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Difference between revisions of "1951 AHSME Problems"

(could someone put this in wiki form? Lunch time.)
m (fix spaces)
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== Problem 1 ==
 
== Problem 1 ==
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[[1951 AHSME Problems/Problem 1|Solution]]
 
[[1951 AHSME Problems/Problem 1|Solution]]
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<math> \mathrm{(A) \ } \frac {100(M - N)}{M} \qquad \mathrm{(B) \ } \frac {100(M - N)}{N} \qquad \mathrm{(C) \ } \frac {M - N}{N} \qquad \mathrm{(D) \ } \frac {M - N}{M} \qquad \mathrm{(E) \ } \frac {100(M + N)}{N} </math>
 
<math> \mathrm{(A) \ } \frac {100(M - N)}{M} \qquad \mathrm{(B) \ } \frac {100(M - N)}{N} \qquad \mathrm{(C) \ } \frac {M - N}{N} \qquad \mathrm{(D) \ } \frac {M - N}{M} \qquad \mathrm{(E) \ } \frac {100(M + N)}{N} </math>
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[[1951 AHSME Problems/Problem 2|Solution]]
 
[[1951 AHSME Problems/Problem 2|Solution]]
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== Problem 3 ==
 
== Problem 3 ==
 
If the length of a diagonal of a square is <math>a + b</math>, then the area of the square is:
 
If the length of a diagonal of a square is <math>a + b</math>, then the area of the square is:
−
 
  
 
<math> \mathrm{(A) \ (a+b)^2 } \qquad \mathrm{(B) \ \frac{1}{2}(a+b)^2 } \qquad \mathrm{(C) \ a^2+b^2 } \qquad \mathrm{(D) \ \frac {1}{2}(a^2+b^2) } \qquad \mathrm{(E) \ \text{none of these} }  </math>
 
<math> \mathrm{(A) \ (a+b)^2 } \qquad \mathrm{(B) \ \frac{1}{2}(a+b)^2 } \qquad \mathrm{(C) \ a^2+b^2 } \qquad \mathrm{(D) \ \frac {1}{2}(a^2+b^2) } \qquad \mathrm{(E) \ \text{none of these} }  </math>
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== Problem 4 ==
 
== Problem 4 ==
−
A barn with a roof is rectangular in shape, 10 yd. wide, 13 yd. long and 5 yd. high.  It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. yd. to be painted is:
+
A barn with a roof is rectangular in shape, <math>10</math> yd. wide, <math>13</math> yd. long and <math>5</math> yd. high.  It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. yd. to be painted is:
−
 
 
  
 
<math> \mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720 </math>
 
<math> \mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720 </math>
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== Problem 5 ==
 
== Problem 5 ==
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Mr. <math>A</math> owns a home worth <math>\</math>10,000.  He sells it to Mr. <math>B</math> at a 10 % profit based on the worth of the house. Mr. <math>B</math> sells the house back to Mr. <math>A</math> at a 10 % loss.  Then:
+
Mr. <math>A</math> owns a home worth <math>\</math>10,000.  He sells it to Mr. <math>B</math> at a 10% profit based on the worth of the house. Mr. <math>B</math> sells the house back to Mr. <math>A</math> at a 10% loss.  Then:
−
 
 
  
−
<math> \mathrm{(A) \ A comes out even  } \qquad \mathrm{(B) \ A makes 1100 on the deal } \qquad \mathrm{(C) \ A makes 1000 on the deal } \qquad \mathrm{(D) \ A loses 900 on the deal } \qquad \mathrm{(E) \ A loses 1000 on the deal }  </math>
+
<math> \mathrm{(A) \ A\ comes\ out\ even  } \qquad</math> <math>\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}</math> <math> \qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad</math> <math>\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }</math> <math>\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }  </math>
  
 
[[1951 AHSME Problems/Problem 5|Solution]]
 
[[1951 AHSME Problems/Problem 5|Solution]]
  
 
== Problem 6 ==
 
== Problem 6 ==
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[[195 AHSME Problems/Problem 6|Solution]]
 
[[195 AHSME Problems/Problem 6|Solution]]
  
