a*****g
发帖数: 1320 | 1 【 以下文字转载自 Seattle 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: Seattle
标 题: mathscounts 数学题求助(2) (转载)
发信站: BBS 未名空间站 (Fri Oct 29 11:09:16 2010, 美东)
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助(2)
发信站: BBS 未名空间站 (Fri Oct 29 11:04:06 2010, 美东)
麻烦大虾们帮忙给出 OCTOBER SESSION 4 "PROBABILITY STRETCH" 的解题步骤，谢谢
你们了。
http://mathcounts.org/Document.Doc?id=116 |
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a*****g
发帖数: 1320 | 2 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
标 题: mathscounts 数学题求助(4)
发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x+3=0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the recip... 阅读全帖 |
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a*****g
发帖数: 1320 | 3 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (洛杉矶推妈), 信区: SanFrancisco
标 题: mathscounts 数学题求助(6)--many thanks!
发信站: BBS 未名空间站 (Wed Feb 2 23:54:18 2011, 美东)
In base b, 321-123=154. What is the value of b? |
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L***m
发帖数: 4594 | 4 【 以下文字转载自 LosAngeles 讨论区 】
发信人: LAiam (老虎油), 信区: LosAngeles
标 题: 有没有孩子参加MATHSCOUNT的？
发信站: BBS 未名空间站 (Tue Oct 12 00:45:25 2010, 美东)
我们交流一下经验，谢谢。 |
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L***m
发帖数: 4594 | 5 【 以下文字转载自 LosAngeles 讨论区 】
发信人: LAiam (老虎油), 信区: LosAngeles
标 题: 有没有孩子参加MATHSCOUNT的？
发信站: BBS 未名空间站 (Tue Oct 12 00:45:25 2010, 美东)
我们交流一下经验，谢谢。 |
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a*****g
发帖数: 1320 | 6 【 以下文字转载自 Seattle 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: Seattle
标 题: mathscounts 数学题求助(3)
发信站: BBS 未名空间站 (Sun Oct 31 22:28:30 2010, 美东)
WHAT IS THE PROBABILITY THAT THE LAST THREE DIGITS OF A RANDOMLY SELECTED
PHONE NUMBER ARE ALL PRIME? EXPRESS YOUR ANSWER AS A COMMON FRACTION.
Please help to give the answer. Thanks, |
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a*****g
发帖数: 1320 | 7 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助
发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
COMMON FRACTION.
2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
FRACTION.
3.THE DIGITS 2,3, 4, 7 AND 8 ARE EACH US... 阅读全帖 |
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a*****g
发帖数: 1320 | 8 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助(2)
发信站: BBS 未名空间站 (Fri Oct 29 11:04:06 2010, 美东)
麻烦大虾们帮忙给出 OCTOBER SESSION 4 "PROBABILITY STRETCH" 的解题步骤，谢谢
你们了。
http://mathcounts.org/Document.Doc?id=116 |
|
a*****g
发帖数: 1320 | 9 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
标 题: mathscounts 数学题求助(4)
发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x=3=
0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the reci... 阅读全帖 |
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a*****g
发帖数: 1320 | 10 【 以下文字转载自 Seattle 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: Seattle
标 题: mathscounts 数学题求助(3)
发信站: BBS 未名空间站 (Sun Oct 31 22:28:30 2010, 美东)
WHAT IS THE PROBABILITY THAT THE LAST THREE DIGITS OF A RANDOMLY SELECTED
PHONE NUMBER ARE ALL PRIME? EXPRESS YOUR ANSWER AS A COMMON FRACTION.
Please help to give the answer. Thanks, |
|
a*****g
发帖数: 1320 | 11 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
标 题: mathscounts 数学题求助(4)
发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x+3=0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the recip... 阅读全帖 |
|
a*****g
发帖数: 1320 | 12 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助
发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
COMMON FRACTION.
2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
FRACTION.
