Difference between revisions of "2022 AMC 10B Problems"
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==Problem 6 == | ==Problem 6 == | ||
− | How many of the first ten numbers of the sequence <math>121, 11211, 1112111, \ | + | How many of the first ten numbers of the sequence <math>121, 11211, 1112111, \ldots</math> are prime numbers? |
<math>\textbf{(A) } 0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4</math> | <math>\textbf{(A) } 0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4</math> |
Revision as of 15:48, 17 November 2022
2022 AMC 10B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
| ||
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 |
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
Define to be
for all real numbers
and
What is the value of
Problem 2
XXX
Problem 3
How many three-digit positive integers have an odd number of even digits?
Problem 4
A donkey suffers an attack of hiccups and the first hiccup happens at one afternoon. Suppose that
the donkey hiccups regularly every
seconds. At what time does the donkey’s
th hiccup occur?
Problem 5
What is the value of
Problem 6
How many of the first ten numbers of the sequence are prime numbers?
Problem 7
XXX
Problem 8
Consider the following sets of
elements each:
How many of these sets contain exactly two multiples of ?
Problem 9
The sum
can be expressed as
, where
and
are positive integers. What is
?
Problem 10
XXX
Problem 11
XXX
Problem 12
A pair of fair -sided dice is rolled
times. What is the least value of
such that the probability that the sum of the numbers face up on a roll equals
at least once is greater than
?
Problem 13
XXX
Problem 14
Suppose that is a subset of
such that the sum of any two (not necessarily distinct) elements of
is never an element of
. What is the maximum number of elements
may contain?
Problem 15
XXX
Problem 16
XXX
Problem 17
XXX
Problem 18
XXX
Problem 19
XXX
Problem 20
Let be a rhombus with
. Let
be the midpoint of
, and let
be the point on
such that
is perpendicular to
. What is the degree measure of
?
Problem 21
XXX
Problem 22
Let be the set of circles in the coordinate plane that are tangent to each of the three circles with equations
,
, and
. What is the sum of the areas of all circles in
?
Problem 23
Ant Amelia starts on the number line at and crawls in the following manner. For
Amelia chooses a time duration
and an increment
independently and uniformly at random from the interval
During the
th step of the process, Amelia moves
units in the positive direction, using up
minutes. If the total elapsed time has exceeded
minute during the
th step, she stops at the end of that step; otherwise, she continues with the next step, taking at most
steps in all. What is the probability that Amelia’s position when she stops will be greater than
?
Problem 24
XXX
Problem 25
XXX
See also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by 2021 Fall AMC 10B Problems |
Followed by 2023 AMC 10B Problems | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.