Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 1
CÁC BÀI TOÁN ĐIỂN HÌNH BỒI DƯỠNG HỌC SINH GIỎI
§ 1. CẤU TẠO SỐ TỰ NHIÊN
Bài 1:



Hd:

abc

Ta có: b = c


 suy ra c = 3.
+  
Th

2 + 2; 7 = 3

2 + 1.

Bài 2:
 
c 2000.
Hd:

10,,,0;0,  dcbaaabcd




b6

= 66.


Bài 4:
Tìm 


Hd:

)10,;0(,  baaab


ab
= (a  b) 15 +2
Hay b  16 = a  5 + 2
 
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 2
 
+ Vì a  5 + 2

0 nên b


Hd:

abc


( ) 11abc a b c   
(theo bài ra)

100 10 11 11 11a b c a b c         
 89 10a b c   

11 10a b c   
)

89 1, 89 198a cb a cb abc      
Bài 7:
 


Hd:

- 

- 


Hd:
 208 =





Bài 9:



Hd:

ab
, ( 0

a, b < 10, a

0).
Ta có
ab
= (a  b)  28 + 1.
 
ab


 b = 1 thì
ab



Bài 11:
có 3 

Hd:

abc
, ( 0

a, b, c < 10, a

0).
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 4
Theo bài ra ta có:
abc
= 5  a  b  c.  
5abc

5.


5 25ab
.


 



0).
Theo bài ra ta có:
abc = 7 bc a 100 = 6 bc  

a 50 = 3 bc  
  a = 3,
bc = 50

 

Bài 14:
có 3 
.

Hd:

abc
, ( 0

a, b, c < 10, a

0).
Theo bài ra ta có:
cba - abc = 693

 99  (c  a) = 693


Hd:

abcd
, ( 0

a, b, c, d < 10, a

0).
Theo bài ra ta có:
abcd - ab = 4455


cd = 99 ( 45 - ab )

( 45 - ab ) = 0, ( 45 - ab ) = 1


( 45 - ab ) = 0:


( 45 - ab ) = 1:

Bài 17:

.

Hd:

abcd


Hd:


Ab
, ( 0

b < 10, A > 0).
Theo bài ra ta có:
Ab 7 = A0b

 b  6 = A  5  6  b = A  5  b = 5 (Vì A > 0)  A =
 

Bài 19:

.
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 6

Hd:
 

Abc
, ( 0

b, c < 10, A > 0).
Theo bài ra ta có:

 11) : 2 + 1]  
có [(175  101) : 2 + 1] x 3 = 1


 , 175.




175 = (11 + 175) 83 : 2 = 7719

Bài 3:



 
Hd:
không

 4) : 4 + 1 = 502.
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b) [(96  12) : 4 + 1] × 2 = 44 
c  2  22 × 2 



Bài 4:


 
+ Ta có: 13 : 3 = 
 
108 b 10) : 2 + 1 = 65
(10 + 138)  65 : 2 = 4810.

Bài 7:
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 8

 



Hd:
 101) : 1 + 1 = 1905.
 1) × 1 + 101 = 175.
 × 3 + 1006 × 4 = 8721.
Vì có: 116 < 899  3 
Ta o
 (39  1)  

Bài 8:



Bài 10:
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 9


 

Hd:
97 có 3 + [(97  13) : 4 + 1]  
 101) : 4 + 1]  

 


, 9 1)  

b 1)  4 + 1 = 797.
 200 : 2 = 79800.
Bài 11:

a)  ?


Hd:
 1)  3] + 5 = 620
 102 = 62500 + 1250 = 63750


1
3
,
2
3
3
, 7,
1
10
3

a) ?
?  


