國中數學題~20點

1. (53+3/5)^2+2*(53+3/5)*(6+2/5)+(6+2/5)^2
=(53+3/5+6+2/5)^2
=3600

2. (70+2/3)^2－2*(70+2/3)*(2/3)+(2/3)^2
=(70+2/3－2/3)^2
=4900

3.(299+2/3)^2
=(300－1/3)^2
=300^2－2*300*(1/3)+(1/3)^2
=90000－200+1/9
=89800+1/9

4. 10.5*9.5
=10^2－0.5^2
=99.75

5. (30+2/3)*(29+1/3)
=(30+2/3)*(30－2/3)
=900－4/9
=899+5/9

6. 若983=1000^2－m，m的值為_____
m=1000^2－983
=1000000－983
=999017

7.若(29+1/2)^2 =30^2 +m,m的值為_______
-m=30^2-(29+1/2)^2
=(1/2)*(59+1/2)
=29.5+1/4
=29+3/4
m=-29.75

8.(15+2/3)^2=15^2+(2/3)^2+n,n的值為_______
n=(15+2/3)^2-15^2-(2/3)^2
=2*15*(2/3)
=20

9.(a+2)(a－2)－a ² 的值為_______
(a+2)(a－2)－a^2
=(a^2－4)－a^2
=－4

10. 432*5432*(5432/432－432/5432)
=432*5432*(5432/432)－432*5432*(432/5432)
=5432^2－432^2
=(5432－432)*(5432+432)
=5000*5864
=59320000

11. 15.2^2
=(15+0.2)^2
=15^2+2*15*0.2+0.2^2
=225+6+0.04
=231.04

12. 99.9^2
=(100－0.1)^2
=100^2－2*100*0.1+0.01
=9980.01
13. 30.2*29.8
=(30+0.2)*(20－0.2)
=900－0.04
=899.96

14. 計算(2010^2+2*2010+1)/2011-(2011^2 -1)/2012之值
(2010^2+2*2010+1)/2011－(2011^2 －1)/2012
=2011^2/2011－2012*2010/2012
=2011－2010
=1

15. 求2001*2002－1999*2004之值為何?
=(2000+1)*(2000+2)－(2000－1)*(2000+4)
=(2000^2+3*2000+2)－(2000^2+3*2000－4)
=6

1.
(53 3/5)²+2x53 3/5x6 2/5+(6 2/5)²=________
(53+(3/5))^2+2*(53+(3/5))*(6+(2/5)+(6+(2/5)^2
=(53+(3/5)+(6+(2/5))^2=60^2=36002.
(70 2/3) ² -2x70 2/3x2/3+(2/3) ² =________
(70+(2/3))^2-2*(70+(2/3))*(2/3)+(2/3)^2
=(70+(2/3)-(2/3))^2=49003.
(299 2/3) ² =________
(300-(1/3))^2=300^2-2*300*(1/3)+(1/3)^2
=89800+(1/9)4.
10.5x9.5=________
(10+0.5)(10-0.5)=10^2-0.5^2=99.755.
30 2/3x29 1/3=________
(30+(2/3))(30-(2/3))=30^2-(2/3)^2=899+(5/9)
7.
若(29 1/2) ² =30 ² +m,m的值為_______
m=(30-(1/2))^2-30^2=(60-(1/2)(-1/2)=-119/48.
(15 2/3) ² =15 ² +(2/3) ² +n,n的值為_______
n=(15+(2/3))^2-15^2-(2/3)^2=20
9.
(a+2)(a-2)-a ² 的值為_______
a^2-4-a^2=-4 11.
15.2 ² =_______
(15+0.2)^2=15^2+2*15*0.2+0.2^2=231.0412.
99.9 ² =_______
(100-0.1)^2=100^2-2*100*0.1+0.1^2=9980.0113.
30.2x29.8=_______
(30+0.2)(30-0.2)=30^2-0.2^2=899.96
15.
求2001x2002-1999x2004之值為何?
原式=(2000+1)(2000+2)-(2000-1)(2000+4)=2000^2+3*2000+2-(2000^2+3*2000-4)=6

2012-09-23 17:04:39 補充：
6.
若983=1000 ² -m,m的值為_____ m=1000000-983=999017 ,(題目應是983 ²=1000 ² -m)

10.
432x5432x(5432/432-432/5432)=_______
原式=5432^2-432^2=(5432+432)(5432-432)=5864*5000=29320000
14.
計算2010 ² +2x2010+1/2011-2011 ² -1/2012之值
(2010^2+2*2010+1)/2011－(2011^2 －1)/2012
=(2010+1)^2/2011-(2011+1)(2011-1)/2012
=1

這些題目很棒
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人的一生不會重來的
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