原创2006年8月数学机井讨论稿第1遍（答案给出

xin_xin13

以下是引用aprilfly在2006-8-2 22:48:00的发言：

更正

1.（（根号2）+1））*2*a,a是小圆半径

7.3

right

dasani

以下是引用aprilfly在2006-8-2 22:48:00的发言：

更正

1.（（根号2）+1））*2*a,a是小圆半径

hi, how can i get it? thx...

scujean

10. how many intersections can a triangle has with a circle? A) 1, 2, 3; B) 1, 2, 3, 6; C) 1, 2, , 4, 6; D) 1, 2, 3, 4, , 6; E) 1, 2, 3, 4, 5, 6
[解] 選E  intersections交點

[attachimg]49163[/attachimg]

scujean

11.  DS: a line in x-y coordinate system goes through the origin and point (a,b), is a < b? 1) slope < 0; 2) a < 0 
[ans]C

[attachimg]49165[/attachimg]

xin_xin13

我的答案，大家看看是否正确：

1.有一个图形体，两个同样大小的小圆一上一下斜放在一个正方形内和正方形相切，告诉小圆的半径，求正方形的对角线。

(2^0.5+1)*2*r

2.X, y, z三点在一条直线上面，y在x，z之间，w到x, z的具体相等，然后选下面那个必然成立有xw>xy; xy>yz; xw>yw等

xw>yw

3.一个条件2的N次方=N的平方，一个条件是N>0,问n的值。

设两个方程：y=2^x, y=x^2。 在X－Y坐标上画出这两个方程的曲线，可以看到在x>0的时候，有两个交点，一个交点在0<x<1的区域，另一个是在x＝4。

所以N的值不唯一。选E

4.(七月JJ)50millions people in 6 cities 那一道，人口最少的city的population给的不是百分比，而是2million,我差点看成2%了（人口第四多的city给的还是21%);

5.(七月JJ)DS: M, N integers, is M^N integer? 1) N^M > 0; 2) N^M integer

6.DS: appartments avg. rent $600, what is the percentage of appartments with rent under $600? 1) exactly half of the appartments with rent under $500; 2) the rents of differnt appartments are either $450, $550, $650, or $800.

E

7.[(1+5^(1/2))/2]^2 + [(1-5^(1/2))/2]^2 = ?

a＝5^(1/2))/2，(1+a)^2+(1-a)^2=1+2a+a*a+1-2a+a*a=2*(1+a*a)=2*(1+5/4)=9/2

8.DS: right triangle, area = ? 1) sum of two shorter edge is 15; 2) longest edge is 12.

C

9.DS: formula for profit margin (M) for Sales (S) and Cost (C) is M = (S-C)/S, is M in 1999 more than 10% more than M in 1998? 1) S in 1999 is twice S in 1998; 2) C in 1999 is 50% more than C in 1998.

C

10. how many intersections can a triangle has with a circle? A) 1, 2, 3; B) 1, 2, 3, 6; C) 1, 2, , 4, 6; D) 1, 2, 3, 4, , 6; E) 1, 2, 3, 4, 5, 6

E

11.  DS: a line in x-y coordinate system goes through the origin and point (a,b), is a < b? 1) slope < 0; 2) a < 0 

C

[此贴子已经被作者于2006-8-2 23:30:12编辑过]

sen4sun

以下是引用scujean在2006-8-2 22:15:00的发言：
5. [(1+5^(1/2))/2]^2 + [(1-5^(1/2))/2]^2 = ?
利用（a+b）^2= a^2+b^2+2ab→a^2+b^2=（a+b）^2-2AB
[解]3

以下是引用skyinseas在2006-8-2 22:44:00的发言：
我同意scujean的答案和解法

这题3 是怎么生出来的? 我怎么都算成4.5

[此贴子已经被作者于2006-8-2 23:49:35编辑过]

sen4sun

以下是引用scujean在2006-8-2 22:15:00的发言：
4  DS: apartments avg. rent $600, what is the percentage of apartments with rent under $600? 1) exactly half of the apartments with rent under $500;  2) the rents of different apartments are either $450, $550, $650, or $800.
[解]选E吗？
（1）只能知道[小于$600/全]>1/2

这题有办法列式证明是E吗?

miaomiaomiao

11题是不是两个条件都可以啊？都过第二象限所以a<b

aprilfly

以下是引用miaomiaomiao在2006-8-3 0:27:00的发言：
11题是不是两个条件都可以啊？都过第二象限所以a<b

nod,刚贴答案的时候太快了，这个题应该选C

aprilfly

以下是引用sen4sun在2006-8-2 23:44:00的发言：

以下是引用scujean在2006-8-2 22:15:00的发言：
5. [(1+5^(1/2))/2]^2 + [(1-5^(1/2))/2]^2 = ?
利用（a+b）^2= a^2+b^2+2ab→a^2+b^2=（a+b）^2-2AB
[解]3

这题3 是怎么生出来的? 我怎么都算成4.5

sen4sun再看看那几个括号，如果括号不对就会算成4.5

：）