2024年4月3日发(作者：)

Problem 3

What is the value of the expression ?

化简的标准和顺序

Problem 6

If the degree measures of the angles of a triangle are in the ratio

degree measure of the largest angle of the triangle?

角度制与弧度制

Problem 7

Let be a 6-digit positive integer, such as 247247, whose first three digits are the

same as its last three digits taken in the same order. Which of the following numbers

must also be a factor of ?

整除特征

Problem 10

A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected

randomly without replacement from the box. What is the probability that 4 is the

largest value selected?

离散概率

Problem 11

, what is the

A square-shaped floor is covered with congruent square tiles. If the total number of

tiles that lie on the two diagonals is 37, how many tiles cover the floor?

tiles

n.

英

[taɪlz]

美

[taɪlz]

瓦片，瓷砖( tile的名词复数 ); 扁平的小棋子;

Problem 13

Peter, Emma, and Kyler played chess with each other. Peter won 4 games and lost

2 games. Emma won 3 games and lost 3 games. If Kyler lost 3 games, how many

games did he win?

Problem 14

Chloe and Zoe are both students in Ms. Demeanor's math class. Last night they each

solved half of the problems in their homework assignment alone and then solved the

other half together. Chloe had correct answers to only

alone, but overall

to

of the problems she solved

of her answers were correct. Zoe had correct answers

of the problems she solved alone. What was Zoe's overall percentage of correct

answers? C

设数

Problem 15

In the arrangement of letters and numerals below, by how many different paths can

one spell AMC8? Beginning at the A in the middle, a path allows only moves from one

letter to an adjacent (above, below, left, or right, but not diagonal) letter. One

example of such a path is traced in the picture.

乘法原理加法原理

Problem 16

In the figure below, choose point on so that and

have equal

perimeters. What is the area of ?

D如果在AC上呢

Problem 17

Starting with some gold coins and some empty treasure chests, I tried to put 9 gold

coins in each treasure chest, but that left 2 treasure chests empty. So instead I put

6 gold coins in each treasure chest, but then I had 3 gold coins left over. How many

gold coins did I have?

盈亏问题 图示法

Problem 18

In the non-convex quadrilateral shown below, is a right

angle, , , , and

?

.

What is the area of quadrilateral

勾股定理与逆定理 “凸”定义

Problem 19

For any positive integer

integers through

sum

, the notation denotes the product of the

is a factor of the . What is the largest integer for which

?

Problem 20

An integer between and , inclusive, is chosen at random. What is the

probability that it is an odd integer whose digits are all distinct?

5*8*8*7

Problem 21

Suppose , , and are nonzero real numbers, and

possible value(s) for ?

. What are the

可能性列全 或者变个形

Problem 22

In the right triangle , , , and angle is a right angle. A

semicircle is inscribed in the triangle as shown. What is the radius of the semicircle?

相切，连接切点和圆心。或者连心线。切线长定理。

Problem 23

Each day for four days, Linda traveled for one hour at a speed that resulted in her

traveling one mile in an integer number of minutes. Each day after the first, her speed

decreased so that the number of minutes to travel one mile increased by 5 minutes

over the preceding day. Each of the four days, her distance traveled was also an

integer number of miles. What was the total number of miles for the four trips?

Problem 24

Mrs. Sanders has three grandchildren, who call her regularly. One calls her every

three days, one calls her every four days, and one calls her every five days. All three

called her on December 31, 2016. On how many days during the next year did she

not receive a phone call from any of her grandchildren?

容斥原理

Problem 25

In the figure shown,

and

and are line segments each of length 2,

are each one-sixth of a circle with radius 2. . Arcs and

What is the area of the region shown?

segments

英

[seɡ'mənts]

n.

美

[seɡ'mənts]

部分( segment的名词复数 ); 瓣; [计算机] （字符等的） 分段; [动物学] 节片;

弧度制 弧的表示法 补全图形即可

Problem 6

The following bar graph represents the length (in letters) of the names of 19 people.

What is the median length of these

names?

众数 中位数

众数

[词典] [统] mode;

Problem 7

Which of the following numbers is not a perfect square?

Problem 11

Determine how many two-digit numbers satisfy the following property: when the

number is added to the number obtained by reversing its digits, the sum is

Problem 13

Two different numbers are randomly selected from the set

multiplied together. What is the probability that the product is ?

集合的概念与表示方法

1.列举法：常用于表示有限集合，把集合中的所有元素一一列举出来，写在大括号内，这种表示

集合的方法叫做列举法。{1，2，3，……}

2.描述法：常用于表示无限集合，把集合中元素的公共属性用文字，符号或式子等描述出来，写

在大括号内，这种表示集合的方法叫做描述法。{x|P}（x为该集合的元素的一般形式，P为这个

集合的元素的共同属性）如：小于π的正实数组成的集合表示为：{x|0

3.图示法（Venn图）：为了形象表示集合，我们常常画一条封闭的曲线（或者说圆圈），用它

的内部表示一个集合。

4.自然语言（不常用）

Problem 15

What is the largest power of that is a divisor of

平方差公式 把4改成1024试试

?

and

Problem 18

In an All-Area track meet, sprinters enter a meter dash competition. The

track has lanes, so only sprinters can compete at a time. At the end of each race,

the five non-winners are eliminated, and the winner will compete again in a later

race. How many races are needed to determine the champion sprinter?

列式

Problem 19

The sum of

these

consecutive even integers is . What is the largest of

consecutive integers?

Problem 20

The least common multiple of and is

of and is

of and ?

Lcm简写 用特值法

Problem 21

A top hat contains 3 red chips and 2 green chips. Chips are drawn randomly, one at

a time without replacement, until all 3 of the reds are drawn or until both green chips

are drawn. What is the probability that the 3 reds are drawn?

折线法

, and the least common multiple

. What is the least possible value of the least common multiple