2024年1月22日发(作者：幼儿园上中下数学试卷题)

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?

tilesn.

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

Problem 23

Two congruent circles centered at points and each pass through the other

circle\'s center. The line containing both and is extended to intersect the circles

at points and . The circles intersect at two points, one of which is . What is the

?

同余全等都是这个词

Problem 25

A semicircle is inscribed in an isosceles triangle with base and height so that the

degree measure of

diameter of the semicircle is contained in the base of the triangle as shown. What is

the radius of the semicircle?

三线合一 圆心连切点都是好辅助线

Problem 2

Point is the center of the regular octagon

of the side

, and is the midpoint

What fraction of the area of the octagon is shaded?

Problem 5

Billy\'s basketball team scored the following points over the course of the

first games of the season:If his team scores 40

in the 12th game, which of the following statistics will show an increase?

极差又称范围误差或全距(Range)，以R表示，是用来表示统计资料中的变异量数(measures of variation)，其最大值与最小值之间的差距，

The mid-range is the midpoint of the range，两个最值的平均。

Problem 6

In , , and . What is the area of

Problem 7

Each of two boxes contains three chips numbered , , . A chip is drawn randomly

from each box and the numbers on the two chips are multiplied. What is the

probability that their product is even?

列一下所有情况

Problem 12

?

How many pairs of parallel edges, such as

have?

and or and , does a cube

Problem 14

Which of the following integers cannot be written as the sum of four consecutive odd

integers?

Problem 18

Each row and each column in this

terms. What is the value of x?

array is an arithmetic sequence with five

算术级数 几何级数 算术数列 几何数列

Problem 20

Ralph went to the store and bought

socks he bought cost

pairs of socks for a total of . Some of the

a pair, some of the socks he bought cost a pair, and some

of the socks he bought cost

many pairs of

a pair. If he bought at least one pair of each type, how

socks did Ralph buy?

不定方程 凑数

Problem 23

Tom has twelve slips of paper which he wants to put into five cups

labeled , , , , . He wants the sum of the numbers on the slips in each cup to

be an integer. Furthermore, he wants the five integers to be consecutive and

increasing from to . The numbers on the papers

are and . If a slip with goes into cup and a slip

must go into what cup?

The numbers have a sum of , which averages to , which means

will have values , respectively. Now it\'s process of elimination: Cup

will have a sum of , so putting a slip in the cup will leave ; However, all

of our slips are bigger than , so this is impossible. Cup has a sum of , but we are told

that it already has a slip, leaving , which is too small for the slip. Cup is a

little bit trickier, but still manageable. It must have a value of , so adding the slip leaves

room for . This looks good at first, as we do have slips smaller than that, but

upon closer inspection, we see that no slip fits exactly, and the smallest sum of two slips is

, which is too big, so this case is also impossible. Cup has a sum of , but we

are told it already has a slip, so we are left with , which is identical to the Cup C

case, and thus also impossible. With all other choices removed, we are left with the answer:

Cup

with goes into cup , then the slip with

Problem 24

A baseball league consists of two four-team divisions. Each team plays every other

team in its division games. Each team plays every team in the other

division games with and . Each team plays a -game schedule.

How many games does a team play within its own division?

M模3余1，简化计算。

Problem 25

One-inch squares are cut from the corners of this inch square. What is the area in

square inches of the largest square that can fit into the remaining space?

Problem 11

Jack wants to bike from his house to Jill\'s house, which is located three blocks east and

two blocks north of Jack\'s house. After biking each block, Jack can continue either east

or north, but he needs to avoid a dangerous intersection one block east and one block

north of his house. In how many ways can he reach Jill\'s house by biking a total of five

blocks?

要看出这是一道折线问题

Problem 12

A magazine printed photos of three celebrities along with three photos of the

celebrities as babies. The baby pictures did not identify the celebrities. Readers were

asked to match each celebrity with the correct baby pictures. What is the probability

that a reader guessing at random will match all three correctly?

Problem 15

The circumference of the circle with center is divided into 12 equal arcs, marked

the letters through as seen below. What is the number of degrees in the sum of

the angles and ?

Problem 17

George walks mile to school. He leaves home at the same time each day, walks at a

steady speed of miles per hour, and arrives just as school begins. Today he was

distracted by the pleasant weather and walked the first mile at a speed of

only miles per hour. At how many miles per hour must George run the last mile

in order to arrive just as school begins today?

能做对不讲

Problem 18

Four children were born at City Hospital yesterday. Assume each child is equally likely

to be a boy or a girl. Which of the following outcomes is most likely?

all 4 are boys all 4 are girls 2 are girls and 2 are boys 3 are of one

gender and 1 is of the other gender

Problem 22

all of these outcomes are equally likely

A 2-digit number is such that the product of the digits plus the sum of the digits is

equal to the number. What is the units digit of the number?

Problem 23

Three members of the Euclid Middle School girls\' softball team had the following

conversation.

Ashley: I just realized that our uniform numbers are all 2-digit primes.

Bethany: And the sum of your two uniform numbers is the date of my birthday earlier

this month.

Caitlin: That\'s funny. The sum of your two uniform numbers is the date of my

birthday later this month.

Ashley: And the sum of your two uniform numbers is today\'s date.

What number does Caitlin wear?

The maximum amount of days any given month can have is 31, and the smallest two digit

primes are 11, 13, and 17. There are a few different sums that can be deduced from the

following numbers, which are 24, 30, and 28, all of which represent the three days. Therefore,

since Brittany says that the other two people\'s uniform numbers are earlier, so that means

Caitlin and Ashley\'s numbers must add up to 24. Similarly, Caitlin says that the other two

people\'s uniform numbers is later, so the sum must add up to 30. This leaves 28 as today\'s

date. From this, Caitlin was referring to the uniform wearers 13 and 17, telling us that her

number is 11, giving our solution as

Problem 24

One day the Beverage Barn sold 252 cans of soda to 100 customers, and every

customer bought at least one can of soda. What is the maximum possible median

number of cans of soda bought per customer on that day?

In order to maximize the median, we need to make the first half of the numbers as small as

possible. Since there are people, the median will be the average of the and

largest amount of cans per person. To minimize the first 49, they would each have one can.

Subtracting these cans from the cans gives us cans left to divide among

people. Taking gives us and a remainder of . Seeing this, the largest number of

cans the person could have is , which leaves to the rest of the people. The average

of and is . Thus our answer is


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