 
== Problem 7 ==
 
== Problem 7 ==
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[[1951 AHSME Problems/Problem 7|Solution]]
 
[[1951 AHSME Problems/Problem 7|Solution]]
  
 
== Problem 8 ==
 
== Problem 8 ==
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[[1951 AHSME Problems/Problem 8|Solution]]
 
[[1951 AHSME Problems/Problem 8|Solution]]
  
 
== Problem 9 ==
 
== Problem 9 ==
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[[1951 AHSME Problems/Problem 9|Solution]]
 
[[1951 AHSME Problems/Problem 9|Solution]]
  
 
== Problem 10 ==
 
== Problem 10 ==
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[[1951 AHSME Problems/Problem 10|Solution]]
 
[[1951 AHSME Problems/Problem 10|Solution]]
  
 
== Problem 11 ==
 
== Problem 11 ==
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[[1951 AHSME Problems/Problem 11|Solution]]
 
[[1951 AHSME Problems/Problem 11|Solution]]
  
 
== Problem 12 ==
 
== Problem 12 ==
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[[1951 AHSME Problems/Problem 12|Solution]]
 
[[1951 AHSME Problems/Problem 12|Solution]]
  
 
== Problem 13 ==
 
== Problem 13 ==
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[[1951 AHSME Problems/Problem 13|Solution]]
 
[[1951 AHSME Problems/Problem 13|Solution]]
  
 
== Problem 14 ==
 
== Problem 14 ==
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[[1951 AHSME Problems/Problem 14|Solution]]
 
[[1951 AHSME Problems/Problem 14|Solution]]
  
 
== Problem 15 ==
 
== Problem 15 ==
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[[1951 AHSME Problems/Problem 15|Solution]]
 
[[1951 AHSME Problems/Problem 15|Solution]]
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If in applying the quadratic formula to a quadratic equation
 
If in applying the quadratic formula to a quadratic equation
  
−
<cmath>f(x) \equiv ax^2 + bx + c = 0</cmath>,
+
<cmath>f(x) \equiv ax^2 + bx + c = 0,</cmath>
−
 
 
−
it happens that <math>c = b^2/4a</math>, then the graph of <math>y = f(x)</math> will certainly:
 
  
−
<math> \mathrm{(A) \ \text{have a maximum} } \qquad \mathrm{(B) \ \text{have a minimum} } \qquad \mathrm{(C) \ \text{be tangent to the x-axis} } \qquad \mathrm{(D) \ \text{be tangent to the y-axis} } \qquad \mathrm{(E) \ \text{lie in one quadrant only} }  </math>
+
it happens that <math>c = \frac{b^2}{4a}</math>, then the graph of <math>y = f(x)</math> will certainly:
  
 +
<math>\mathrm{(A) \ have\ a\ maximum  } \qquad \mathrm{(B) \ have\ a\ minimum} \qquad</math> <math>\mathrm{(C) \ be\ tangent\ to\ the\ xaxis} \qquad</math> <math>\mathrm{(D) \ be\ tangent\ to\ the\ yaxis} \qquad</math> <math>\mathrm{(E) \ lie\ in\ one\ quadrant\ only}</math>
  
 
[[1951 AHSME Problems/Problem 16|Solution]]
 
[[1951 AHSME Problems/Problem 16|Solution]]
  
 
== Problem 17 ==
 
== Problem 17 ==
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[[1951 AHSME Problems/Problem 17|Solution]]
 
[[1951 AHSME Problems/Problem 17|Solution]]
  
 
== Problem 18 ==
 
== Problem 18 ==
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[[1951 AHSME Problems/Problem 18|Solution]]
 
[[1951 AHSME Problems/Problem 18|Solution]]
  
 
== Problem 19 ==
 
== Problem 19 ==
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[[1951 AHSME Problems/Problem 19|Solution]]
 
[[1951 AHSME Problems/Problem 19|Solution]]
  
 
== Problem 20 ==
 
== Problem 20 ==
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[[1951 AHSME Problems/Problem 20|Solution]]
 
[[1951 AHSME Problems/Problem 20|Solution]]
  
 
== Problem 21 ==
 
== Problem 21 ==
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[[1951 AHSME Problems/Problem 21|Solution]]
 
