Difference between revisions of "2023 AMC 8 Problems"
MRENTHUSIASM (talk | contribs) (→Problem 20) |
MRENTHUSIASM (talk | contribs) |
||
Line 3: | Line 3: | ||
==Problem 1== | ==Problem 1== | ||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
[[2023 AMC 8 Problems/Problem 1|Solution]] | [[2023 AMC 8 Problems/Problem 1|Solution]] | ||
==Problem 2== | ==Problem 2== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 2|Solution]] | [[2023 AMC 8 Problems/Problem 2|Solution]] | ||
==Problem 3== | ==Problem 3== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 3|Solution]] | [[2023 AMC 8 Problems/Problem 3|Solution]] | ||
==Problem 4== | ==Problem 4== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 4|Solution]] | [[2023 AMC 8 Problems/Problem 4|Solution]] | ||
==Problem 5== | ==Problem 5== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 5|Solution]] | [[2023 AMC 8 Problems/Problem 5|Solution]] | ||
==Problem 6== | ==Problem 6== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 6|Solution]] | [[2023 AMC 8 Problems/Problem 6|Solution]] | ||
==Problem 7== | ==Problem 7== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 7|Solution]] | [[2023 AMC 8 Problems/Problem 7|Solution]] | ||
==Problem 8== | ==Problem 8== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 8|Solution]] | [[2023 AMC 8 Problems/Problem 8|Solution]] | ||
==Problem 9== | ==Problem 9== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 9|Solution]] | [[2023 AMC 8 Problems/Problem 9|Solution]] | ||
==Problem 10== | ==Problem 10== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 10|Solution]] | [[2023 AMC 8 Problems/Problem 10|Solution]] | ||
==Problem 11== | ==Problem 11== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 11|Solution]] | [[2023 AMC 8 Problems/Problem 11|Solution]] | ||
==Problem 12== | ==Problem 12== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 12|Solution]] | [[2023 AMC 8 Problems/Problem 12|Solution]] | ||
==Problem 13== | ==Problem 13== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 13|Solution]] | [[2023 AMC 8 Problems/Problem 13|Solution]] | ||
==Problem 14== | ==Problem 14== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 14|Solution]] | [[2023 AMC 8 Problems/Problem 14|Solution]] | ||
==Problem 15== | ==Problem 15== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 15|Solution]] | [[2023 AMC 8 Problems/Problem 15|Solution]] | ||
==Problem 16== | ==Problem 16== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 16|Solution]] | [[2023 AMC 8 Problems/Problem 16|Solution]] | ||
==Problem 17== | ==Problem 17== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 17|Solution]] | [[2023 AMC 8 Problems/Problem 17|Solution]] | ||
==Problem 18== | ==Problem 18== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 18|Solution]] | [[2023 AMC 8 Problems/Problem 18|Solution]] | ||
==Problem 19== | ==Problem 19== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 19|Solution]] | [[2023 AMC 8 Problems/Problem 19|Solution]] | ||
Line 69: | Line 124: | ||
==Problem 21== | ==Problem 21== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 21|Solution]] | [[2023 AMC 8 Problems/Problem 21|Solution]] | ||
Line 87: | Line 145: | ||
[insert asy] | [insert asy] | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
[[2023 AMC 8 Problems/Problem 23|Solution]] | [[2023 AMC 8 Problems/Problem 23|Solution]] | ||
==Problem 24== | ==Problem 24== | ||
+ | |||
+ | <math>\textbf{(A)}\ X \qquad \textbf{(B)}\ X \qquad \textbf{(C)}\ X \qquad \textbf{(D)}\ X \qquad \textbf{(E)}\ X</math> | ||
+ | |||
[[2023 AMC 8 Problems/Problem 24|Solution]] | [[2023 AMC 8 Problems/Problem 24|Solution]] | ||
Line 99: | Line 162: | ||
What is the sum of digits of <math>a_{14}</math>? | What is the sum of digits of <math>a_{14}</math>? | ||
− | <math>\textbf{(A)} | + | <math>\textbf{(A)}\ 8 \qquad \textbf{(B)}\ 9 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 11 \qquad \textbf{(E)}\ 12</math> |
[[2023 AMC 8 Problems/Problem 25|Solution]] | [[2023 AMC 8 Problems/Problem 25|Solution]] |
Revision as of 18:28, 24 January 2023
2023 AMC 8 (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
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Two integers are inserted into the list to double it's range. The mode and median remain unchanged. What is the maximum possible sum of two additional numbers?
Problem 21
Problem 22
In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term is . What is the first term?
Problem 23
Each square in a 3x3 grid is randomly filled with one of the 4 gray-and-white tiles as shown below.
[insert asy]
What is the probability that the tiling will contain a large gray diamond in one of the smaller 2x2 grids? Below is such a tiling
[insert asy]
Problem 24
Problem 25
Fifteen integers are arranged in order on a number line. The integers are equally spaced and have the property that What is the sum of digits of ?
See Also
2023 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by 2022 AMC 8 |
Followed by 2024 AMC 8 | |
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 AJHSME/AMC 8 Problems and Solutions |