2024年AMC 12A 真题:
Problem 1
What is the value of
Problem 2
A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form where and are constants, is the time in minutes, is the length of the trail in miles, and is the altitude gain in feet. The model estimates that it will take minutes to hike to the top if a trail is miles long and ascends feet, as well as if a trail is miles long and ascends feet. How many minutes does the model estimates it will take to hike to the top if the trail is miles long and ascends feet?
Problem 3
The number is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?
Problem 4
What is the least value of such that is a multiple of ?
Problem 5
A data set containing numbers, some of which are , has mean . When all the 6s are removed, the data set has mean . How many 6s were in the original data set?
Problem 6
The product of three integers is . What is the least possible positive sum of the three integers?
Problem 7
In , and . Points lie on hypotenuse so that . What is the length of the vector sum
Problem 8
How many angles with satisfy ?
Problem 9
Let be the greatest integer such that both and are perfect squares. What is the units digit of ?
Problem 10
Let be the radian measure of the smallest angle in a right triangle. Let be the radian measure of the smallest angle in a right triangle. In terms of , what is ?
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