2-x1),
(10
)
(11
)
Q(2,3).
y=mx+n,
y=mx+n, 2m+n=3,
1
,∴EG=GC= BC=4,EG⊥BC,
2
BECF
∴∠ADC=∠BCD=∠EGC=90 ,
∴
CDHG
,
(6
)
(7
)
(8
)
∴DH=CG=4,GH=CD=6,∠DHE=90 ,
∴HE=HG-EG=2.
Rt
DHE ,
DE= 2 + 2 = 22 + 42 =2 5.
(5
)
22.(
10
)
☉A BC
∵∠BAC=90 ,
ED= EC.
(2)
AD, Rt ABC ,∠C=30 ,
∴∠B=90 -∠C=60 .
∵AD=AB=6,∴ ABD
,
∴∠BAD=60 ,
(7
)
∴∠DAC=∠BAC-∠BAD=30 .
(8
)
Rt
ADE

,tan∠DAE= ,

∴DE=AD·tan∠DAE=6
3
=2
3
3.
(10

y=

x
ABC,
4,
A,C
B,C
,
BAC=90 ,
(m,n),(m+4,n).
k=
8
24
.
ABC
.
B(m,n),C(m+4,n), BC=4.
,
A x
,
ABC
4,
B,C
1
(m+m+4)=m+2,
2
2,
A(m+2,4).
A,C, 4(m+2)=2(m+4),
A'B'C'
,
-4(m+2)=-6(m+4),
∴DE=CE,∠DEC=90 .
Rt
DEC

2
,cos∠ECD= = .
2
∵∠BAC=90 ,AB=AC,∴∠ACB=45 .
(8
)
(9
)
Rt
ABC

2
,cos∠ACB= = .
2

∴ = .

(10
)
(11
)
(12
)
∵∠ACB=∠ECD=45 ,∴∠ACE=∠BCD,
(4
3) 2
+
22 =2
13, CF=2 13,
13−1
.
2
1
1
FG= (CF-2)= (2
2
2
13-2)= 13-1,
11.
12.
,
c
a,b
x2-x=0
. a∥b,∠1=54 , ∠2=
x1=0,x2=1
.
54
.
13.
,
, ∠C=130 , ∠A=
ABCD ☉O
14.
,
,
,
4
9
,
.
50
.
.
,
15.