Kì thi học kì II năm học 2015 - 2016 môn thi: Toán lớp 8 thời gian: 90 phút

Trường THCS Hũa Bỡnh
Họ và tờn:..
Lớp 8A
Kè THI HỌC Kè II NĂM HỌC 2015-2016
MễN THI: TOÁN LỚP 8
THỜI GIAN: 90 Phỳt 
ĐỀ BÀI
Cõu 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.
Cõu 2: (1điểm)
     a. Biểu diễn tập nghiệm của mỗi bất phương trỡnh sau trờn trục số: x ≥ -1 ;  x < 3.
     b. Cho a < b, so sỏnh  – 3a +1 với – 3b + 1.
Cõu 3: (1,5 điểm) Một người đi xe đạp từ A đến B với vận tốc trung bỡnh 15km/h. Lỳc về, người đú chỉ đi với vận tốc trung bỡnh 12km/h, nờn thời gian về nhiều hơn thời gian đi là 45 phỳt. Tớnh độ dài quóng đường AB (bằng kilụmet).
Cõu 4: (1,0 điểm) Cho tam giỏc ABC cú AD là phõn giỏc trong của gúc A. Tỡm x trong hỡnh vẽ sau với độ dài cho sẵn trong hỡnh.  
 Cõu 5: (1,5 điểm)   a. Viết cụng thức tớnh thể tớch của hỡnh hộp chữ nhật.
   b. Áp dụng: Tớnh thể tớch của hỡnh hộp chữ nhật với AA’ = 5cm, AB = 3cm, AD = 4cm (hỡnh vẽ trờn).                                               
Cõu 6:(2,5 điểm) Cho tam giỏc ABC vuụng tại A cú 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) Tớnh độ dài cỏc cạnh BC, AH. 
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ĐỀ BÀI
Cõu 1: (3 điểm) Giải cỏc phương trỡnh sau: 
a) 2x - 10 = 0	
b) 3x + 2(x + 1) = 6x - 7	
c) 	
Cõu 2: (1,5 điểm) 
Một số tự nhiờn cú hai chữ số với tổng cỏc chữ số bằng 14. Nếu viết ngược lại thỡ được số tự nhiờn cú hai chữ số, lớn hơn số ban đầu 18 đơn vị. Tỡm số tự nhiờn ban đầu. 
Cõu 3: (1,5 điểm) 
a) Giải bất phương trỡnh 7x + 4 ≥ 5x - 8 và biểu diễn tập hợp nghiệm trờn trục số.
b) Chứng minh rằng nếu: a + b = 1 thỡ a2 + b2 
Cõu 4: (1 điểm) 
Cho hỡnh lăng trụ đứng ABC.A’B’C’ cú chiều cao AA’ = 6cm, đỏy là tam giỏc vuụng cú hai cạnh gúc vuụng AB = 4cm và AC = 5cm. Tớnh thể tớch của hỡnh lăng trụ.
Cõu 5: (3 điểm) 
Cho tam giỏc ABC vuụng ở A. Vẽ đường thẳng (d) đi qua A và song song với đường thẳng BC, BH vuụng gúc với (d) tại H .
a) Chứng minh ∆ABC ∆HAB.
b) Gọi K là hỡnh chiếu của C trờn (d). Chứng minh AH.AK = BH.CK
c) Gọi M là giao điểm của hai đoạn thẳng AB và HC. Tớnh độ dài đoạn thẳng HA và diện tớch ∆MBC, khi AB = 3cm, AC = 4cm, BC = 5cm.
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