3.THE DIGITS 2,3, 4, 7 AND 8 ARE EACH US... 阅读全帖 |
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y****i
发帖数: 12114 | 13 1. （-3，-7）
2. (-12,47,-60) |
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B******1
发帖数: 9094 | 14 Without my glasses on, I read "What is the sum" as "What is the scum!" |
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B******1
发帖数: 9094 | 15 3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
Express your answer as a common fraction
Apparently X=1 is a solution. Therefore,
x3-3x2-13x+15=(x-1)(X2-2x-15)=(x-1)(X-5)(X+3)
1/1 + 1/5 +(-1/3)= 13/15
Another way to solve this is to realize that if x1, x2, and x3 are the three
roots of this equation,
then, x1*x2*x3 = -15, and x1*x2+x1*x3 +x2*x3 = -13.
Hence, 1/x1 + 1/x2 + 1/x3 = (-13)/(-15)=13/15 |
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B******1
发帖数: 9094 | 16 What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
(x1)^2 + (x2)^2 + (x3)^2 = (x1 + x2 + x3)^2 - 2*(x1x2 + x1x3 + x2x3)
= 80^2 -2*(66)=6400 - 132 = 6268 |
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B******1
发帖数: 9094 | 17 The solutions of X3-63x2+cx-1728=0 form a geometric sequence. What is the
value of c?
roots: x, x^2, x^3
x*x^2*x^3=1728; x*x^2 + x*x^3 + x^2*x^3 = C;
x^2=12
C=12(2*3^(1/2) +12 + 24*3^(1/2))=144 + 312*3^(1/2) |
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Y****a
发帖数: 243 | 18 geometric sequence 不是 x x^2 & x^3 吧
应该是 x, xy, and xyy,
我算的 这个方程的解是 3，12，和48 |
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u*h
发帖数: 397 | 19 本着授人以渔的方针， 解释一下，
对于一个三元一次方程（其他高次方程类似）：
X^3 + aX^2+bX+c = 0
如果它的解是:x1, x2, and x3;
那么有如下关系：
(X-x1)*(X-x2)*(X-x3) = X^3 + aX^2+bX+c
将方程左边展开， 合并同类项， 对照等号左右两边，
可以得出三个关系式。
对照题目的要求， 通过这三个关系式的一些简单组合，
一般就可以得到题目所求的答案。
本类题目的解法均类似。
点到这里， 小孩就应该能够自己完成这些题目了。 |
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a*****g
发帖数: 1320 | 20 Super many thanks you guys great help!! |
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a*****g
发帖数: 1320 | 21 1.How many of the letters in MATHCOUNTS have a horizontal line of symmetry?
2.Billy takes two marbles, without replacement, from a bag that contains
only six yellow marbles and three blue marbles. What is the probability that
he gets one marble of each color? Express your answer as a common fraction. |
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B******1
发帖数: 9094 | 22 1) Three: H C O
2) 6*3*2/9*8 = 1/2 |
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y****i
发帖数: 12114 | 23 北大能不能解释一下第二题的思路？
我是这么算的：(6/9)*(3/8)+(3/9)*(6/8)=1/2,思路是：两个球，要么是先黄后绿，要
么是先绿后黄，把两个概率加起来得到总概率。 |
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E*********e
发帖数: 10297 | 24 C (1,6)*C(1,3)/C(2,9)=6*3/(9*8/2)=1/2
here C(1,6)=find one from 6=6 |
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a*****g
发帖数: 1320 | 28 4 (3^N+2)+45 (3^N)=3 What is the value of N? |
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y****i
发帖数: 12114 | 29 题目会不会是 4 (3^(N+2))+45 (3^N)=3 ?
如果是这样，答案是 N=-3 |
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a*****g
发帖数: 1320 | 31 1) What is the units digit of N in the following equation?
（3x3x3x3x3）/N =1/2 X 1/3 X 1/3
2) A rectangle with sides of length 5 units and 6 units that are parallel to
the x-axis and y-axis has one vertex at (1,3). What is the largest possible
sum of the coordinates of any of the other vertices of this rectangle? |
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B******1
发帖数: 9094 | 32 (2) 1+3+5+6 = 15
For (1), you'd better upload a jpg picture of the question for clarity. |
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a*****g
发帖数: 1320 | 33 谢谢。我把题目重新编辑了一下，希望这次好点。苯妈再次请教第二题究竟是什么意思
？ |
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B******1
发帖数: 9094 | 34 1) What is the units digit of N in the following equation?
