Difference between revisions of "2021 AMC 12B Problems"
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==Problem 8== | ==Problem 8== | ||
− | + | Three equally spaced parallel lines intersect a circle, creating three chords of lengths <math>38,38,</math> and <math>34</math>. What is the distance between two adjacent parallel lines? | |
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+ | <math>\textbf{(A) }5\frac12 \qquad \textbf{(B) }6 \qquad \textbf{(C) }6\frac12 \qquad \textbf{(D) }7 \qquad \textbf{(E) }7\frac12</math> | ||
[[2021 AMC 12B Problems/Problem 8|Solution]] | [[2021 AMC 12B Problems/Problem 8|Solution]] |
Revision as of 15:47, 11 February 2021
2021 AMC 12B (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
How many integer values of satisfy
Problem 2
At a math contest, students are wearing blue shirts, and another
students are wearing yellow shirts. The
students are assigned into
points. In exactly
of these pairs, both students are wearing blue shirts. In how many pairs are both studets wearing yellow shirts?
Problem 3
SupposeWhat is the value of
Problem 4
Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is , and the afternoon class's mean score is
. The ratio of the number of students in the morning clas to the number of students in the afternoon class is
. What is the mean of the score of all the students?
Problem 5
The point in the
-plane is first rotated counterclockwise by
around the point
and then reflected about the line
. The image of
after these two transformations is at
. What is
Problem 6
An inverted cone with base radius and height
is full of water. The water is poured into a tall cylinder whose horizontal base has a radius of
. What is the height in centimeters of the water in the cylinder?
Problem 7
Let What is the ratio of the sum of the odd divisors of
to the sum of the even divisors of
Problem 8
Three equally spaced parallel lines intersect a circle, creating three chords of lengths and
. What is the distance between two adjacent parallel lines?
Problem 9
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 10
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 11
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 12
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 13
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 14
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 15
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 16
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 17
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 18
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 19
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 20
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 21
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 22
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 23
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 24
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
Problem 25
These problems will not be posted until the 2021 AMC 12B is released on Wednesday, February 10, 2021.
See also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by 2021 AMC 12A Problems |
Followed by 2022 AMC 12A 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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.