The document is a math exam for 8th grade students containing 5 questions. Question 1 has 4 parts involving solving equations. Question 2 involves solving and graphing an inequality. Question 3 requires setting up and solving an equation from a word problem about travel times and distances. Question 4 is a geometry word problem about finding the height of a building based on shadow lengths. Question 5 has 3 parts involving geometry proofs about triangles. The exam is 90 minutes long and students may not use outside materials.
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Vista's Learning is one of the leading e-learning platforms shaping the future of the country's education sector.
With the latest AR technology in the web application and personalized methods of learning concepts, Vista's Learning offers a wide variety of features - live classes, pre-recorded classes covering state boards and CBSE, one-on-one coaching, social media and many more. Classes are provided for K-12 and in different regional languages to understand the concepts even better. Languages include - English, Hindi, Kannada, Telugu, Malayalam and Tamil.
https://v-learning.in/live-course/1879/kseeb-cbse-maths-sample-paper-term-1-vistas-learning
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Đề Thi HK2 Toán 8 - THCS Diên Hồng
1. SỞ GIÁO DỤC VÀ ĐÀO TẠO
TP. HỒ CHÍ MINH
TRƯỜNG THCS-THPT DIÊN HỒNG
KIỂM TRA HỌC KỲ II – NĂM HỌC 2019 – 2020
MÔN TOÁN – LỚP 8
Thời gian làm bài: 90phút (không kể thời gian phát đề)
ĐỀ CHÍNH THỨC
(Đề thi gồm01 trang)
Câu 1: Giải các phương trình sau. ( 3,5đ )
a) 15
6
6
15
x
x
b)
2𝑥 − 5
6
+ 1 =
3 − 𝑥
4
c) 0
25
1
2
x
d)
𝑥
𝑥 − 3
−
5
𝑥 + 3
=
𝑥2
+ 9
𝑥2 − 9
Câu 2: Giải bất phương trình sau và biểu diễn tập nghiệm trên trục số. ( 1,5đ )
3
3
5
4
1
x
x
x
Câu 3 : Giải bài toán sau bằng cách lập phương trình .( 1,0đ )
Một ô tô đi từ A đến B với vận tốc 42km/h, rồi đi từ B về A với vận tốc lớn hơn vận tốc lúc đi là
6km/h. Tính quãng đường AB, biết thời gian cả đi và về mất 5 giờ.
Câu 4 : (1,0đ)
Một cột đèn cao 7m có bóng trên mặt đất 4m. Cùng
thời điểm đó, một tòa nhà cao tầng có bóng trên mặt đất là
60m. Hãy cho biết tòa nhà đó có bao nhiêu tầng (không kể
tầng hầm), biết rằng mỗi tầng cao 3m.
(Học sinh nhìn vào hình để làm bài không phải vẽ hình lại )
Câu 5 : (3,0đ). Cho tam giác nhọn ABC, vẽ các đường cao BD, CE
a) Chứng minh: ADB ∽ AEC và AE. AB = AD. AC
b) Vẽ EF vuông góc với AC tại F. Chứng minh rằng: AE. DF = AF. BE
c) Gọi M, N lần lượt là trung điểm của BD và CE. Chứng minh rằng hai góc BAC và MAN
có chung tia phân giác.
----------- HẾT -----------
Học sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm.
Họ và tên học sinh:……………..………………………………………………………………………
4 60
7
E
B
D A C
F
2. SỞ GD VÀ ĐT TP. HỒ CHÍ MINH
TRƯỜNG THCS – THPT DIÊN HỒNG
KIỂM TRA HỌC KÌ II
NĂM HỌC 2019 – 2020
Môn: Toán – Lớp: 8
CÂU NỘI DUNG TRẢ LỜI
ĐIỂM TỪNG
PHẦN
Câu 1
a
(0,75đ)
15
6
6
15
x
x
9
9
x
1
x
Vậy S = {- 1}
(0,5đ)
(0,25đ)
b
(1,0đ) 1 +
2𝑥 − 5
6
=
3 − 𝑥
4
<=> 12 + 2(2𝑥 − 5) = 3(3 − 𝑥)
<=> 12 + 4𝑥 − 10 = 9 − 3𝑥
<=> 7𝑥 = 7
<=> 𝑥 = 1
Vậy 𝑆 = {1}
(0,5đ)
(0,25đ)
(0,25đ)
c
(0,75đ)
0
25
1
2
x
( x + 1 + 5)( x + 1 – 5) = 0
( x + 6)( x – 4) = 0
x + 6 = 0 hoặc x – 4 = 0
x = - 6 hoặc x = 4
Vậy S = {-6 ; 4}
(0,25đ)
(0,25đ)
(0,25đ)
d
(1,0đ) 9
9
3
5
3 2
2
x
x
x
x
x
ĐKXĐ: 3
x
)
3
)(
3
(
9
)
3
)(
3
(
)
3
(
5
)
3
( 2
x
x
x
x
x
x
x
x
x2 + 3x – 5x + 15 = x2 + 9
6
2
x
3
x (loại)
Vậy phương trình vô nghiệm.
