Đề thi học kì 1 môn Toán lớp 10 trường THPT Nguyễn Huệ, Phú Yên năm học 2014 - 2015

/

Trueng THPT
Nglly~n Hll~
TB toan

DE THI

HQC KY I
Mon: Toan-KhBi 10 -Nam hoc 2014-2015
Thai gian: 90 phut

Call 1(1.5diim) Giai cac phuong trinh sau:
1. 12x + 31 = Ix - 21 ;
2.

-V'X2

+ 1 = x2

-

1 (HD: d~t fin phu).

Cau2(1.5diim)

Cho phuong trinh sau:
x - 3x + 2m - 1 = 0 (1)
1. Tim t~t ca cac gia tri cua tham s6 m dS phuong trinh (1)
co nghiem.
2. Tim t~t ca cac gia tri cua tham s6 m dS plnrong trinh (1)

.~ XlIX
co, l'rai ng 1uem
sao c110 A =X12 + Xl Z - Xl'2 Xz2 d at
Z
2

gia tri 16n nh~t.
Call 3(1.5diim) Giai he phuong trinh sau:
fX+ y -xy = 1
2
+ ,2 + 5(x + Y)
Call 4(1diem) Cho h~ plnrong trinh sau:

tx

.mx
{

+ 4y

x +my

=2
=2

=

6

+ In

..

Tim t~t ca cac gia tri cua tham s6 m dS h~ phuong trinh co
vo s6 nghiem.
Call 5(2didm) Trong m~t phang toa d9 Oxy cho A(-1;2), B(4;3)
1. Tim toa d9 diSm M thoa h~ thirc 3AM - 2Bf,l

=0.

2. Tim tren true Ox diem N sao cho tam giac NAB vucng tai
N.

Call 6(2didm) Cho tam giac ABC co

A

=

1200, AB=7 va AC=4.

G9i I la Him dirong tron n9i tiep cua tam giac ABC.
1. Tinh tich vo huong AB .AC;
2. Tinh d9 dai canh BC va ban kinh duong tron ngoai ti~p
tam giac IBC.
Call 7(O.5didm) Chox, y» Ovax+y=3. Chirng minh : X.y2 < 4.

I


I Call

Loi giai

i

1)12x+31= Ix_21~[2X+3=X-2
.2x

Can
1

1.5i1

1.5i1

+ 1 = x2

2) .Jx2

- 1

PT dacho c 0 dang:
V6i

Can
2

~.[X=-5
x

t

=

2 ¢=} ..,/x2

3x + 2m-l

-

.
0.75

./£1. + 1 = x2

+1-

¢::> ••

e· ., t -2=0~

+ 1=2~

[t _ -1

t-2
= 3 ¢:::> x =

x2

B~t t=../x1. + 1, BK t~ 0

2.

0.25

(lo'iti)

±-/3.

.

V~y PT co hai nghiem x

=±-/3

xrx~

(xl

f

+ sex + y) = 6

¢:::>

x

l(x

+y

+ y)2

0.25

+ 5(x + y} = 6

- 2xy

+ 5S = 6

+ V6i S=I va P=O: x, y Ia hai nghiem cua PT
Do do

0.25

- xy = 1.

B-tS
+ 'P
H"tr'th'nhfS-P=1.
~ =x y va =xy. v (J a l52 _ 2P

1.5i1

1

-x;' x;

xy = 1.

+:v2

0.5

= 0 (1)

1) Phuong trinh (1) co nghiem ¢::} ts> 0 ~ :13 - 8m > 0 ¢::} m ~ 13/8
2) Dk Phuong trinh (1) co nghiem: 1'n < 13:/8
A=x~ +X~ = (Xl + x2? - 2X1X2
= -4m2 + 10
Vi A~10 nen A Ian nhat khi m=O (thoa dk).

fX + y -

Can
3

= -1/3

.

V~y PT co hai nghi~m [; ~ =~/3

•

x2

+ 3 = -x + 2

X2 - X

~

=0

0.5

{P=S-1
S2 _ 3S ¢::} ~

~

0.5
4 =0

~

(x = 0
(x =:1
br = 1ho~c 1y = 0

+ 4X -

+ V6i S=-4 va P=-5: x, y la hai nghiem cua PT X2

5 = 0 ~ f'X :=-5

0.5

. X=l

Do do x = -15hoac f x = 1.-(y =
. ty =-::.
. Vay he co c nghiem CO;1),(1;O}.(-S;1),(1~-5).
f.

r:

(Neil thiiu kit luiin -0,25)

+ 4Y. = 2 + m

Can

4
Iii

x+m:y=2
+ D = m2 - 4''ill:.
D

+ H~ co vo

=

m - 2'':Y D

s6 nghiem

khi D

= m2

= DX'

=

2m - 8

0.5

o; = 0 ¢:? m=2

0.5

T'

A( -1; 2),B( 4; 3)
•

1) G01 M(x;y):

Can

--

----;t

{3(X

-')

3AM - 2BM = 0

¢::>

V~y M(-II ;0).
2) GOi N(x;O)E Ox. NA = (-1 - x; 2);

5

!J.NABvllong tai N khi

2i1

NA.NB

NB = (4 -

= 0 ¢:} (-1¢:>

A
Can
6

= 1200 , AB=7

+ 1) -

2(x - 4)

=

0

3(y _ 2) _ 2(y- 3) = 0

x2

-

¢:}

fx = -11
ly = 0

x; 3)

x)(4 - x)
3x

+2=0

.

1
0.5

+ 6= 0
~ x = 1 Vx

0.5

=2

va AC=4

1) "AlrifC = AB.AC.cosA =

4.7.( -D = -14

1


ea

2) *Tinh dQ dai canh BC:
BC2 = AB2 +AC2 -:-2AB_AC .cosA' = 93.
V~y BC = -J93

\.1

-:.

i;!!,

,* Tinhban

kinh duong tron ngoai !i~p }am giacIlst,"

', '; Trong MBC : fj
r

J '\

'/j!i,:·l .·

. Trong

!1lBC :

+ C = 60° =?!!. +£

f = 1800 _.~ +2;)

2

= 30° .

0.25'

1500C Do I Ia tam dirong tron nQi ti€p

i

,~!

,: ';"":" , : MBC)

~:'

0.5

1 7.'

'

Khi d6 2R fBC=

;.

~c~::::}R!Be = 4'93

sm.1

Chox, y> O va x+y=S. Clnrng minh : X.y2
Can
7

O.5d

Ta c6 :

3 =x
x-y2
¢::} -

+. y

=x

1
1
+ -y
+
y >3
2
2

< 1 ¢:::} XJ12 < 4

0.25

~
~XY'l

4

.. -"4.

0.5