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KHO ST CHT LNG MN TON LP 11

Thi gian lm bi 180 pht (khng k thi gian pht )


Cu I ( 2 im)
Gii cc phng trnh sau:
1.

sin 2 x + sin 4 x = sin 6 x

2.

( 1 t anx ) ( 1 + sin 2 x ) = 1 + t anx


1
3

= 4cos x +
sinx cosx
3

3.

Cu II (1 im)
1. Tnh gii hn: lim
x1

2. Cho hm s y =

x+3 3 x+7
x2 1

1 2x
, vit phng trnh tip tuyn ca th hm s bit tip tuyn i qua
x +1

im A(0; -2).
Cu III ( 3 im)
1. Gii bt phng trnh:

1 2
6
A2 x Ax2 Cx3 + 10 .
2
x

0
1
2
n
2. Tnh tng: S = ( n + 1) Cn + nCn + ( n 1) Cn + ... + Cn .

3. T cc ch s { 1; 2; 3; 4; 5; 6 } lp cc s c 4 ch s khc nhau, ly ngu nhin mt s


trong cc s va lp c. Tnh xc sut s ly c l s chia ht cho 5.
n

4. Khai trin biu thc 1 + x 4 + 2 thnh a thc, tm h s ca s hng cha x 6 bit n tha
x

3
2
mn h thc: Cn1 Cn1

2 2
An2
3

Cu IV (4 im)
Cho hnh chp S.ABCD c y ABCD l hnh vung tm O, cnh bng a, SA = a 3 v
SA ( ABCD ) .
1. Chng minh: ( SBC ) ( SAB )
2. Mi im M thuc mt phng (SAC) u tha mn: MB = MD.
3. Tnh khong cch t im A n mt phng (SBC)
4. Dng v tnh di on vung gc chung ca hai hai ng thng SO v BC.
....... HT .......
H v tn th sinh: ........................................................................................

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