Difference between revisions of "2012 AMC 8 Problems"
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==Problem 3== | ==Problem 3== | ||
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On February 13 <math>\emph{The Oshkosh Northwester}</math> listed the length of daylight as 10 hours and 24 minutes, the sunrise was <math> 6:57\textsc{am} </math>, and the sunset as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? | On February 13 <math>\emph{The Oshkosh Northwester}</math> listed the length of daylight as 10 hours and 24 minutes, the sunrise was <math> 6:57\textsc{am} </math>, and the sunset as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? | ||
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==Problem 4== | ==Problem 4== | ||
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Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat? | Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat? | ||
<math> \textbf{(A)}\hspace{.05in}\frac{1}{24}\qquad\textbf{(B)}\hspace{.05in}\frac{1}{12}\qquad\textbf{(C)}\hspace{.05in}\frac{1}8\qquad\textbf{(D)}\hspace{.05in}\frac{1}6\qquad\textbf{(E)}\hspace{.05in}\frac{1}4 </math> | <math> \textbf{(A)}\hspace{.05in}\frac{1}{24}\qquad\textbf{(B)}\hspace{.05in}\frac{1}{12}\qquad\textbf{(C)}\hspace{.05in}\frac{1}8\qquad\textbf{(D)}\hspace{.05in}\frac{1}6\qquad\textbf{(E)}\hspace{.05in}\frac{1}4 </math> | ||
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| + | |||
| + | ==Problem 5== | ||
| + | In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , <math> X </math> in centimeters? | ||
| + | |||
| + | <asy> | ||
| + | pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R; | ||
| + | A=(4,0); | ||
| + | B=(7,0); | ||
| + | C=(7,4); | ||
| + | D=(8,4); | ||
| + | E=(8,5); | ||
| + | F=(10,5); | ||
| + | G=(10,7); | ||
| + | H=(7,7); | ||
| + | I=(7,8); | ||
| + | J=(5,8); | ||
| + | K=(5,7); | ||
| + | L=(4,7); | ||
| + | M=(4,6); | ||
| + | N=(0,6); | ||
| + | O=(0,5); | ||
| + | P=(2,5); | ||
| + | Q=(2,3); | ||
| + | R=(4,3); | ||
| + | draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle); | ||
| + | label("$X$",(3.4,1.5)); | ||
| + | label("6",(7.6,1.5)); | ||
| + | label("1",(7.6,3.5)); | ||
| + | label("1",(8.4,4.6)); | ||
| + | label("2",(9.4,4.6)); | ||
| + | label("2",(10.4,6)); | ||
| + | label("3",(8.4,7.4)); | ||
| + | label("1",(7.5,7.8)); | ||
| + | label("2",(6,8.5)); | ||
| + | label("1",(4.7,7.8)); | ||
| + | label("1",(4.3,7.5)); | ||
| + | label("1",(3.5,6.5)); | ||
| + | label("4",(1.8,6.5)); | ||
| + | label("1",(-0.5,5.5)); | ||
| + | label("2",(0.8,4.5)); | ||
| + | label("2",(1.5,3.8)); | ||
| + | label("2",(2.8,2.6));</asy> | ||
| + | |||
| + | <math> \textbf{(A)}\hspace{.05in}1\qquad\textbf{(B)}\hspace{.05in}2\qquad\textbf{(C)}\hspace{.05in}3\qquad\textbf{(D)}\hspace{.05in}4\qquad\textbf{(E)}\hspace{.05in}5 </math> | ||
Revision as of 14:19, 23 November 2012
Problem 1
Rachelle uses 
pounds of meat to make 
hamburgers for her family. How many pounds of meat does she need to make 
hamburgers for a neighborhood picnic?
Problem 2
In the country of East Westmore, statisticians estimate there is a baby born every hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
Problem 3
On February 13 
listed the length of daylight as 10 hours and 24 minutes, the sunrise was 
, and the sunset as 
. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
Problem 4
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
Problem 5
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , 
in centimeters?
![[asy] pair A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R; A=(4,0); B=(7,0); C=(7,4); D=(8,4); E=(8,5); F=(10,5); G=(10,7); H=(7,7); I=(7,8); J=(5,8); K=(5,7); L=(4,7); M=(4,6); N=(0,6); O=(0,5); P=(2,5); Q=(2,3); R=(4,3); draw(A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--cycle); label("$X$",(3.4,1.5)); label("6",(7.6,1.5)); label("1",(7.6,3.5)); label("1",(8.4,4.6)); label("2",(9.4,4.6)); label("2",(10.4,6)); label("3",(8.4,7.4)); label("1",(7.5,7.8)); label("2",(6,8.5)); label("1",(4.7,7.8)); label("1",(4.3,7.5)); label("1",(3.5,6.5)); label("4",(1.8,6.5)); label("1",(-0.5,5.5)); label("2",(0.8,4.5)); label("2",(1.5,3.8)); label("2",(2.8,2.6));[/asy]](http://latex.artofproblemsolving.com/b/c/d/bcd57a9d78159bce4d3873f81f5d879beaed1d5a.png)
