De thi tuyen sinh lop 10 toan hoc chuyen

DAI HOC TAN TAO
TRU'ONG THPT NANG KIIIEU
---*--IDE CHiNH THirC

Kil THI TUYEN SINH LOP 10 NAM HOC 2015-2016
MON THI: TOAN HOC (CHUYEN)
Ngay thi: 05/06/2015
ThZri gian lam bai: 150 phut

Cau 1. (1,25 diem) Cho cac bieu thirc:
a3 +1
A = a2
-1

a2-1
a+1'

B=

2a2+7a+3

2a2-a-1

a) Rut gon cac bieu thirc A va B.
b) Tim tat ca cac gia tri nguyen cila a 6 bieu thirc C = A + B la so nguyen.
Cau 2. (1,5 diem) Trong N true toa do vuong g6c Oxy, cho throng thing
d: y = (m + 2)x + 3

(m # —2).

Goi A, B lin luol là giao diem dm d viii true hoanh va true tung.

a

a) Tim m dien tich tam gide OAB bang 4.
b) Xac dinh gia tri dm m de khoang each ter gOc tea de den clueing thing d bang 2.
Cau 3. (1,75 diem) Giai phtrung trinh va N phucmg trinh sau:
a) (x + 1)(2x + 3)(4x + 5)2 = !

b)

(x2 + y2 = 13
txy — x — y = 1

Can 4. (2,5 diem) Cho tam gide ABC c6 ba goc nhon not tip trong duZyng tron (0; R). Ba
duemg cao AD, BE, CF cat nhau tai H. Goi K la trung diem cila BC, AM la dual-1g kinh cila
dtrong ton (0).
a)
b)
c)
d)

Chimg minh ba diem H, K, M thing hang.
ChUng minh ABC = AEF.
Chimg minh OA vuong goc voi EF.
Goi p la nira chu vi dm tam giac DEF. ChUng minh: SABc = Rp.

Cau 5. (1,0 diem) Tim cac so tv nhien x, y thOa man:
x2 + y 2 =x+y+8
Cau 6. (1,0 diem) Cho hai s6 thvc &rang a va b thoa: ab = 1. Tim gia tri nho nhAt dm bieu
thuc:

P=

a3
1+ b

+

b3
1+ a

Cau 7. (1,0 diem) Cho tam gide ABC co trong tam G. MOt dtrong thing d di qua G cat cac
doan thing AB, AC lin luert tai M va N. Chung minh:
SABC

<9

SAMN

4

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