2024年4月11日发(作者：数学试卷泄露事件分析怎么写)

2003 AMC 10A

1、What is the difference between the sum of the first even

counting numbers and the sum of the first odd counting numbers?

Solution

The first

The first

Thus, the

even counting numbers are

odd counting numbers are

problem is asking for

.

.

.

the value of

.

Alternatively, using the sum of an arithmetic progression formula, we

can write .

2、Members of the Rockham Soccer League buy socks and T-shirts.

Socks cost per pair and each T-shirt costs more than a pair of

socks. Each member needs one pair of socks and a shirt for home

games and another pair of socks and a shirt for away games. If the

total cost is , how many members are in the League?

Solution

Since T-shirts cost dollars more than a pair of socks, T-shirts cost

dollars.

Since each member needs pairs of socks and T-shirts, the total cost

for member is

Since

dollars.

was the cost per

.

dollars was the cost for the club, and

member, the number of members in the League is

- 1 -

3、A solid box is cm by cm by cm. A new solid is formed by

removing a cube cm on a side from each corner of this box. What

percent of the original volume is removed?

Solution

The volume of the original box is

The volume of each cube that is removed is

Since there are corners on the box, cubes are removed.

So the total volume removed is

Therefore, the desired percentage is

.

.

4、It takes Mary minutes to walk uphill km from her home to

school, but it takes her only minutes to walk from school to home

along the same route. What is her average speed, in km/hr, for the

round trip?

Solution

Since she walked km to school and km back home, her total

distance is km.

Since she spent minutes walking to school and

minutes =

minutes walking

hours. back home, her total time is

Therefore her average speed in km/hr is

5、Let and denote the solutions of

value of

Solution

Using factoring:

- 2 -

. What is the

?


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