Difference between revisions of "2015 AMC 12B Problems/Problem 1"

(Problem)
(Solution)
 
(One intermediate revision by the same user not shown)
Line 2: Line 2:
 
What is the value of <math>2-(-2)^{-2}</math> ?
 
What is the value of <math>2-(-2)^{-2}</math> ?
  
<math>\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?</math>
+
<math>\textbf{(A) } -2\qquad\textbf{(B) } \dfrac{1}{16}\qquad\textbf{(C) } \dfrac{7}{4}\qquad\textbf{(D) } \dfrac{9}{4}\qquad\textbf{(E) } 6</math>
  
 
==Solution==
 
==Solution==
 
+
<math>2-(-2)^{-2}=2-\frac{1}{(-2)^2}=2-\frac{1}{4}=\frac{8}{4}-\frac{1}{4}=\boxed{\textbf{(C) }\frac{7}{4}}</math>
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2015|ab=B|before=First Problem|num-a=2}}
 
{{AMC12 box|year=2015|ab=B|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 15:45, 3 March 2015

Problem

What is the value of $2-(-2)^{-2}$ ?

$\textbf{(A) } -2\qquad\textbf{(B) } \dfrac{1}{16}\qquad\textbf{(C) } \dfrac{7}{4}\qquad\textbf{(D) } \dfrac{9}{4}\qquad\textbf{(E) } 6$

Solution

$2-(-2)^{-2}=2-\frac{1}{(-2)^2}=2-\frac{1}{4}=\frac{8}{4}-\frac{1}{4}=\boxed{\textbf{(C) }\frac{7}{4}}$

See Also

2015 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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. AMC logo.png

Invalid username
Login to AoPS