ĐỀ THI HỌC KÌ II

Trường THCS Hòa Bình
Họ và tên:………………………..
Lớp 8A

KÌ THI HỌC KÌ II NĂM HỌC 2015-2016
MÔN THI: TOÁN LỚP 8
THỜI GIAN: 90 Phút

ĐỀ BÀI
Câu 1: (2,5 điểm) Cho biểu thức :

a) Rút gọn A. b) Tính giá trị của biểu thức A tại x thoả mãn: 2x2 + x = 0
c) Tìm x để A=
d) Tìm x nguyên để A nguyên dương.
Câu 2: (1điểm)
     a. Biểu diễn tập nghiệm của mỗi bất phương trình sau trên trục số: x ≥ -1 ;  x < 3.
     b. Cho a < b, so sánh  – 3a +1 với – 3b + 1.
Câu 3: (1,5 điểm) Một người đi xe đạp từ A đến B với vận tốc trung bình 15km/h. Lúc về, người đó chỉ đi với vận tốc trung bình 12km/h, nên thời gian về nhiều hơn thời gian đi là 45 phút. Tính độ dài quãng đường AB (bằng kilômet).
Câu 4: (1,0 điểm) Cho tam giác ABC có AD là phân giác trong của góc A. Tìm x trong hình vẽ sau với độ dài cho sẵn trong hình.  



 Câu 5: (1,5 điểm)   a. Viết công thức tính thể tích của hình hộp chữ nhật.
   b. Áp dụng: Tính thể tích của hình hộp chữ nhật với AA’ = 5cm, AB = 3cm, AD = 4cm (hình vẽ trên).                                               
Câu 6:(2,5 điểm) Cho tam giác ABC vuông tại A có AB = 6cm; AC = 8cm. Kẻ đường cao AH.
a) Chứng minh: ∆ABC và ∆HBA đồng dạng với nhau.
            b) Chứng minh: AH2 = HB.HC.
            c) Tính độ dài các cạnh BC, AH. 
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ĐỀ BÀI
Câu 1: (3 điểm) Giải các phương trình sau:
a) 2x - 10 = 0
b) 3x + 2(x + 1) = 6x - 7
c)


Câu 2: (1,5 điểm)
Một số tự nhiên có hai chữ số với tổng các chữ số bằng 14. Nếu viết ngược lại thì được số tự nhiên có hai chữ số, lớn hơn số ban đầu 18 đơn vị. Tìm số tự nhiên ban đầu.

Câu 3: (1,5 điểm)
a) Giải bất phương trình 7x + 4 ≥ 5x - 8 và biểu diễn tập hợp nghiệm trên trục số.
b) Chứng minh rằng nếu: a + b = 1 thì a2 + b2


Câu 4: (1 điểm)
Cho hình lăng trụ đứng ABC.A’B’C’ có chiều cao AA’ = 6cm, đáy là tam giác vuông có hai cạnh góc vuông AB = 4cm và AC = 5cm. Tính thể tích của hình lăng trụ.
Câu 5: (3 điểm)
Cho tam giác ABC vuông ở A. Vẽ đường thẳng (d) đi qua A và song song với đường thẳng BC, BH vuông góc với (d) tại H .
a) Chứng minh ∆ABC ∆HAB.
b) Gọi K là hình chiếu của C trên (d). Chứng minh AH.AK = BH.CK
c) Gọi M là giao điểm của hai đoạn thẳng AB và HC. Tính độ dài đoạn thẳng HA và diện tích ∆MBC, khi AB = 3cm, AC = 4cm, BC = 5cm.

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DẪN CHẤM
Câu
Tóm tắt giải
Điểm

Câu 1: (3điểm)


a) Giải phương trình.
2x - 10 = 0 <=> 2x = 10 <=> x = 5
=> Tập nghiệm của phương trình là {5}

0,75
0,25


b) 3x + 2(x + 1) = 6x - 7 <=> 3x + 2x + 2 - 6x + 7 = 0
<=> - x + 5 = 0 <=> - x = - 5 <=> x = 5
0,5
0,5


c)
ĐK: x ≠ -1 và x ≠ 4
với x ≠ -1 và x ≠ 4 thì

=> 5(x - 4) + 2x = 2(x + 1)
<=> 5x = 22 <=> x =

Tập hợp nghiệm của phương trình là {
}
0,25


0,25

0,25
0,25

Câu 2: (1,5điểm)

Gọi chữ số hàng chục của số tự nhiên ban đầu là: a. ( a =
)
Khi đó:
+ Chữ số hàng đơn vị của số tự nhiên ban đầu là: 14 - a