Difference between revisions of "User:Geometry285"

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<math>\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 15</math>
 
<math>\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 15</math>
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[[G285 MC10A Problems/Problem 2|Solution]]
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==Problem 3==
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Let <math>ABCD</math> be a unit square. If points <math>E</math> and <math>F</math> are chosen on <math>AB</math> and <math>CD</math> respectively such that the area of <math>\triangle AEF = \frac{3}{2} \triangle CFE</math>. What is <math>EF^2</math>?
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<math>\textbf{(A)}\ \frac{13}{9}\qquad\textbf{(B)}\ \frac{8}{9}\qquad\textbf{(C)}\ \frac{37}{36}\qquad\textbf{(D)}\ \frac{5}{4}\qquad\textbf{(E)}\ \frac{13}{36}</math>

Revision as of 11:58, 11 May 2021

Posting here until I find a place for an upcoming mock I’m creating

Template:G285 Mock Problems

Problem 1

What value of $x$ minimizes $|2^x - 1|$?

$\textbf{(A)}\ -1\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \infty$

Solution

Problem 2

Suppose Mark wanted to arrange $5$ books onto a bookshelf, $3$ of which are math books and $2$ of which are science. If both science and math books are indistinguishable, in how many ways can Mark arrange the books on the shelf?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 15$

Solution

Problem 3

Let $ABCD$ be a unit square. If points $E$ and $F$ are chosen on $AB$ and $CD$ respectively such that the area of $\triangle AEF = \frac{3}{2} \triangle CFE$. What is $EF^2$?

$\textbf{(A)}\ \frac{13}{9}\qquad\textbf{(B)}\ \frac{8}{9}\qquad\textbf{(C)}\ \frac{37}{36}\qquad\textbf{(D)}\ \frac{5}{4}\qquad\textbf{(E)}\ \frac{13}{36}$

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