Difference between revisions of "2022 AMC 12B Problems"
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==Problem 4 == | ==Problem 4 == | ||
− | + | For how many values of the constant <math>k</math> will the polynomial <math>x^{2}+kx+36</math> have two distinct integer roots? | |
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+ | <math>\textbf{(A) }6 \qquad \textbf{(B) }8 \qquad \textbf{(C) }9 \qquad \textbf{(D) }14 \qquad \textbf{(E) }16</math> | ||
[[2022 AMC 12B Problems/Problem 4|Solution]] | [[2022 AMC 12B Problems/Problem 4|Solution]] |
Revision as of 15:34, 17 November 2022
2022 AMC 12B (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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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
Problem 1
Define to be for all real numbers and . What is the value of
Problem 2
In rhombus , point lies on segment such that , , and . What is the area of ?
[asy] import olympiad; size(180); real r = 3, s = 5, t = sqrt(r*r+s*s); defaultpen(linewidth(0.6) + fontsize(10)); pair A = (0,0), B = (r,s), C = (r+t,s), D = (t,0), P = (r,0); draw(A--B--C--D--A^^B--P^^rightanglemark(B,P,D)); label("",A,SW); label("", B, NW); label("",C,NE); label("",D,SE); label("",P,S); [/asy]
Problem 3
How many of the first ten numbers of the sequence , , , ... are prime numbers?
Problem 4
For how many values of the constant will the polynomial have two distinct integer roots?
Problem 5
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Problem 6
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Problem 7
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Problem 8
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Problem 9
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Problem 10
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Problem 11
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Problem 12
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Problem 13
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Problem 14
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Problem 15
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Problem 16
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Problem 17
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Problem 18
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Problem 19
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Problem 20
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Problem 21
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Problem 22
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Problem 23
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Problem 24
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Problem 25
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