Difference between revisions of "2024 AMC 8"

(See also)
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* [[Mathematics competition resources]]
 
* [[Mathematics competition resources]]
 
* [[Math books]]
 
* [[Math books]]
Let <math>P</math> be the parabola with equation <math>y=ax^2+bx+c</math> and let <math>Q=(d,e).</math> There are real numbers <math>r</math> and <math>s</math> such that the line through <math>Q</math> with slope <math>m</math> does not intersect <math>P</math> if and only if <math>r<m<s.</math> What is <math>r+s</math>?
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Let <math>P</math> be the parabola with equation <math>y=ax^2+bx+c</math> and let <math>Q=(d,e)</math>. There are real numbers <math>r</math> and <math>s</math> such that the line through <math>Q</math> with slope <math>m</math> does not intersect <math>P</math> if and only if <math>r<m<s.</math> What is <math>r+s</math>?

Revision as of 01:04, 11 February 2024

2024 AMC 8 problems and solutions. The test is held from January 18th, 2024 to January 24th, 2024. The first link contains the full set of test problems. The second link contains the answer key. The rest contain each individual problem and its solution.


See also

2024 AMC 8 (Problems,Resources)
Preceded by
2023 AMC 8
AMC 8 Followed by
2025 AMC 8

Let $P$ be the parabola with equation $y=ax^2+bx+c$ and let $Q=(d,e)$. There are real numbers $r$ and $s$ such that the line through $Q$ with slope $m$ does not intersect $P$ if and only if $r<m<s.$ What is $r+s$?