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Difference between revisions of "2010 AMC 10A Problems"

(Just setting up the template)
 
Line 1: Line 1:
 
== Problem 1 ==
 
== Problem 1 ==
−
 
+
Mary’s top book shelf holds five books with the following widths, in centimeters: <math>6</math>, <math>\dfrac{1}{2}</math>, <math>1</math>, <math>2.5</math>, and <math>10</math>. What is the average book width, in centimeters?
  
 
<math>
 
<math>
−
\mathrm{(A)}\  
+
\mathrm{(A)}\ 1
 
\qquad
 
\qquad
−
\mathrm{(B)}\  
+
\mathrm{(B)}\ 2
 
\qquad
 
\qquad
−
\mathrm{(C)}\  
+
\mathrm{(C)}\ 3
 
\qquad
 
\qquad
−
\mathrm{(D)}\  
+
\mathrm{(D)}\ 4
 
\qquad
 
\qquad
−
\mathrm{(E)}\  
+
\mathrm{(E)}\ 5
 
</math>
 
</math>
  
Line 18: Line 18:
 
== Problem 2 ==
 
== Problem 2 ==
  
 +
Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?
 +
 +
<center><asy>
 +
unitsize(8mm);
 +
defaultpen(linewidth(.8pt));
 +
 +
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle);
 +
draw((0,3)--(0,4)--(1,4)--(1,3)--cycle);
 +
draw((1,3)--(1,4)--(2,4)--(2,3)--cycle);
 +
draw((2,3)--(2,4)--(3,4)--(3,3)--cycle);
 +
draw((3,3)--(3,4)--(4,4)--(4,3)--cycle);
 +
 +
</asy></center>
  
 
<math>
 
<math>
−
\mathrm{(A)}\  
+
\mathrm{(A)}\ \dfrac{5}{4}
 
\qquad
 
\qquad
−
\mathrm{(B)}\  
+
\mathrm{(B)}\ \dfrac{4}{3}
 
\qquad
 
\qquad
−
\mathrm{(C)}\  
+
\mathrm{(C)}\ \dfrac{3}{2}
 
\qquad
 
\qquad
−
\mathrm{(D)}\  
+
\mathrm{(D)}\ 2
 
\qquad
 
\qquad
−
\mathrm{(E)}\  
+
\mathrm{(E)}\ 3
 
</math>
 
</math>
  
Line 34: Line 47:
  
 
== Problem 3 ==
 
== Problem 3 ==
 +
Tyrone had <math>97</math> marbles and Eric had <math>11</math> marbles. Tyrone then gave some of his marbles ot Eric so that Tyrone ended with twice as many marbles as Eric. How many marbles did Tyrone give to Eric?
  
 
<math>
 
<math>
−
\mathrm{(A)}\  
+
\mathrm{(A)}\ 3
 
\qquad
 
\qquad
−
\mathrm{(B)}\  
+
\mathrm{(B)}\ 13
 
\qquad
 
\qquad
−
\mathrm{(C)}\  
+
\mathrm{(C)}\ 18
 
\qquad
 
\qquad
−
\mathrm{(D)}\  
+
\mathrm{(D)}\ 25
 
\qquad
 
\qquad
−
\mathrm{(E)}\  
+
\mathrm{(E)}\ 29
 
</math>
 
</math>
  
Line 50: Line 64:
  
 
== Problem 4 ==
 
== Problem 4 ==
−
 
+
A book that is to be recorded onto compact discs takes <math>412</math> minutes to read aloud. Each disc can hold up to <math>56</math> minutes of reading. Assume that the smallest possible number of discs is used and that each disc contains the same length of reading. How many minutes of reading will each disc contain?
  
 
<math>
 
<math>
−
\mathrm{(A)}\  
+
\mathrm{(A)}\ 50.2
 
\qquad
 
\qquad
−
\mathrm{(B)}\  
+
\mathrm{(B)}\ 51.5
 
\qquad
 
\qquad
−
\mathrm{(C)}\  
+
\mathrm{(C)}\ 52.4
 
\qquad
 
\qquad
−
\mathrm{(D)}\  
+
\mathrm{(D)}\ 53.8
 
\qquad
 
\qquad
−
\mathrm{(E)}\  
+
\mathrm{(E)}\ 55.2
 
</math>
 
</math>
  
Line 67: Line 81:
  
 
== Problem 5 ==
 
== Problem 5 ==
−
 
+
The area of a circle whose circumference is <math>24\pi</math> is <math>k\pi</math>. What is the value of <math>k</math>?
  
