SỞGD&ĐTHÀNỘI ĐỀTHIGIỮAHỌCKÌ1NĂMHỌC2015-2016 ...

VnDoc - Ti t?i liu, vn bn ph?p lut, biu mu min ph?

S GD&T H? NI

THI GIA HC K? 1 NM HC 2015 - 2016

TRNG THPT NGC TO

M?N: TO?N I S - LP 11

Thi gian l?m b?i: 45 ph?t

s 1

B?i 1 (5,0 im): Gii c?c phng tr?nh lng gi?c sau

1)

2sin

x

4

3 0

2) 2sin2 x 5sin x 2 0 3) sin 3x sin 5x

3

5

B?i 2 (3,0 im)

1) Vit khai trin theo c?ng thc nh thc Niu-tn: 2x y6

2) T?m tng c?c h s trong khai trin

2 xn

bit n tha m?n

4C2n

288

A

2 2

n

B?i 3 (2,0 im)

T c?c ch s 0, 1, 2, 3, 4, 5, 6 ta lp c?c s t nhi?n gm by ch s kh?c nhau. Hi:

1) C? tt c bao nhi?u s?

2) C? bao nhi?u s b? hn 4232000?

--------Ht-------

VnDoc - Ti t?i liu, vn bn ph?p lut, biu mu min ph?

S GD&T H? NI

THI GIA HC K? 1 NM HC 2015 - 2016

TRNG THPT NGC TO

M?N: TO?N I S - LP 11

Thi gian l?m b?i: 45 ph?t

s 2

B?i 1 (5,0 im): Gii c?c phng tr?nh lng gi?c sau

1)

2

cos

x

6

2 0

2) 3cos2 x 10cos x 3 0 3) cos3x cos5x

3

5

B?i 2 (3,0 im)

1) Vit khai trin theo c?ng thc nh thc Niu-tn: x 3y6

2) T?m tng c?c h s trong khai trin

3 xn

bit n tha m?n

C22n

A

2 n

121 .

B?i 3 (2,0 im)

T c?c ch s 0, 1, 2, 3, 4, 5, 6 ta lp c?c s t nhi?n gm by ch s kh?c nhau. Hi:

1) C? tt c bao nhi?u s?

2) C? bao nhi?u s b? hn 4323000?

-------Ht-------

VnDoc - Ti t?i liu, vn bn ph?p lut, biu mu min ph?

S GD&T H? NI TRNG THPT NGC TO

?P ?N THI GIA HC K? 1 NM HC 2015 - 2016

M?N: TO?N I S - LP 11

C?u

Li gii 1

2

sin

x

4

3 0

sin

x

4

3 2

1.1

x x

4 4

k2 3 2 k2 3

;

k

x

x

k2 12 k2 12

;

k

sin x 2

2

sin 2

x

5

sin

x

2

0

sin

x

1 2

1.2

sin x 1 sin

2

6

x

x

k2 6 5 k2 6

;

k

sin5x sinx 4x sin xcos 4x cos xsin 4x

1.3 sin x cos 4x 4sin x cos2 x cos 2x

sin x 4cos2 2x 2cos 2x 1

Li gii 2

2

cos

x

6

2 0

cos

x

6

2 2

x x

6 6

k2 4 k2 4

;

k

x x

12 12

k2 k2

;

k

3 cos2 x 10 cos x 3 0

cos x 3

cos

x

1 3

cos x 1 3

x

arccos

1 3

k2

;k

x

arccos

1 3

k2

cos5x cosx4x cosxcos4xsinxsin4x

cosxcos4x4sin2 xcosxcos2x

cosx 4cos2 2x2cos2x1

im 1,0

0,5 0,5 1,0 0,5 0,5 0,25

VnDoc - Ti t?i liu, vn bn ph?p lut, biu mu min ph?

* 5sin3x3sin5x

*5cos3x3cos5x

5 3sinx4sin3 x 3sinx 4cos2 2x2cos2x1 5 4cos3x3cosx 3cosx 4cos22x2cos2x1 0,25

5sinx12cos2x 3sinx 4cos2 2x2cos2x1 5cosx2cos2x13cosx 4cos22x2cos2x1

sin x 0

cos x 0

51 2cos 2x 3 4cos2 2x 2cos 2x 1 52cos2x1 3 4cos2 2x2cos2x1 0,25

x k; k 12 cos2 2x 4 cos 2x 8 0

x / 2 k; k 12cos2 2x16cos2x2 0

x k; ccooss22xx

1k23xxxkm;arckcmos223

nn

cxos2x/246k1;0kxxka;rcckos24610m;m

0,25

?ng c?ng thc khai trin 2.1

T?nh c?c s hng

?ng c?ng thc khai trin

0,5

T?nh c?c s hng

0,5

4C2n 288 A22n dk : n 2, n C22n A2n +121 dk : n 2, n

0,25

4

n

n!

