BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ
1. Sè tù nhiªn - D·y sè tù nhiªn
Bµi 11: T×m x , biÕt:
a) x lµ sè trßn chôc vµ 28 < x < 48
b) x lµ sè tù nhiªn vµ 145 < x < 150
c) x lµ sè ch½n vµ 200 < x < 210
d) x lµ sè tù nhiªn vµ x < 3
e) x lµ sè tù nhiªn vµ 2 < x < 5
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Bµi 12: Sè tù nhiªn x gåm mÊy ch÷ sè, biÕt sè ®ã:
a) Cã ch÷ sè hµng cao nhÊt thuéc líp ngh×n?
b) Cã ch÷ sè hµng cao nhÊt thuéc líp triÖu?
c) BÐ h¬n 10?
d) BÐ h¬n 1 000 000 vµ lín h¬n 1 00 000?
e) §øng liÒn sau mét sè cã ba ch÷ sè?
f) §øng liÒn tr-íc mét sè cã ba ch÷ sè?
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Bµi 13: ViÕt sè tù nhiªn nhá nhÊt, biÕt sè ®ã:
a) Gåm cã: - Mét ch÷ sè
-

Ba ch÷ sè

-

Ba ch÷ sè lÎ kh¸c nhau
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b) Cã ®ñ n¨m ch÷ sè 5, 4, 7, 0, 1
c) Cã ba ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 20.
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Bµi 14: T×m sè tù nhiªn x, biÕt:
a) x lµ sè tù nhiªn bÐ nhÊt;
b) x lµ sè liÒn sau sè 999;
c) x lµ sè liÒn tr-íc sè 1001;
d) x lµ sè võa lín h¬n 99 võa bÐ h¬n 1000;
e) x lµ sè cã hai ch÷ sè vµ lín h¬n 15;
f) x lµ sè cã ba ch÷ sè vµ bÐ h¬n 105;
g) x lµ sè ë gi÷a sè 1 vµ sè 11;
h) x lµ sè gi÷a sè tù nhiªn a vµ sè (a + 1)
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Bµi 16: H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 3.
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Bµi 17:

Cho 3 ch÷ sè 1; 2; 3.
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a) H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 3 ch÷ sè ®· cho.
b) TÝnh nhanh tæng c¸c sè võa viÕt ®-îc.
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Bµi 18: Víi bèn ch÷ sè 1,2,3,4;
a) H·y viÕt tÊt c¶ c¸c sè cã ®ñ bèn ch÷ sè Êy.
b) TÝnh tæng cña tÊt c¶ c¸c sè ë c©u a.
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Bµi 19: Cho 5 ch÷ sè 0, 1, 2, 3, 6.
a) H·y lËp tÊt c¶ c¸c sè cã bèn ch÷ sè kh¸c nhau tõ 5 ch÷ sè trªn?
b) TÝnh nhanh tæng c¸c sè võa lËp ®-îc?
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Bµi 22: Cho d·y sè:

2, 3, 4, 5, ..., 30, 31, 32, 33, 34.

a) D·y sè trªn cã bao nhiªu sè h¹ng?
b) TÝnh nhanh tæng cña d·y sè trªn?
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Bµi 25: Cho d·y sè ch½n liªn tiÕp 2, 4, 6, 8, 10, ... , 2468. Hái d·y cã:
a) Bao nhiªu sè h¹ng?
b) Bao nhiªu ch÷ sè ?
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2. BÀI TOÁN LIÊN QUAN DÃY SỐ THEO QUY LUẬT
Cho các số 1;4;7;10;.....................
a.Số 2221;2234 có thuộc dãy số đó không ?
b.Số thứ 134 ,số thứ 205 là số nào ?
c.Tính tổng của 50 số đầu của dãy số.
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3/CẤU TẠO SỐ
D¹ng 1: ViÕt sè TN tõ nh÷ng ch÷ sè cho tr-íc
Bµi 2 : Cho 5 ch÷ sè : 0; 1; 2; 3; 4.
a) H·y viÕt c¸c sè cã 4 ch÷ sè kh¸c nhau tõ 5 ch÷ sè ®· cho ?
b) T×m sè ch½n lín nhÊt, sè lÎ nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 5 ch÷ sè ®· cho ?
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Bµi 1 : Cho bèn ch÷ sè : 0; 3; 8 vµ 9.
a) ViÕt ®-îc tÊt c¶ bao nhiªu sè cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho ?
b) T×m sè lín nhÊt, sè nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho?
c) T×m sè lÎ lín nhÊt, sè ch½n nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho ?
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D¹ng 2: C¸c bµi to¸n gi¶i b»ng ph©n tÝch sè :
Bµi 1: T×m 1 sè TN cã 2 ch÷ sè, biÕt r»ng nÕu viÕt thªm ch÷ sè 9 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp
13 lÇn sè ®· cho ?
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Bµi 2: T×m mét sè cã 3 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã th× nã t¨ng thªm 1112
®¬n vÞ.
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Bµi 3: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm sè 21 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp 31
lÇn sè ph¶i t×m.
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Bµi 4: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã ta ®-îc sè míi lín h¬n
sè ph¶i t×m lµ 230 ®¬n vÞ.
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D¹ng 3: Nh÷ng bµi to¸n vÒ xÐt c¸c ch÷ sè tËn cïng cña
sè
Bµi 1: Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau :
+ 1992
+....+
 (( 1991
a) ( 1991 + 1992 + ...+ 1999 ) –
11 + 12
+ .....+
19 ).1999 )
c)
21
23
25
27
–
11
13
15
17