（3x3x3x3x3）/N =1/2 X 1/3 X 1/3
N = 2 x (3^7) = 2 x (9 x 9 x 9 x3)
If you only count the units digit, then
N = 2 x (1 x 7) = 4 ( 9 x 9 = 81; 9 x 3 = 27; 2 x 7 = 14)
So the units digit of N is 4 |
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B******1
发帖数: 9094 | 35 2) A rectangle with sides of length 5 units and 6 units that are parallel to
the x-axis and y-axis has one vertex at (1,3). What is the largest possible
sum of the coordinates of any of the other vertices of this rectangle.
Basically this question tells you that one vertex of a rectangle is at (1,3)
and that the length and width of the rectangle is 6 and 5. In addition, the
rectangle's side are parallel to either the x-axis or the y-axis.
Therefore, only 8 possibilities exit if you draw them ou... 阅读全帖 |
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a*****g
发帖数: 1320 | 36 非常非常地感谢。北大学子果真不是浪得虚名。
to
possible
3)
the
the
requirements |
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a*****g
发帖数: 1320 | 37 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
football and 29 students play basketball. Of these students 15 play both
soccer and football, 18 play both basketball and football and 13 play both
soccer and basketball. What is the smallest possible number of students that
play all three sports?
2. If x and y are two triangular numbers less than 100 that when added,
produce a sum that is a square number, what is the largest possible value of
x or y?
3. Suppose that six ... 阅读全帖 |
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B******1
发帖数: 9094 | 38 1.At Marsh Mel Low Middle School 34 students play soccer, 36 students play
football and 29 students play basketball. Of these students 15 play both
soccer and football, 18 play both basketball and football and 13 play both
soccer and basketball. What is the smallest possible number of students that
play all three sports?
Since there are 18 play both basketball and football and 13 play both soccer
and basketball, but there there are 29 students playing basketball, then at
least there are 2 person... 阅读全帖 |
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B******1
发帖数: 9094 | 39 2. If x and y are two triangular numbers less than 100 that when added,
produce a sum that is a square number, what is the largest possible value of
x or y?
Triangular numbers less than 100: 1,3, 6, 10,15,21,28,36,45,55,66,78,91
A squre number less than 200: 1, 4, 9, 16,25,36,49,64,81,100,121,144,169,196
Apparently 45 + 55 =100. So we know at least 55 is one possible choice.
Can we go any higher? Let's try 91. 196 is out. 169-91 = 78
Bingo.
The answer is 91. |
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A******s
发帖数: 292 | 41
play
both
both
students that
2
added,
value of
78 and 91
Martin)
even
8/42 |
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B******1
发帖数: 9094 | 42 3. Suppose that six brothers (George, John, Thomas, Fred, Andrew, Martin)
each roll a fair 6-sided die. At least three of them have rolled an even
number. What is the probability that John, Fred and Martin have each rolled
an even number? Express your answer as a common fraction.
Since "At least three of them have rolled an even number", let's do it one
step at a time.
If all 6 dices are even, there is only one way to do it and there is one way
the three brothers have all even.
If 5 dices are ev... 阅读全帖 |
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a*****g
发帖数: 1320 | 44
我也苯的可以，花了2小时才想明白第一题。第二，第三还在思考中。 |
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a*****g
发帖数: 1320 | 47 1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
COMMON FRACTION.
2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
FRACTION.
3.THE DIGITS 2,3, 4, 7 AND 8 ARE EACH USED ONCE TO FORM A FIVE DIGIT NUMBER
. WHAT IS THE PROBABILITY THAT THE TENS DIGIT IS ODD AND THE NUMBER IS
DIVISIBLE BY 4? EXPRESS YOUR ANSWER AS... 阅读全帖 |
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D*****r
发帖数: 6791 | 48 第一题：7/90. 10-99一共90个数，平方数6个（16，25，36，49，64，81），立方数2
个（27，64），其中64是公共的，所以概率是7/90
THE
NUMBER |
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s*******e
发帖数: 4188 | 50 这种情况是不是应该请专业辅导或是放弃数学竞赛? |
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