Difference between revisions of "1951 AHSME Problems"
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The percent that <math>M</math> is greater than <math>N</math>, is: | The percent that <math>M</math> is greater than <math>N</math>, is: | ||
− | (A) | + | <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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− | (B) | ||
− | |||
− | (C) | ||
− | |||
− | (D) | ||
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− | (E) | ||
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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: | ||
− | (A) | + | |
− | (B) | + | <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> |
− | (C) | ||
− | (D) | ||
− | (E) | ||
[[1951 AHSME Problems/Problem 3|Solution]] | [[1951 AHSME Problems/Problem 3|Solution]] | ||
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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, 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) 360 | + | |
− | (B) 460 | + | <math> \mathrm{(A) \ } 360 \qquad \mathrm{(B) \ } 460 \qquad \mathrm{(C) \ } 490 \qquad \mathrm{(D) \ } 590 \qquad \mathrm{(E) \ } 720 </math> |
− | (C) 490 | ||
− | (D) 590 | ||
− | (E) 720 | ||
[[1951 AHSME Problems/Problem 4|Solution]] | [[1951 AHSME Problems/Problem 4|Solution]] | ||
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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: | ||
− | (A) | + | |
− | (B) | + | <math> \mathrm{(A) \ } \text{A comes out even} \qquad \mathrm{(B) \ } \text{A makes 1100 on the deal} \qquad \mathrm{(C) \ } \text{A makes 1000 on the deal} \qquad \mathrm{(D) \ } \text{A loses 900 on the deal} \qquad \mathrm{(E) \ } \text{A loses 1000 on the deal} </math> |
− | (C) | ||
− | (D) | ||
− | (E) | ||
[[1951 AHSME Problems/Problem 5|Solution]] | [[1951 AHSME Problems/Problem 5|Solution]] | ||
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it happens that <math>c = b^2/4a</math>, then the graph of <math>y = f(x)</math> will certainly: | it happens that <math>c = b^2/4a</math>, then the graph of <math>y = f(x)</math> will certainly: | ||
− | (A) have a maximum | + | |
− | (B) have a minimum | + | <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> |
− | (C) be tangent to the | + | |
− | (D) be tangent to the | ||
− | (E) lie in one quadrant only | ||
[[1951 AHSME Problems/Problem 16|Solution]] | [[1951 AHSME Problems/Problem 16|Solution]] |
Revision as of 11:40, 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, 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:
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: