ĐỀ THI HỌC KỲ 2 TOÁN LỚP 7 có đáp án chi tiết

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? S? 01
Cu 1:(1,5d)

i ?m ki?m tra m?t ti?t mn Ton c?a h?c sinh m?t l?p 7 du?c ghi l?i trong b?ng sau:

6 4 3 2 10 5

7 9 5 10 1 2

5 7 9 9 5 10

9 10 2 1 4 3

1 2 4 6 8 9

a/ Hy l?p b?ng t?n s? c?a d?u hi?u v tm m?t c?a d?u hi?u?
b/ Hy tnh di?m trung bnh c?a h?c sinh l?p d?

Cu 2:(1,5d)

a/Tm cc don th?c d?ng d?ng trong cc don th?c sau:

3 3

2 2 2 2

5x y ; (xy) ; 4xy ; -2xy ; x y

2 2

2 2 1 2

b/ Hy thu g?n v tm b?c c?a don th?c : B = ? xy . (? x y)

3 2

Cu 3:(2,5d)

Cho cc da th?c

2

P(x) = 2x 3x 4

2

Q(x) = x 3x + 5

a/ Tnh gi tr? c?a da th?c P(x) t?i x = 1 .
b/Tm H(x) = P(x) - Q(x) .

c/ Tm nghi?m c?a da th?c H(x) .
Cu 4 : (2d)

00

? ?

a/ Cho ?ABC c A80,B60?? . So snh ba c?nh c?a ?ABC

0

?

b/ Cho ABC cn t?i A bi? ?t A70? . Tnh s? do cc gc cn l?i c?a ABC.?

Cu 5 :(2.5d)

Cho ABC vung t?i A? , c AB = 9cm, AC = 12cm.
a/ TnhBC.

b/u ?ng trung tuy?n AM v du?ng trung tuy?n BN c?t nhau t?i G. Tnh AG.
CDAC?

c/ Trn tia d?i c?a tia NB, l?y di?m D sao cho NB=ND.Ch?ng minh: .
H ?T

P N ? S? 01

Cu Hu ?ng d?n ch?m S? di?m

1

a/ 0,75d

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T?n s? (n) 3 4 2 3 4 2 2 1 5 4 N= 20

M = 90 0,25d

1.3 ? 2.4 ? 3.2 ? 4.3? 5.4 ? 6.2 ? 7.2 ? 8.1? 9.5 ? 10.4

X ? ? 5,53

b/ 0,5d

30

2

3

2 2

Cc don th?c d?ng d?ng: 5x y v x y

a/ 0,5d

2

2 2 1 2 ? 2?? 1? 2 2

Thu g?n: B = ? xy . (? x y) = ?? ??. ? ?.

?

x.x

?

.

?

y .y

?

0,25d
3 2 ? 3?? 2?

b/ 1 3 3

= x y 0,25d

3

B?c c?a don th?c B l: 6 0,5d

3

2

a/ P(1) = 2.1 3.1 4 = 5 0,5d

b/ 2 2

H(x) = P(x) Q(x) = (2x 3x 4) (x 3x + 5) 0,5d

2

= x 9 0,5d

2

Ta c H(x)=0 => x 9 = 0 0,5d

c/ 2

? 3

x = 9 hay x = 0,5d

4

Theo d?nh l v? t?ng ba gc trong tam gic ABC, ta c:

0,25d

0

A+ B + C = 180

a/ 0 0 0 0 0 0,25d

Suy ra: C = 180 (A+ B) = 180 (80 + 60) = 40

0,25d

0 0 0

Ta c A > B > C (80> 60> 40) nn BC > AC > AB 0,25d
0,25d
?ABC

V cn t?i A nn B = C 0,25d

b/ 0 0

180 ? 70 0,25d

0 0

Ta c + B + C = 180 suy ra B = C = ? 55

0,25d

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C

D

M

5

_G

N

0,5 d

B

A

V ? hnh vi?t GT-KL

p d ?ng d?nh l Pytago trong tam gic vung ABC, ta c:
0,5d

2 2 2 2 2

BC = AB + AC = 9 + 12 = 225
a/

BC = 15 (cm) 0,5d

Ta c AM l du?ng trung tuy?n trong tam gic vung ABC, nn:
0,25d
AM = BC/2 = 15 / 2 = 7,5 (cm)

b/ _{Ta c G l tr}_?ng_{tm c?a tam gic ABC, nn:}

2 2 _0,25d

AG = AM ? .7,5 ? 5 (cm)

3 3

Xt hai tam gic: ?DCN v ?BAN, c:
ND = NB (gt)

? DNC ? ? BNA (dd) 0,25d

c/

NC = NA (gt)

Do d, ?DCN = BAN ( c g c)?

