PHÒNG GIÁO DỤC VÀ ĐÀO TẠO
ĐỀ KIỂM TRA CUỐI HỌC KÌ I
THIỆU HOÁ
NĂM HỌC 2021 - 2022
Môn: Toán – Lớp 7
Số báo danh: ………………
(Thời gian làm bài 90 phút)
Số phách
Trường:…………….…………….………Lớp…………… Giám thị số 1:………….....….…………….
Họ tên:………………………………………….............…….. Giám thị số 2:……………......…………….
----------------------Chủ tịch hội đồng chấm thi cắt phách theo đường kẻ này------------------------
Điểm của bài thi Số phách
Giám khảo số 1:…………….…………….
Bằng số Bằng chữ
Giám khảo số 2:…………………….…….
( Học sinh làm bài trực tiếp vào tờ đề thi này )
ĐỀ BÀI
Bài 1: (2 điểm). Thực hiện các phép tính sau:
 3 2 5  1 1 5
10 −27
a) b) − +::+ − +
.
   

32 4 3 11 4 3 11
   

1 3 7 1
c) ..+
3 5 5 3
Bài 2: (2 điểm). Tìm x biết:
32 12
a) −=x b) +=x
45 25
Câu 3: (1,5 điểm). Số đo ba góc của một tam giác tỉ lệ với 4;6;8. Tính số đo mỗi góc
của tam giác đó?
Câu 4: (3,5 điểm). Cho tam giác ABC vuông tại A, kẻ AD vuông góc với BC (D thuộc
BC). Trên đường thẳng vuông góc với BC tại C lấy điểm E sao cho CE = AD (E và A
thuộc hai mặt khác phía bờ chứa cạnh DC). Chứng minh rằng:
a) ADC=ECD
b) DE⊥AB
c) CED=ABC
x y z t
Bài 5: (1,0 điểm). Cho dãy tỉ số bằng nhau: = = =
y+ z+t z+t+ x t+ x+ y x+ y+ z
x+ y y+ z z+t t+ x
Chứng minh rằng: P= = + + có giá trị nguyên.
z+t t+ x x+ y y+ z
BÀI LÀM
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Học sinh không viết vào phần gạch chéo này
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PHÒNG GD&ĐT THIỆU HOÁ ĐÁP ÁN ĐỀ KHẢO SÁT CL CUỐI HỌC KÌ I
NĂM HỌC 2021 - 2022
Môn : TOÁN – Lớp 7
Biểu
Câu Đáp án
điểm
10 −27 10.(−27) 0,5 đ
Câu1: . = =−45

3 2 3.2

a
3 2 1 1 5 5
 0,75 đ
− + − + : = −1+1 : = 0
( )
b

4 3 4 3 11 11

1 3 7 1 1 10 1 2
1 3 7 0,75 đ

..+ = + = . ==.2
c

3 5 5 3 3 5 3 3
3 5 5

32
−=x
a.
45 0,5 đ
32
x=−
45 0,5 đ
Câu2:
7
x=
a
20
7
Vậy x=
20
12
b. +=x
25
12
 +x=
0,25 đ
25
0,25 đ
1 2 2 1 −1
b
Trường hợp 1: +xx=  = − =
0,25 đ
2 5 5 2 10
0,25 đ
1 2 2 1 −9
Trường hợp 2: +xx=−  =− − =
2 5 5 2 10
−1 −9
Vậy x= ; x=
10 10
Gọi số đo ba góc của tam giác là a, b, c (a ,b , c >0 ) 0,25đ
a b c
Ta có:
==
4 6 8
0
Và a + b + c = 180 (Tổng ba góc của tam giác)
0,25đ
Áp dụng tính chất dãy tỉ sô bằng nhau ta có:
0
a b c a++b c 180
0
0,25đ
= = = = =10
Câu 3
4 6 8 4++6 8 18
a
0 0 0
0,25đ
=10  a=10 .4= 40

4
b
0 0 0
=10  a=10 .6= 60 0,25đ
6
c
0 0 0
=10  c=10 .8= 80
0,25đ
8
0 0 0
Vậy: Số đo ba góc của tam giác đó là: 40 , 60 , 90 .
Câu 4 0,5đ
HS vẽ hình, viết GT, KL
Xét tam giác ADC và tam giác DCE có:
DC chung 0,25đ
AD = CE (GT) 0,25đ
a
0
0,25đ
ADC==DCE 90
0,25đ
ADC=ECD c−g−c
( )
0,25đ
Ta có: ADC=ECD cmt ACD=EDC ( 2 góc tương ứng)
( )
0,25đ
Vì DC cắt AC và DE mà trong các góc tạo thành có cặp góc và
ACD
0,25đ
nằm ở vị trí hai góc so le trong và bằng nhau nên AC//DE (
EDC
0,25đ
b
Dấu hiệu nhận biết hai đường thẳng song song)
⊥AB AC
⊥DE AB
Mặt khác: ( Quan hệ từ vuông góc đến song

AC//DE

song)
0
Xét tam giác BAD vuông tại D có: DBA+=BAD 90 (1)
0,5đ
0
Mà CAD+=BAD 90 (Tam giác ABC vuông) (2)
Từ (1), (2) =CAD ABD (3)
c 0,25đ
Mặt khác: ADC=DCE cmt DAC=DEC ( 2 góc tương ứng)(4)
( )
Từ (3) và (4) ABD=DEC hayABC=DEC
0,25đ
x y z t
Ta có:
= = =
y+ z+t z+t+ x t+ x+ y x+ y+ z
x y z t
 +1= +1= +1= +1
y+ z+t z+t+ x t+ x+ y x+ y+ z
0,25 đ
x+ y+ z+t x+ y+ z+t x+ y+ z+t x+ y+ z+t
 = = =
y+ z+t z+t+ x t+ x+ y x+ y+ z
Trường hợp 1: x+ y+ z+ t= 0
 x+ y=−z−t;;;y+ z=−t− x z+t=−y− x t+ x=−y− z 0,25 đ
Câu 5
−z−t −t− x −x− y −y− z
PZ= + + + =−4 (thoả mãn).
z+t t+ x x+ y y+ z
Trường hợp 2: x+ y+ z+ t 0
0,25 đ
 y+ z+t= z+t+ x= t+ x+ y= x+ y+ z x= y= z= t
Thay các biến y,,z t bởi x ta được:
x++++x x x x x x x
PZ= + + + = 4 (thoả mãn)
0 ,25 đ
x++++x x x x x x x
x+ y y+ z z+t t+ x
Vậy có giá trị nguyên
P= + + +
z+t t+ x x+ y y+ z
Chú ý: Học sinh làm cách giải khác nếu đúng vẫn cho điểm tối đa.

onthicaptoc.com Đề kiểm tra học kỳ 1 môn Toán lớp 7 Huyện Thiệu Hóa năm 2021 2022