 
<math>
 
<math>
−
\mathrm{(A)}\  
+
\mathrm{(A)}\ 6
 
\qquad
 
\qquad
−
\mathrm{(B)}\  
+
\mathrm{(B)}\ 12
 
\qquad
 
\qquad
−
\mathrm{(C)}\  
+
\mathrm{(C)}\ 24
 
\qquad
 
\qquad
−
\mathrm{(D)}\  
+
\mathrm{(D)}\ 36
 
\qquad
 
\qquad
−
\mathrm{(E)}\  
+
\mathrm{(E)}\ 144
 
</math>
 
</math>
  

Revision as of 13:12, 2 April 2010

Problem 1

Mary’s top book shelf holds five books with the following widths, in centimeters: $6$, $\dfrac{1}{2}$, $1$, $2.5$, and $10$. What is the average book width, in centimeters?

$\mathrm{(A)}\ 1 \qquad \mathrm{(B)}\ 2 \qquad \mathrm{(C)}\ 3 \qquad \mathrm{(D)}\ 4 \qquad \mathrm{(E)}\ 5$

Solution

Problem 2

Four identical squares and one rectangle are placed together to form one large square as shown. The length of the rectangle is how many times as large as its width?

[asy] unitsize(8mm); defaultpen(linewidth(.8pt)); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle); draw((0,3)--(0,4)--(1,4)--(1,3)--cycle); draw((1,3)--(1,4)--(2,4)--(2,3)--cycle); draw((2,3)--(2,4)--(3,4)--(3,3)--cycle); draw((3,3)--(3,4)--(4,4)--(4,3)--cycle); [/asy]

$\mathrm{(A)}\ \dfrac{5}{4} \qquad \mathrm{(B)}\ \dfrac{4}{3} \qquad \mathrm{(C)}\ \dfrac{3}{2} \qquad \mathrm{(D)}\ 2 \qquad \mathrm{(E)}\ 3$

Solution

Problem 3

Tyrone had $97$ marbles and Eric had $11$ marbles. Tyrone then gave some of his marbles ot Eric so that Tyrone ended with twice as many marbles as Eric. How many marbles did Tyrone give to Eric?

$\mathrm{(A)}\ 3 \qquad \mathrm{(B)}\ 13 \qquad \mathrm{(C)}\ 18 \qquad \mathrm{(D)}\ 25 \qquad \mathrm{(E)}\ 29$

Solution

Problem 4

A book that is to be recorded onto compact discs takes $412$ minutes to read aloud. Each disc can hold up to $56$ minutes of reading. Assume that the smallest possible number of discs is used and that each disc contains the same length of reading. How many minutes of reading will each disc contain?

$\mathrm{(A)}\ 50.2 \qquad \mathrm{(B)}\ 51.5 \qquad \mathrm{(C)}\ 52.4 \qquad \mathrm{(D)}\ 53.8 \qquad \mathrm{(E)}\ 55.2$

Solution

Problem 5

The area of a circle whose circumference is $24\pi$ is $k\pi$. What is the value of $k$?

$\mathrm{(A)}\ 6 \qquad \mathrm{(B)}\ 12 \qquad \mathrm{(C)}\ 24 \qquad \mathrm{(D)}\ 36 \qquad \mathrm{(E)}\ 144$

Solution

Problem 6

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 7

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 8

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 9

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 10

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 11

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 12

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 13

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 14

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 15

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 16

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 17

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 18

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 19

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 20

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 21

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 22

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 23

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 24

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

Problem 25

$\mathrm{(A)}\ \qquad \mathrm{(B)}\ \qquad \mathrm{(C)}\ \qquad \mathrm{(D)}\ \qquad \mathrm{(E)}$

Solution

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