Đề số 2
ĐỀ THI HỌC KÌ 1 – Năm học
Môn TOÁN Lớp 11
I. Phần chung dành cho tất cả thí sinh.
Câu 1: !"
y x4cos 3= −
Câu 2:#$%& '"
(
x
1
cos 3 0
2 2
π
+ − =
÷
)
x x3 cos2 sin2 2+ =
)
x xtan 3cot 2 0
+ + =
Câu 3:) !*+,-x.+/"
x
x
6
3
+
÷
Câu 4:01234 5674 89474 /':;6<=
>? ' .."
)8$74 %@45
83>A4
Câu 5:8.3BCD8E3FCD8EG0'/.*B8GH'
/.*IDI./DE6C8
).'FJKKL"BCD6B8E
)./MBE6KLC0H
#4N'/BC8-O0NPPCD8E
II. Phần riêng:
A. Theo chương trình chuẩn
Câu 6a"
()8. !Q
( )
n
u
3
u u
1 4
2, 54= =
,1R6>2
S
10
A) !1
n
u( )
3< !*GJ"
u u
u u
1 5
3 3
7
9
+ =
+ =
Câu 6b: .KLOxy, ./CSTUADUSTA6%L:"
x y3 4 12 0− + =
()$/DR'V!?-QI
A)$/CR'V!?-W:
B. Theo chương trình nâng cao
Câu 7a:)#$%&"
x xtan4 .tan 1 0+ =
Câu 7b: ).KL41Ixy,.VJXJY/0?TF/
0Z?ZTFZ .."
x ax by
y cx dy
'
'
= +
= +
G.3
a c b d
2 2 2 2
1+ = + =
6
a b c d. . 0+ =
8-X
V:
UUUUUUUUUUUUUUUUUUUU[JUUUUUUUUUUUUUUUUUUU
Họ và tên thí sinh". . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD ". . . . . . . . . .
(
Đề số 2
ĐỀ THI HỌC KÌ 1 – Năm học
Môn TOÁN Lớp 11
8Q' H1:' \/
(
y x4cos 3= −
3
x1 cos 1
− ≤ ≤
x4 4cos 4
⇔ − ≤ ≤
x7 4cos 3 1⇔ − ≤ − ≤
max
y khi x k y khi x k
min
1 2 ; 7 2
π π π
= = = − = +
A
A
A
x
1
cos 3
2 2
π
+ =
÷
⇔
xcos 3 cos
2 3
π π
+ =
÷
x k
x k
3 2
2 3
3 2
2 3
π π
π
π π
π
+ = +
⇔
+ = − +
x k
x k
2
18 3
5 2
18 3
π π
π π
= − +
⇔
= − +
]^F="
x k
x k
2
18 3
5 2
18 3
π π
π π
= − +
= − +
A
A
A
A
A
x x3 cos2 sin2 2+ =
⇔
xsin 2 1
6
π
+ =
÷
⇔
x k2 2
6 2
π π
π
+ = +
⇔
x k
6
π
π
= +
A
A
x xtan 3cot 2 0
− + =
\_'+="
.
x
x
≠
≠
x x
x x k
k Z
x x k
2
tan 2tan 3 0
tan 1
( )
4
tan 3
π
π
α π
⇔ + − =
= ⇔ = +
⇔ ∈
= − ⇔ = +
A
A
A
S
B!*2R'
+`(
a
k
k k
C x
x
6
12
3
−
÷
≤+≤b
a
k k k k k k k
C x x C x
6 6 6 2 6
12 12
3 . . 3 .
− − + − −
=
\/ !*+,-xAkUba⇔kaS
]^F !*+,-x"
7
a
C
3 3
6
.3
a7
A
A
A
7
8474 3
C
4
9
4
8474 53
C
4
5
4
c '/4%@74 5"
C
C
4
5
4
9
5
126
=
A
A
A
A
7 c '/3>A4 "
C C C C C
C
2 2 3 1 4
4 5 4 5 4
4
9
9
14
+ +
=
B/'BCD6B8E
]CDPP8EdBCD
B8EaBPPCD
A
C0H
CD8EaCH
CHe8E*fGC0H
B8Eaf0
f0eBE*MB'FC0HeBE*M
A
A
A
0NPPC8C8CD8E
B'F0NPPCD8E
A
A
b
(3
u u q
3
4 1
=
q 3 =
u q
S
q
10
1
10
( 1)
1
=
S
10
10
3 1 59048= =
A
A
A
u u
u u
1 5
3 3
7
9
+ =
+ =
u d
u d
1
1
2 4 7
2 5 9
+ =
+ =
u
d
1
1
2
2
=
=
]^F !19"
1 3 7 11 15
; ; ; ;
2 2 2 2 2
A
A
A
b
(g'V!QI/DJDZ
Eh6.413"
x x
y y
' 3
' 2
= =
= =
]^F0ZSTUA
Ag'V!?-W:/CJ/CZ
\
V
R'C66',3:
V
"7?`SF`a
E.
A
d8aUb
d A
1
12 66
( ; )
25 25
=
B'FCZ
99 182
;
25 25
ữ
A
A
A
A
A
A
)
x x
x x
x x
x x
x x x x x
x k k Z
l l
ủk : cos4 .cos 0
sin4 .sin
tan4 .tan 1 1 0
cos4 .cos
cos4 .cos sin4 .sin 0 cos3 0
,( )
6 3
so saựnh ủieu kieọn, keỏt luaọn :
5
x ; x (l )
6 6
= + =
+ = =
= +
= + = +
A
A
A
A
A
A
)
F
F
x ax by
M x y M x y
y cx dy
x ax by
N x y N x y
y cx dy
1 1 1
1 1 1 1
1 1 1
'
( ; ) '( '; ')
'
'
( ; ) '( '; ')
'
= +
= +
= +
= +
A
A
A
A
S
MN x x y y
M N x x y y
x x a c y y b d x x y y ab cd
x x y y MN
2 2
1 1
2 2
1 1
2 2 2 2 2 2
1 1 1 1
2 2
1 1
( ) ( )
' ' ( ' ') ( ' ')
( ) (. ) ( ) .( ) 2( )( )( )
( ) ( ) .
= − + −
= − + −
= − + + − + + − − +
= − + − =
A
A
A
Ma trận đề
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