[[1951 AHSME Problems/Problem 21|Solution]]
  
 
== Problem 22 ==
 
== Problem 22 ==
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[[1951 AHSME Problems/Problem 22|Solution]]
 
[[1951 AHSME Problems/Problem 22|Solution]]
  
 
== Problem 23 ==
 
== Problem 23 ==
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[[1951 AHSME Problems/Problem 23|Solution]]
 
[[1951 AHSME Problems/Problem 23|Solution]]
  
 
== Problem 24 ==
 
== Problem 24 ==
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[[1951 AHSME Problems/Problem 24|Solution]]
 
[[1951 AHSME Problems/Problem 24|Solution]]
  
 
== Problem 25 ==
 
== Problem 25 ==
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[[1951 AHSME Problems/Problem 25|Solution]]
 
[[1951 AHSME Problems/Problem 25|Solution]]
  
 
== Problem 26 ==
 
== Problem 26 ==
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[[1951 AHSME Problems/Problem 26|Solution]]
 
[[1951 AHSME Problems/Problem 26|Solution]]
  
 
== Problem 27 ==
 
== Problem 27 ==
−
 
  
 
[[1951 AHSME Problems/Problem 27|Solution]]
 
[[1951 AHSME Problems/Problem 27|Solution]]
  
 
== Problem 28 ==
 
== Problem 28 ==
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[[1951 AHSME Problems/Problem 28|Solution]]
 
[[1951 AHSME Problems/Problem 28|Solution]]
  
 
== Problem 29 ==
 
== Problem 29 ==
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[[1951 AHSME Problems/Problem 29|Solution]]
 
[[1951 AHSME Problems/Problem 29|Solution]]
  
 
== Problem 30 ==
 
== Problem 30 ==
−
 
  
 
[[1951 AHSME Problems/Problem 30|Solution]]
 
[[1951 AHSME Problems/Problem 30|Solution]]

Revision as of 19:45, 10 January 2008

Problem 1

Solution

Problem 2

The percent that $M$ is greater than $N$, is:

$\mathrm{(A) \ } \frac {100(M - N)}{M} \qquad \mathrm{(B) \ } \frac {100(M - N)}{N} \qquad \mathrm{(C) \ } \frac {M - N}{N} \qquad \mathrm{(D) \ } \frac {M - N}{M} \qquad \mathrm{(E) \ } \frac {100(M + N)}{N}$

Solution

Problem 3

If the length of a diagonal of a square is $a + b$, then the area of the square is:

$\mathrm{(A) \ (a+b)^2 } \qquad \mathrm{(B) \ \frac{1}{2}(a+b)^2 } \qquad \mathrm{(C) \ a^2+b^2 } \qquad \mathrm{(D) \ \frac {1}{2}(a^2+b^2) } \qquad \mathrm{(E) \ \text{none of these} }$

Solution

Problem 4

A barn with a roof is rectangular in shape, $10$ yd. wide, $13$ yd. long and $5$ yd. high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of sq. yd. to be painted is:

$\mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720$

Solution

Problem 5

Mr. $A$ owns a home worth $$10,000. He sells it to Mr. $B$ at a 10% profit based on the worth of the house. Mr. $B$ sells the house back to Mr. $A$ at a 10% loss. Then:

$\mathrm{(A) \ A\ comes\ out\ even } \qquad$ $\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}$ $\qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad$ $\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }$ $\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }$

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

If in applying the quadratic formula to a quadratic equation

\[f(x) \equiv ax^2 + bx + c = 0,\]

it happens that $c = \frac{b^2}{4a}$, then the graph of $y = f(x)$ will certainly:

$\mathrm{(A) \ have\ a\ maximum } \qquad \mathrm{(B) \ have\ a\ minimum} \qquad$ $\mathrm{(C) \ be\ tangent\ to\ the\ xaxis} \qquad$ $\mathrm{(D) \ be\ tangent\ to\ the\ yaxis} \qquad$ $\mathrm{(E) \ lie\ in\ one\ quadrant\ only}$

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

Problem 26

Solution

Problem 27

Solution

Problem 28

Solution

Problem 29

Solution

Problem 30

Solution

See also

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