b) ( 1981 + 1982 + ...+ 1989 )
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Bµi 2 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ?
a) 136  136 – 42 = 1960
b)

ab  ab

- 8557 = 0

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Bµi 3 : Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau :
86 –
51  )61
71 
81 + 736 + 89 )
 66+ 2378
 76+4545
a) ( 1999
+ 7956
–( 315
+ 598
.b). .56
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Bµi 4 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ?
a) abc 
b) 11  21

abc

- 853467 = 0

 31  41 – 19  25  37 = 110
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4. C¸c bµi to¸n vÒ dÃy sè
I. §iÒn thªm sè h¹ng vµo sau, gi÷a hoÆc tr-íc mét d·y sè
Bµi 1. ViÕt tiÕp ba sè h¹ng vµo d·y sè sau :
a) 1; 3; 4; 7; 11; 18;...
b) 0; 2; 4; 6; 12; 22;...
c) 0 ; 3; 7; 12;...
d) 1; 2; 6; 24;...
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Bµi 2 : T×m sè h¹ng ®Çu tiªn cña c¸c d·y sè sau :
a). ...; 17; 19; 21.
b). .: 64; 81; 100.
BiÕt r»ng mçi d·y cã 10 sè h¹ng.
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Bµi 3 : ViÕt tiÕp hai sè h¹ng cña d·y sè sau :
a) 100; 93; 85; 76;.....
b) 10; 13; 18; 26;...
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II. X¸c ®Þnh sè a cã thuéc d·y ®· cho hay kh«ng
Bµi 1: H·y cho biÕt:
a) C¸c sè 50 vµ 133 cã thuéc d·y 90; 95; 100;...hay kh«ng ?
b) Sè 1996 thuéc d·y 2;5;8;11;... hay kh«ng ?
c) Sè nµo trong c¸c sè 666; 1000; 9999 thuéc d·y 3; 6; 12; 24;... hay kh«ng ?
Gi¶i thÝch t¹i sao ?
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III. T×m sè sè h¹ng cña d·y
Bµi1. Cho d·y sè 11; 14; 17;.....;65; 68.
a) H·y x¸c ®Þnh d·y sè trªn cã bao nhiªu sè h¹ng?
b) NÕu ta tiÕp tôc kÐo dµi c¸c sè h¹ng cña d·y sè ®ã th× sè h¹ng thø 1996 lµ sè mÊy?
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Bµi 2 . Trong c¸c sè cã ba ch÷ sè, cã bao nhiªu sè chia hÕt cho 4?
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Bµi 3: Cã bao nhiªu sè : cã 3 ch÷ sè khi chia cho 5 d- 1? D- 2 ?
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IV. T×m tæng c¸c sè h¹ng cña d·y sè
Bµi 1 . TÝnh tæng cña 50 sè lÎ ®Çu tiªn .
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Bµi 2: T×m tæng cña :
a) C¸c sè cã 2 ch÷ sè chia hÕt cho 3.
b) C¸c sè cã 2 ch÷ sè chia cho 4 d- 1.
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5. Bèn phÐp tÝnh víi sè tù nhiªn
5.1. PhÐp céng
Bµi 1: T×m hai sè cã tæng b»ng 1149, biÕt r»ng nÕu gi÷ nguyªn sè lín vµ gÊp sè bÐ lªn 3 lÇn th× ta ®-îc
tæng míi b»ng 2061.
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Bµi 2: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè thø nhÊt, gÊp sè thø hai lªn 6 lÇn th× ®-îc tæng míi
b»ng 6789. H·y t×m hai sè h¹ng ban ®Çu.
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Bµi 3: T×m hai sè cã tæng b»ng 140, biÕt r»ng nÕu gÊp sè h¹ng thø nhÊt lªn 5 lÇn vµ gÊp sè h¹ng thø hai
lªn 3 lÇn th× tæng míi lµ 508.
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Bµi 4: T×m hai sè tù nhiªn cã tæng lµ 254. NÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt vµ gi÷
nguyªn sè thø hai th× ®-îc tæng míi lµ 362.
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Bµi 5: T×m hai sè cã tæng b»ng 586. NÕu viÕt thªm ch÷ sè 4 vµo bªn ph¶i sè thø hai vµ gi÷ nguyªn sè thø
nhÊt th× tæng míi b»ng 716.
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