hinh ve

KIM TRA 1 TIT MễN: I S 11
Họ tên:
Lớp:
Điểm Lời phê của giáo viên
A/ PHN TRC NGHIM (3):
Gm 03 câu (Hãy khoanh tròn vào chữ cái đầu dòng phơng án đợc chọn):
Cõu 1 (0,5 ) Tp xỏc nh ca hm s: y =
1cos
sin
+
x
x
l:
a/ D = R. b/ D = R\
{ }
Zkk
+
;)12(

. c/ D = R\
{ }
Zkk

;2

. d/ D = R\

+ Zkk ;
2


Cõu 2(0,5 ): Trong cỏc khng nh sau, khng nh no sai:
a/ Hm s y = cos x l hm s chn b/ Hm s y = sin x l hm s chn
c/ Hm s y = tan x l hm s l d/ Hm s y = cot x l hm s l
Cõu 3(0,5 ) : Nghim ca phng trỡnh: sin 4x = 0 l: (vi k Z)
a/ x = k

b/ x = k
2

c/ x = k
3

d/ x = k
4

Cõu 4(0,5 ): phng trỡnh: cosx =(m + 1) cú nghim thỡ iu kin ca m l
a/ -1 m 1b/ - 1 m 0 c/ -2 m 0 d/ 0 m 2
Cõu 5(1,0 ): Phng trỡnh: tanx = cot2x cú nghim l (vi k Z)
a/
36

kx
+=
b/

kx
+=
2
c/


kx
+=
6
d/
3
2
6

kx
+=
B/ PHN T LUN: (7)
Cõu 1(1,5): Gii phng trỡnh: Sin
2
x 8sinxcosx + 7cos
2
x = 0
Cõu 2 (1,5): gii phng trỡnh: Sin
2
3x = 1- cos
2
x
Cõu 3 (2,5): Gii phng trỡnh:
0

2cossin
1cos22cos
=
+
+
xx
xx
Cõu 4(1,5 ): Tỡm giỏ tr ln nht ca hm s: y = 3sinx + 4 cosx 1. Xỏc nh cỏc giỏ tr ca
x hm s t giỏ tr ln nht ú.
Bài làm
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ĐÁP ÁN
A/ TRẮC NGHIỆM: (5điểm) (Mỗi câu đúng được tính 0,5đ)
Câu hỏi 1 2 4 5 6
Đáp án b b d c a
B/ TỰ LUẬN: (5 điểm)Câu 1:(1đ)
- Nhận xét: x =
π
π
k
+

2
không phải là nghiệm của pt (0.25)
- Đưa về pt: tan
2
x – 8tanx + 7 = 0 (0.25)
- Với tanx = 1 <=> x =
π
π
k
+
4
(k
∈
Z) (0.25)
tanx = 7 <=> x = arctan 7 + k
π
(0.25)
Câu 2: (0,75đ) pt <=> sin
2
3x = sin
2
x
<=> sin3x = sinx (1)
∨
sin 3x = - sinx (2) (0,25)
(1) <=> x = k
π
∨
x =
24

ππ
k
+
(0.25)
(2) <=> x = k
2
π
∨
x =
2
π
+ k
π
<=> x = k .
2
π
(k
∈
Z) (0.25)
Câu 3: (1.5đ)* Điều kiện: sinx + cosx -
2

≠
0
<=> sin(x +
4
π
)
≠
1 (0.25)

<=> x
≠

π
π
2
4
k
+
(0.25)
* pt <=> cos 2x -
2
cos x + 1 = 0
<=> cos x (2cosx -
2
) = 0 (0.25)
cos x = 0 <=> x =
π
π
k
+
2
(0.25)
Hoặc cos x =
2
2
<=> x =
π
π
2

4
k
+±
(0.25)
* Đối chiếu đk, chọn nghiệm: x =
π
π
2
2
k
+
, x = -
π
π
2
4
k
+
(0.25)
Câu 5: (0.75đ)
Biến đổi: y = 5(
5
4
sin.
5
3
+
x
.cosx) – 1 = 5sin (x +
α

) – 1 (với cos
α
=
5
3
; sin
α
=
5
4
) (0.25)
y
4
≤
=> GTLN của y là: 4 (0.25)
<=> sin (x +
α
) = 1
<=> x =
α
π
−
2
+ k2
π
(k
∈
Z) (0.25)