Difference between revisions of "2024 AMC 10A Problems"
MRENTHUSIASM (talk | contribs) (I am copying and pasting 2023 AMC 10A problems here. Now edit procedurally.) |
MRENTHUSIASM (talk | contribs) |
||
Line 3: | Line 3: | ||
==Problem 1== | ==Problem 1== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 1|Solution]] |
==Problem 2== | ==Problem 2== | ||
− | + | XXX | |
− | <math>\textbf{(A) | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 2|Solution]] |
==Problem 3== | ==Problem 3== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 3|Solution]] |
==Problem 4== | ==Problem 4== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 4|Solution]] |
==Problem 5== | ==Problem 5== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 5|Solution]] |
==Problem 6== | ==Problem 6== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 6|Solution]] |
==Problem 7== | ==Problem 7== | ||
− | + | XXX | |
− | <math>\textbf{(A) | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 7|Solution]] |
==Problem 8== | ==Problem 8== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 8|Solution]] |
==Problem 9== | ==Problem 9== | ||
− | + | XXX | |
− | <math>\textbf{(A)} | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 9|Solution]] |
==Problem 10== | ==Problem 10== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 10|Solution]] |
==Problem 11== | ==Problem 11== | ||
− | + | XXX | |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 11|Solution]] |
==Problem 12== | ==Problem 12== | ||
− | + | XXX | |
− | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> | |
− | + | [[2024 AMC 10A Problems/Problem 12|Solution]] | |
− | |||
− | |||
− | |||
− | [[ | ||
==Problem 13== | ==Problem 13== | ||
− | + | XXX | |
− | <math>\textbf{(A) } | + | <math>\textbf{(A) }\qquad\textbf{(B) }\qquad\textbf{(C) }\qquad\textbf{(D) }\qquad\textbf{(E) }</math> |
− | [[ | + | [[2024 AMC 10A Problems/Problem 13|Solution]] |
==Problem 14== | ==Problem 14== |
Revision as of 15:02, 8 November 2024
2024 AMC 10A (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
[hide]- 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
XXX
Problem 2
XXX
Problem 3
XXX
Problem 4
XXX
Problem 5
XXX
Problem 6
XXX
Problem 7
XXX
Problem 8
XXX
Problem 9
XXX
Problem 10
XXX
Problem 11
XXX
Problem 12
XXX
Problem 13
XXX
Problem 14
A number is chosen at random from among the first positive integers, and a positive integer divisor of that number is then chosen at random. What is the probability that the chosen divisor is divisible by
?
Problem 15
An even number of circles are nested, starting with a radius of and increasing by
each time, all sharing a common point. The region between every other circle is shaded, starting with the region inside the circle of radius
but outside the circle of radius
An example showing
circles is displayed below. What is the least number of circles needed to make the total shaded area at least
?
Problem 16
In a table tennis tournament every participant played every other participant exactly once. Although there were twice as many right-handed players as left-handed players, the number of games won by left-handed players was more than the number of games won by right-handed players. (There were no ties and no ambidextrous players.) What is the total number of games played?
Problem 17
Let be a rectangle with
and
. Point
and
lie on
and
respectively so that all sides of
and
have integer lengths. What is the perimeter of
?
Problem 18
A rhombic dodecahedron is a solid with congruent rhombus faces. At every vertex,
or
edges meet, depending on the vertex. How many vertices have exactly
edges meet?
Problem 19
The line segment formed by and
is rotated to the line segment formed by
and
about the point
. What is
?
Problem 20
Each square in a grid of squares is colored red, white, blue, or green so that every
square contains one square of each color. One such coloring is shown on the right below. How many different colorings are possible?
Problem 21
Let be the unique polynomial of minimal degree with the following properties:
has a leading coefficient
,
is a root of
,
is a root of
,
is a root of
, and
is a root of
.
The roots of are integers, with one exception. The root that is not an integer can be written as
, where
and
are relatively prime integers. What is
?
Problem 22
Circle and
each have radius
, and the distance between their centers is
. Circle
is the largest circle internally tangent to both
and
. Circle
is internally tangent to both
and
and externally tangent to
. What is the radius of
?
Problem 23
If the positive integer has positive integer divisors
and
with
, then
and
are said to be
divisors of
. Suppose that
is a positive integer that has one complementary pair of divisors that differ by
and another pair of complementary divisors that differ by
. What is the sum of the digits of
?
Problem 24
Six regular hexagonal blocks of side length unit are arranged inside a regular hexagonal frame. Each block lies along an inside edge of the frame and is aligned with two other blocks, as shown in the figure below. The distance from any corner of the frame to the nearest vertex of a block is
unit. What is the area of the region inside the frame not occupied by the blocks?
Problem 25
If and
are vertices of a polyhedron, define the distance
to be the minimum number of edges of the polyhedron one must traverse in order to connect
and
. For example,
is an edge of the polyhedron, then
, but if
and
are edges and
is not an edge, then
. Let
,
, and
be randomly chosen distinct vertices of a regular icosahedron (regular polyhedron made up of
equilateral triangles). What is the probability that
?
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by 2023 AMC 10B Problems |
Followed by 2024 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 |