De thi HSG cuoi nam Toan 7

Trường THCS Bình Phú

BÀI THI HSG CẤP TRƯỜNG

SBD:……………………

MÔN: TOÁN 7

Họ và tên:………………

Thời gian: 120 phút

Điểm

Lời phê của thầy, cô giáo

§Ò bµi
Câu 1(3 điểm) : Tính giá trị biểu thức sau bằng cách hợp lý nhất :
−7 5 7 8
. − : +2
A=
12 8 12 19
1 0
3

2 1
−2
B = 2 + 3( ) − 1 + (−2) :  .(3) .18
2
2


2 2 2
1 1 1
− +
+ −
5 7 11
2 3 4
C=
+
3 3 3
−5 5 5
− +
− +
5 7 11
4 6 8
Câu 2 (4điểm): Tìm x , y , z biết:
3 7
2
a) − : x =
4 5
5
b) 2x = 3y = 5z và x + y – z = 95
c) 5x − 3 − x = 7
d) ( (x − 2)30 + (y + 3)50 ≤ 0
Câu 3 (1điểm): Chứng minh rằng :
A = 3n +3 − 22.3n + 2n +5 − 33.2n chia hết cho 23
Câu 4 (3điểm): Cho biểu thức :
15 − 2x
A=
6−x
1

a) Tìm x để A có giá trị bằng .
2
b) Tìm x∈ Z để A có giá trị lớn nhất và tìm giá trị lớn nhất đó.
Câu 5 (3điểm): Cho các đa thức:
1
3
3
P(x) = 5x 4 + x 3 − x 2 + 2x − x 4 − x 3 − 5x
4
4
4
1 3 3 2
2
4
4
Q(x) = − x + x − x + 2x −
2
4
7
2
R(x) = 4x − 9x − 13
a) Tính P(-1) , Q(2)
b)Tính P(x) + Q(x)
c)Tìm nghiệm của đa thức R(x)


Câu 6 (6điểm):
Cho ∆ABC cân tại A, Kẻ AD ⊥ BC tại D. G là trọng tâm của tam giác .Trên tia đối
của tia DG lấy điểm E sao cho DE = DG
a) Chứng minh rằng: BG = GC = CE = BE

b) Trên tia BG lấy điểm I sao cho GI = GB ; Trên tia CG lấy điểm H sao cho
GH = GC .CMR: ∆ABI = ∆ACH
AE
c) Nếu CG =
thì ∆ABC là tam giác gì ?
2
Bài làm
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