[r]
Trang 1¤n tËp häc sinh giái m«n to¸n 6
§Ò I :
Bµi 1 : TÝnh nhanh :
a) 11 322.37− 915
(2 3 14)2
b) 13 – 12 + 11 + 10 – 9 + 8 – 7 – 6 + 5 – 4 + 3 + 2 – 1
c) 136 (− 47) +36 47
d) 125 (− 61) (−2)3.(− 1) 2n ( n N*)
e) (12+1)(13+1)(14+1) (991 +1)
22.
8
32.
15
42
899
302
Bµi 2 : T×m x Z
a) ( x – 7 )( x + 3 ) < 0
c) (x3+ 5) (x3+10)(x3+15) (x3+30) < 0
d) ( 2x – 15 )3 = ( 2x – 15 )5
Bµi 3 :
a) T×m tÊt c¶ c¸c cÆp sè nguyªn sao cho tæng cña chóng b»ng tÝch cña chóng
b) Cho M =
1
99+
2
98+
3
97+ +
99 1 1
2+
1
3+
1
4+ +
1 100
vµ N =
92 −1
9−
2
10 −
3
11− −
92 100 1
45+
1
50+
1
55+ +
1 500 T×m tØ sè phÇn tr¨m cña M vµ N
c) Chøng minh r»ng S1 + S2 + S3 ≥ 10 biÕt :
S1 = b
a x +
c
a x ; S2 =
a
b x +
c
b y ; S3 =
a
c z +
b
c y
víi a, b, c N* vµ x + y + z = 5
Bµi 4 : §Ó b¬m c¹n níc trong mét hå ngêi ta chuÈn bÞ ba m¸y b¬m N¸y b¬m A