(0,25đ)
(0,25đ)
(0,25đ)
(0,25đ)
Câu 2
3
3
5
4
1
x
x
x
15
3
5
15
15
)
4
(
3
15
x
x
x
15
10
19
3
x
x
34
7
x
(0,25đ)
(0,25đ)
HƯỚNG DẪN CHẤM
3. 7
34
x . Vậy
7
34
/ x
x
S
Biểu diễn tập nghiệm đúng
(0,25đ)
(0,25đ)
(0,5đ)
Câu 3
Gọi x (km) là quãng đường AB. (x > 0)
Thời gian ô tô đi từ A đến B là:
42
x
(h)
Thời gian ô tô đi từ B về A là:
48
6
42
x
x
(h)
Thời gian cả đi và về là 5 giờ, nên ta có PT: 5
48
42
x
x
Giải PT tìm được x = 112
Vậy quãng đường AB dài 112 km
(0,25đ)
(0,25đ)
(0,25đ)
(0,25đ)
Câu 4
ABC ∽ DEF (g.g)
4
60
7
AB
DF
AC
DE
AB
105
4
60
.
7
AB
Tòa nhà cao 105m
Số tầng của tòa nhà là: 105:3=35 (tầng)
(0,25đ)
(0,25đ)
(0,25đ)
(0,25đ)
Câu 5
a
(1,0đ)
C/m đúng ADB ∽ AEC (g.g)
Suy ra:
AC
AB
AE
AD
AE. AB = AD. AC
(0,75đ)
(0,25đ)
b
(1,0đ)
Ta có : EF AC, BD AC EF // BD
ABD có EF // BD :
DF
AF
BE
AE
AE. DF = AF. BE
(0,25đ)
(0,75đ)
c
(1,0đ)
Ta có :
CN
BM
CN
BM
CE
BD
AC
AB
2
2
Suy ra: ΔABM∽ ΔACN (c.g.c) 𝐵𝐴𝑀
̂ = 𝐶𝐴𝑁
̂
(0,25đ)
(0,25đ)
(0,25đ)
x
N
M
A
B C
D
E
F
4. Gọi Ax là tia phân giác của góc MAN𝑥𝐴𝑀
̂ = 𝑥𝐴𝑁
̂
Nên : 𝑥𝐴𝑀
̂ + 𝐵𝐴𝑀
̂ = 𝑥𝐴𝑁
̂ + 𝐶𝐴𝑁
̂ 𝑥𝐴𝐵
̂ = 𝑥𝐴𝐶
̂
Suy ra : Ax là tia phân giác của góc BAC.
(0,25đ)
HẾT
5. MA TRẬN ĐỀ KIỂM TRA HK2 TOÁN 8
Cấp độ
Tên chủ đề
Nhận biết Thông hiểu
Vận dụng
Tổng
Cấp độ thấp Cấp độ cao
Giải phương trình
Số câu:
Số điểm:
Tỉ lệ: %
2
2
20%
1
1
10%
1
1
10%
4
3,5
35%
Bất phương trình
Số câu
Số điểm:
Tỉ lệ: %
1
1,5
15%
1
1,5
15%
Giải bài toán bằng
cách lập phương
trình
Số câu:
Số điểm:
Tỉ lệ: %
1
1
10%
1
1
10%
Bài toán thực tế
1
1
10%
1
1
10%
Hình học
1
1
10%
1
1
10%
1
1
10%
3
3
30%
Tổng số câu:
Tổng số điểm:
Tỉ lệ: 100%
1
1
10%
3
3
30%
4
5
50%
1
1
10%
9
10
100%