2024年4月11日发(作者：高考2000真题数学试卷)

USA AMC 10 2001

1

The median of the list

is

mean?

Solution

2

A number is more than the product of its reciprocal and its additive

inverse. In which interval does the number lie?

Solution

3

The sum of two numbers is . Suppose 3 is added to each number

and then each of the resulting numbers is doubled. What is the sum of

the final two numbers?

Solution

4

What is the maximum number of possible points of intersection of a

circle and a triangle?

Solution

5

How many of the twelve pentominoes pictured below have at least

one line of symettry?

. What is the

Solution

6

Let and denote the product and the sum, respectively, of the

and . Suppose

. What is the units

digits of the integer . For example,

is a two-digit number such that

digit of

?

Solution

7

When the decimal point of a certain positive decimal number is moved

four places to the right, the new number is four times the reciprocal of

the original number. What is the original number?

Solution

8

Wanda, Darren, Beatrice, and Chi are tutors in the school math lab.

Their schedule is as follows: Darren works every third school day,

Wanda works every fourth school day, Beatrice works every sixth

school day, and Chi works every seventh school day. Today they are

all working in the math lab. In how many school days from today will

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they next be together tutoring in the lab?

Solution

9

The state income tax where Kristin lives is levied at the rate of

the first of annual income plus

of

of any amount above

. Kristin noticed that the state income tax she paid amounted to

of her annual income. What was her annual income?

Solution

10

If , , and are positive with

is

Solution

11

Consider the dark square in an array of unit squares, part of which is

shown. The first ring of squares around this center square contains

unit squares. The second ring contains unit squares. If we continue

this process, the number of unit squares in the ring is

, , and , then

Solution

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12

Suppose that is the product of three consecutive integers and that

is divisible by . Which of the following is not necessarily a divisor of

Solution

13

A telephone number has the form , where each

letter represents a different digit. The digits in each part of the

numbers are in decreasing order; that is, , , and

. Furthermore, , , and are consecutive even

digits; , , , and are consecutive odd digits; and .

Find .

Solution

14

A charity sells 140 benefit tickets for a total of . Some tickets sell

for full price (a whole dollar amount), and the rest sells for half price.

How much money is raised by the full-price tickets?

Solution

15

A street has parallel curbs feet apart. A crosswalk bounded by two

parallel stripes crosses the street at an angle. The length of the curb

between the stripes is feet and each stripe is feet long. Find the

distance, in feet, between the stripes.

Solution

16

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The mean of three numbers is 10 more than the least of the numbers

and 15 less than the greatest. The median of the three numbers is 5.

What is their sum?

Solution

17

Which of the cones listed below can be formed from a

circle of radius by aligning the two straight sides?

sector of a

A cone with slant height of

A cone with height of

and radius

and radius

and radius A cone with slant height of

A cone with height of and radius

and radius A cone with slant height of

Solution

18

The plane is tiled by congruent squares and congruent pentagons as

indicated. The percent of the plane that is enclosed by the pentagons

is closest to

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Solution

19

Pat wants to buy four donuts from an ample supply of three types of

donuts: glazed, chocolate, and powdered. How many different

selections are possible?

Solution

20

A regular octagon is formed by cutting an isosceles right triangle from

each of the corners of a square with sides of length . What is the

length of each side of the octagon?

Solution

21

A right circular cylinder with its diameter equal to its height is

inscribed in a right circular cone. The cone has diameter and

altitude , and the axes of the cylinder and cone coincide. Find the

radius of the cylinder.

Solution

22

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In the magic square shown, the sums of the numbers in each row,

column, and diagonal are the same. Five of these numbers are

represented by , , , , and . Find .

Solution

23

A box contains exactly five chips, three red and two white. Chips are

randomly removed one at a time without replacement until all the red

chips are drawn or all the white chips are drawn. What is the

probability that the last chip drawn is white?

Solution

24

In trapezoid

,

Solution

25

How many positive integers not exceeding

but not ?

, and are perpendicular to , with

, and . What is ?

are multiples of or

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