de thi lai toan 11

Tinh goc gifra SC va mat phang (ABCD).[r]

S6'Giao due va Dao tao Tp.HCM

DE KIEM TRA L~I N.AM HQC 2011 - 2012

MON ToAN LOP 11

ThOi gian: 90 phut Cau 1: (2 diem)

Tim cac gici han sau:

) I 3 x -9

a

lm x +3 X2+2x- 15

b) limrx+3 -2

x +l X 2 -1

Can 2: (l diem)

Tim adS ham s6 sau lien tuc tai x =-1 :

{X 2 -x-2

a+1

khi x : t:-1 khi x =-1

Can 3: (2 diSm)

Tinh dao ham cua cac ham s6 sau:

a) y =(x 2 +x )(5 - 3x2) Can 4: (l diem)

Chirn minh r~n plurong trinh sau co itnhat ba nghiem: x 5 - x 3 - 2x -1 =0

b) y =xsin" x

Can 5: (l diem)

Cho ham s6 y =-2 x 3 + X2 + x-3 co d6 thi (C)

Vi~t phuong trinh ti~p tuyen cua (C) tai diSm co hoanh de>bang 1

Can 6: (3 diem)

Cho hinh chop S.ABCD co day ABCD la hinh vuong canh bang ava SA (ABCD) a) Chung minh BD Sc

b) Chung minh (SAB) 1(SBC) c) Cho SA= a:.Tinh goc gifra SCva mat phang (ABCD)

nET

CAU Y NQID UN G DI EM

x~3 x +5 8

x ~l x2 -1 x - e -l (x 2 -1)("/ x + 3 + 2)

x~- I

0,50

y = x SIn X=> Y = x 0SIn X + SIn X x

j (-2)=-2 1 , j(-1)= 1, j(0) = -1 , j(2 )= 19

=> f (x) =0 co it nhat 3 nghiern 0,25

=> y'(I) =-3

0,50

=> PTTT: y = -3x

I

I

I

0,25

I

; 1 ',- - - B

/ -, '

- 0

< ,

SA.1 (ABCD) => SA.1 BC (4) 0,25

aJ6

-AC aJi 3