Kiểm tra học kỳ 2 toán 8

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. 
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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.

..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................HƯỚNG 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