Difference between revisions of "1951 AHSME Problems"
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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: | ||
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<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. | + | 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: |
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<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 == | ||
− | 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>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: |
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− | <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> |
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− | <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 == | ||
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[[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 == | ||
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[[1951 AHSME Problems/Problem 30|Solution]] | [[1951 AHSME Problems/Problem 30|Solution]] |
Revision as of 19:45, 10 January 2008
Contents
[hide]- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 See also
Problem 1
Problem 2
The percent that is greater than , is:
Problem 3
If the length of a diagonal of a square is , then the area of the square is:
Problem 4
A barn with a roof is rectangular in shape, yd. wide, yd. long and 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:
Problem 5
Mr. owns a home worth 10,000. He sells it to Mr. at a 10% profit based on the worth of the house. Mr. sells the house back to Mr. at a 10% loss. Then:
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
If in applying the quadratic formula to a quadratic equation
it happens that , then the graph of will certainly: