2019年AMC 12B 真题:
Problem 1
Alicia had two containers. The first was full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was
full of water. What is the ratio of the volume of the first container to the volume of the second container?
Problem 2
Consider the statement, "If is not prime, then
is prime." Which of the following values of
is a counterexample to this statement?
Problem 3
Which one of the following rigid transformations (isometries) maps the line segment onto the line segment
so that the image of
is
and the image of
is
reflection in the
-axis
counterclockwise rotation around the origin by
translation by
units to the right and
units down
reflection in the
-axis
clockwise rotation about the origin by
Problem 4
A positive integer satisfies the equation
. What is the sum of the digits of
?
Problem 5
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either pieces of red candy,
pieces of green candy,
pieces of blue candy, or
pieces of purple candy. A piece of purple candy costs
cents. What is the smallest possible value of
?
Problem 6
In a given plane, points and
are
units apart. How many points
are there in the plane such that the perimeter of
is
units and the area of
is
square units?
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