0

0,25d

? C ? ? A ? 90 ? DC ? AC

? S? 02

Cu 1 ( 2d) : .M?t gio vin theo di th?i gian lm m?t bi ton ( tnh theo pht) c?a 30 h?c
sinh l?p 7 (ai cung lm du ?c) v ghi l?i b?ng sau:

9 7 9 10 9 8 10 5 14 8

8 8 8 9 9 10 7 5 14 10

5 5 8 8 9 7 8 9 14 8

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c/ Tnh s? trung bnh c?ng .
d/ Tm m?t c?a d?u hi?u.
Cu 2 ( 1 di?m) :

2 3

a/ Tm b?c c?a don th?c -2x y

b/ Tm cc don th?c d?ng d?ng trong cc don th?c sau:

3 2 3 3 2 2 3

5xy ; 5xy ; -4x y ; 11 xy
Cu 3 (1,5di?m): Cho hai da th?c

3 2

P(x) = 4x + x - x + 5.

2

Q(x) = 2 x+ 4x - 1.
a/ Tnh :P(x) + Q(x)

b/ Tnh: P(x) - Q(x)

2

Cu 4 ( 1,5 di?m) : Cho da th?c A(x) = x 2x .

a/ Tnh gi tr? c?a A(x) t?i x = 2.
b/ Tm cc nghi?m c?a da th?c A(x).
Cu 5 ( 2 di?m)

a/Trong cc tam gic sau ,tam gic no l tam gic vung cn,tam gic d?u .
A O H

B
B C P Q K L

b/ Cho tam gic ABC c AB = 1 cm, AC = 6cm, . Tm d? di c?nh BC ,bi?t d? di ny
l m?t s? nguyn.

Cu 6 (2 d) : Cho tam gic ABC vung t?i A, c AB = 3cm; AC = 4cm.

a/ Tnh d? di BC.
b/ Hai du?ng trung tuy?n AM v BN c?t nhau t?i G. Tnh d? di AG.

P N ? S? 02

Cu N ?i Dung Thang di?m

a) D?u hi?u: th?i gian gi?i m ?t bi ton. 0,5
b) B?ng t?n s?

0,5
Th?i 5 7 8 9 10 14

gian(x)
Cu1

T?n 4 3 9 7 4 3 N=30
( 2d)

s?(n)

c) S? trung bnh c?ng 0.5

X = ( 5.4+7.3+8.9+9.7+10.4+14.3) : 30 = 8,6

d) M?t = 8 0,5

2 3

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2 3 2 3

(1d) b) Cc don th?c d?ng d?ng l 5xy v 11xy . 0,5

3 2

a) P(x) + Q(x) = 4x +3x + 3x + 4 0,75
Cu 3

(1,5d) 3 2

b) P(x) Q(x) = 4x x -5x + 6 0,75

2

a) A(2) = 2 2.2 = 0 0,5

Cu 4

b) A(x) = x(x 2) = 0 0,5

1,5d)

Suy ra x =0 ho?c x=2 0,25-0,25

a)Tam gic ABC d?u 0,5

Tam gic OPQ vung cn. 0,5

Cu 5 b) Theo tnh ch?t cc c?nh c?a tam gic
(2d) ta c AC - AB < BC < AC + AB

Hay 5 < BC < 7 0,5
V d? di BC l m?t s? nguyn nn BC = 6 cm. 0,5

B

M
G

C

A _N

a)Tam gic ABC vung t?i A theo d?nh l Pi-ta-go
Cu 6 _{ta c:}

2 2 2

(2d) _{BC = AB + AC} _0,5

22 22 0,5

BC = ABAC? = 34? = 5 cm.
b) AM l trung tuy?n ?ng v?i c?nh BC

nn AM = BC : 2 = 2,5 cm. 0,5

v G l tr?ng tm c?a tam gic ABC

25 _0,5

nn AG = AMcm?
33

? Ch : - H ?c sinh lm cch khc dng cho di?m t?i da.

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