2021 MECC Mock AMC 10
Contents
[hide]Problem 1
Compute
Problem 2
Define a binary operation . Find the number of possible ordered pair of positive integers
such that
.
Problem 3
can be expressed as
. Find
.
Problem 4
Compute the number of ways to arrange 2 distinguishable apples and five indistinguishable books.
Problem 5
Galieo, Neton, Timiel, Fidgety and Jay are participants of a game in soccer. Their coach, Mr.Tom, will allocate them into two INDISTINGUISHABLE groups for practice purpose(People in the teams are interchangable). Given that the coach will not put Galieo and Timiel into the same team because they just had a fight. Find the number of ways the coach can put them into two such groups.
Problem 6
Let be a sequence of positive integers with
and
and
for all integers
such that
. Find
.
Problem 7
Find the sum of all the solutions of , where
can be any number. The roots may be repeated.
Problem 8
Define the number of real numbers
such that
is a perfect square. Find
.
Problem 9
A unit cube ABCDEFGH is shown below. is reflected across the plane that contains line
and line
. Then, it is reflected again across the plane that contains line
and
. Call the new point
. Find
.
Problem 10
Find the number of nonempty subsets of such that the product of all the numbers in the subset is NOT divisible by
.
Problem 11
In square with side length
, point
and
are on side
and
respectively, such that
is perpendicular to
and
. Find the area enclosed by the quadrilateral
.
Problem 12
Given that ,
, and
, find
.
Problem 13
Let be a
term sequence of positive integers such that
,
,
,
,
. Find the number of such sequences
such that all of
.