2019年AMC 10B 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
In a high school with students,
of the seniors play a musical instrument, while
of the non-seniors do not play a musical instrument. In all,
of the students do not play a musical instrument. How many non-seniors play a musical instrument?
Problem 4
All lines with equation such that
form an arithmetic progression pass through a common point. What are the coordinates of that point?
Problem 5
Triangle lies in the first quadrant. Points
,
, and
are reflected across the line
to points
,
, and
, respectively. Assume that none of the vertices of the triangle lie on the line
. Which of the following statements is not always true?
Triangle
lies in the first quadrant.
Triangles
and
have the same area.
The slope of line
is
.
The slopes of lines
and
are the same.
Lines
and
are perpendicular to each other.
Problem 6
There is a real such that
. What is the sum of the digits of
?
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