Hd:
a) 
10
3


10 1 20081
(2009 - 1) + =
3 3 3

10 1
(2007 - 1) + = 669


Hd:
 là: 8  
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 11
 1 = 1, 4 


1, 4 
i cháu lúc 


 1) 
 8 = 24 )
Bài 2:
Tính

Hd:
 là: 5  1 = 4  
 

 
 




:

:
:
:
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 12


 

Bài 4:



Hd:
: 2, 2  
 2  

 : 



 1)  

6

Tu nay:
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 13

 
 
Bài 7:


Hd:
: 3  
 
 
 

 1)  
 
  
Bài 8:
 
?

Hd:
 là: 2,5   
   
.


Tu:
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 14
Bài 10:


Hd:
Theo bài ra ta có:




  20 : (3 + 2) 
  20  
Bài 11:



Hd:
Theo bài ra ta có:


21
1 - =
33





20




15
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 15
 
 1) × 
 1) × 


 1) × 3 = 
 1) × 

Bài 14:


Hd:
Theo bài ra ta có:
× 
× 
 





14




12
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 16
 

con  20 : (3 - 1) 1 = 10 (tu

2


 × 1 = 
- 20 
  50 - i)
Bài 17:


Hd:
Theo bài ra ta có:
 em sau này






2
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 17  7 : (2 - 1) 
  


5
3



52
- 1 =
33
à

21
1 - =
33

   4 : 1  




7




Hd:
Theo bài ra ta có:

 

 100% - - 
× 
- 
×  § 4. TOÁN CHUYỂN ĐỘNG ĐỀU

Bài 1:
  
ì

Hd:  30 = 156 (km).


242)(
5
2
265:156
h
h 
phút.

Do trên cùn
:  
km/h. Ta có  sau:
 dài là 60  2  2 = 240 (km).


Bài 3:



Hd:

2
3


:
:
 
c xe máy là 60  
 2 = 120 (km).


 là 60  1,2 = 70 (km).
Bài 4:
5 
7 


km?
Hd:

1


2


1

 2 = 10 km

1
 là:
130 + 10 = 140 (km).



Bài 6:
 
là 

hai ng
Hd:


3

g AB).

28 23 5
28 28 28


A
v
1


v
2
= v
1
+5km
B
C
Biên Soạn : Lê Thị Thu Hiền – 0987.615.676 21
+ Vì
5
28

25 : 5  28 = 140 (km).


1
5


1 1 1
( ) : 2
3 5 15

(khúc sông)

1
1 : 15
15


Vì 50m/ph = 3km/h nên khúc sông dài là 3  15 = 45(km).
Bài 10:


Hd:

52 giây tàu  
(210 m).
  210 m là:
52  8 = 42 (giây).
: 210 : 42 = 5(m/s) (= 18km/h)
 10 = 40 (m).
Bài 11:
 
 giây. Tính 



 

  m là: 47  9 = 38 (s)

 9 = 45 (m)
Bài 13:




Hd:  

12
21
t v 20
= =
t v 30


2
 t
1


23
Hd:





12
21
t v 60
= =
t v 40
12
200
t + t =
60

1
, t
2

 520 km.




 Bài 16:


4
5


1
8
 


Hd:
Theo bài ra ta có: + v
ra
=
4
5
 v
vào

+ v
vào
- v
ra

2
, v
2
=60km/h
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 


Hd:
vòi là: v
1
+ v
2
=
1
3


12
2 =
33




21
1 - =
11
+ 1 = 1
11 11

Bài 19:
kim 
kim  nhau?
 Hd:

h

f
, ta
có: v
h
=
1
12
vòng/h, v

 2 kim vuông góc là
1
4
vòng kim 
trùng nhau là:

1 1 3
: [1 - ] =
4 12 11

kim phút vuông g


3 1 4
+ =
11 11 11


kim nhau là:

44
+ 1 = 1
11 11


Hd:
B
1/12
A
D
C
1/4
E
10 km

A
B
C
A

B

Ô tô
Ca nô
2 × 17 = 34 km

13 km

A
B
A

B
48 km
35 km