2!2!

288

2n ! 2n 2

!

2n ! 2n 2 ! 2

!

n

n!

2

!

121

4nnn12n!22!

288

2n 2n 1 2n 2! 2n 2!

2n2n2n122!n22! nnn12n!2!121

0,25

2n n 1 288 2n 2n 1

n 2n 1 n n 1 121

0,25

2.2

n2

144

n n

12

12 L

n2

121

n n

11

11 L

0,25

Vi n = 12 c?

12

2 x 12 C1k2 212k x k k0

Vi x = 1 ta c?

Vi n = 11 c?

11

3 x 11

C1k1311k x k

k0

0,25

Vi x = 1 ta c?

0,25

VnDoc - Ti t?i liu, vn bn ph?p lut, biu mu min ph?

12

2 1 12

C1k2212k 1 k

k0

11

3 1 11

C1k1311k 1 k

k0

12

1

C1k2 212k 1 k

11

211

C1k1311k 1 k

k0

k0

Vy tng c?c h s trong khai trin l?: Vy tng c?c h s trong khai trin 0,5

S=1.

l?: S = 211 2048

S t nhi?n c? dng a1a2a3a4a5a6a7

S t nhi?n c? dng a1a2a3a4a5a6a7

0,5

+ C? 6 c?ch chn a1 (v? a1 kh?c 0); + C? 6 c?ch chn a1 (v? a1 kh?c 0)

+ C?

A66 c?ch chn b (a2, a3, a4, a5,

+ C?

A

6 6

c?ch

chn

b

(a2,

a3,

a4,

3.1

0,25

a6, a7).

a5, a6, a7).

Vy

c?

tt

c

6.

A

6 6

=

4320

s

tha

Vy

c?

tt

c

6.

A

6 6

=

4320

s

tha

0,25

m?n.

m?n.

S t nhi?n c? dng a1a2a3a4a5a6a7

S t nhi?n c? dng a1a2a3a4a5a6a7

X?t c?c trng hp:

X?t c?c trng hp:

+ a1 l? 1, 2 hoc 3 th? c? 3 c?ch chn + a1 l? 1, 2 hoc 3 th? c? 3 c?ch

0,25

a1. Khi ? c?

A

6 6

c?ch

chn

b

(a2,

a3,

chn a1. Khi ? c?

A

6 6

c?ch

chn

a4,

a5,

a6,

a7)

c?

3.

A

6 6

c?ch chn.

b

(a2,

a3,

a4,

a5,

a6,

a7)

c?

3.

A

6 6

c?ch chn.

+ a1 = 4 v? a2 l? 0 hoc 1 th? c? 2 c?ch + a1 = 4 v? a2 l? 0, 1 hoc 2 th? c? 3

3.2 chn cp (a1, a2). Khi ? c? A55 c?ch c?ch chn cp (a1, a2). Khi ? c?

chn b (a3, a4, a5, a6, a7) c? 2. A55

A

5 5

c?ch chn b (a3, a4, a5, a6, a7)

0,25

c?ch chn.

c?

3.

A

5 5

c?ch chn.

+ a1 = 4, a2 = 2 v? a3 l? 0 hoc 1 th? c? + a1 = 4, a2 = 3 v? a3 l? 0 hoc 1 th?

2 c?ch chn b (a1, a2, a3). Khi ? c? c? 2 c?ch chn b (a1, a2, a3). Khi

A

4 4

c?ch

chn

b

(a4,

a5,

a6,

a7)

c?

?

c?

A

4 4

c?ch

chn

b

(a4,

a5,

a6,

a7)

0,25

2.

A

4 4

c?ch

chn.

c? 2.

A

4 4

c?ch

chn.

+ a1 = 4, a2 = 2, a3 = 3 v? a4 l? 0 hoc + a1 = 4, a2 = 3, a3 = 2 v? a4 l? 0 0,25

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