amc10数学竞赛真题中文

Problem 1

A scout troop buys candy bars at a price of five for $. They sell all the candy bars at a price of two for $. What was the profit, in dollars?

Solution

Problem 2

A positive number has the property that

of is . What is ?

Solution

Problem 3

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

Solution

Problem 4

For real numbers

and , d

Problem 1

A scout troop buys candy bars at a price of five for $. They sell all the candy bars at a price of two for $. What was the profit, in dollars?

Solution

Problem 2

A positive number has the property that

of is . What is ?

Solution

Problem 3

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

Solution

Problem 4

For real numbers

and , d

2003 AMC 10B

1、Which of the following is the same as

Solution

2、Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs more than a pink pill, and Al’s pills cost a total of for the two weeks. How much does one green pill cost?

Solution 3、The sum of 5 consecutive even integers is less than the sum of the ?rst consecutive odd counting numbers. What is the smallest of the even integers?

Solution 4、Rose fills each of the

美国数学竞赛AMC 10的常用数学英语单词

1. 有关数学运算 product 积 divide除

dividend被除数 quotient商 remainder余数

divisible可被整除的 divided evenly被整除 divisor因子，除数 factorial阶乘 power乘方

round to / to the nearest四舍五入

2. 有关集合 union并集

intersection 交集 proper subset真子集 solution set解集

3. 有关代数式、方程和不等式

algebraic term 代数项 similar terms同类项 literal coefficient字母系数

numerical coefficient数字系数 range值域

factorization因式分解 original equation原方程 equivalent equation同解方程，等价方程

linear equation线性方程 inequality不等式 4. 有关分数和小数 proper fraction 真分数 improp

2015 AMC 10A Problems Problem 1 What is the value of

Problem 2

A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?

Problem 3

Ann made a 3-step staircase using 18 toothpicks. How many toothpicks does she need to add to complete a 5-step staircase?

Problem 4

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some

. .. .

美国数学竞赛amc8的常用数学英语单词

数学mathematics, maths（BrE）, math（AmE）被除数pidend

除数pisor 商quotient 等于equals, is equal to, is equivalent to 大于is greater than

小于is lesser than

大于等于is equal or greater than

小于等于is equal or lesser than

运算符operator

数字digit

数number

自然数natural number

公理axiom

定理theorem

计算calculation

运算operation

证明prove

假设hypothesis, hypotheses（pl.）

命题proposition

算术arithmetic

加plus（prep.）, add（v.）, addition（n.）

被加数augend, summand

加数addend

i. .w.

. .. . 和sum

减minus（prep.）, subtract（v.）, subtraction（n.）

被减数minuend

减数subtrahend

差remainder

乘times（prep.）, m

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2015 AMC 10A 考题及答案

Problem 1 What is the value of

Problem 2

A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?

Problem 3

Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?

Problem 4

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as m

维普资讯

第 8朝

高中数学教与学

竞赛问题巾硇数学归纳法5平(江苏省南菁中学， 2 1 4 4 0 0 )

一

些较为复杂的与正整数有关的竞赛

“、 b有两种情况，即 a、 b全不等于 P,或 n, b

命题，我们可考虑用数学归纳法来证明，证明的关键在于我们要注意充分利用和灵活运用“归纳假设” .下面两个典型的例子可给我们一些启示.

中仅有一个为 .若 a, b全不等于 P,不妨设 a: P十a , b: P+a i,贝 0l n— b l: l ai~ a j 1 .

a+ b: 2 al a 2…a^+ ( a i+a j ),

由①,②易得，l a— b l l ( a+b ) . 若 a, b仅有一个为 P,不妨设 a= P, b:P+a i,则I a— b l:,

例1 求证：对任意的 n∈ N,≥ 2,都存在个互不相等的正整数组成的集合 M, 使得对任意的 n∈ M, b∈ M, I a—b l都可以整除 a+ b .

a+b= 2" al a2… a k+ a j

证明 ( 1 )当 n=2时，存在 M={ 1, 2} .

:a j ( 2 al a 2…a j~ 1 a j+ l…a^+ 1 )

由a, 6∈ M,易知，I a

论文中文标题中文副标题

研究生姓名：

姓 名 导 师 姓 名：

导师姓名 教授 副导师 副教授 申请学位类别 博士 学位授予单位 东南大学 一级学科名称控制理论与控制工程 论文答辩日期 答辩日期 二级学科名称 学位授予日期 学位授予日期 答辩委员会主席 评 阅 人 2012 年4 月18 日 论文中文标题 中文副标题 专 业 名 称：制理论与制工 研究生姓名：

姓 名 导 师 姓 名：

导师姓名 教授 导师 教授 本论文获国家XXX 计划项目（2012AA00A00）和国家杰出青年科学基金项目（01234567）资助。

Thesis Title subtitle A Dissertation submitted to Southeast University For the Academic Degree of Doctor of Engineering BY Author's Name Supervised by：

Prof. Advisor's Name and Associate Prof. Co-advisor's Name department name Southeast University April 18, 2012 东南大学博

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2015 AMC 10A 考题及答案

Problem 1 What is the value of

Problem 2

A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?

Problem 3

Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?

Problem 4

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as m