1953 AHSME Problems
1953 AHSC (Answer Key) Printable version: | AoPS Resources • PDF | ||
Instructions
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Contents
- 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 Problem 31
- 32 Problem 32
- 33 Problem 33
- 34 Problem 34
- 35 Problem 35
- 36 Problem 36
- 37 Problem 37
- 38 Problem 38
- 39 Problem 39
- 40 Problem 40
- 41 Problem 41
- 42 Problem 42
- 43 Problem 43
- 44 Problem 44
- 45 Problem 45
- 46 Problem 46
- 47 Problem 47
- 48 Problem 48
- 49 Problem 49
- 50 Problem 50
- 51 See also
Problem 1
A boy buys oranges at for cents. He will sell them at for cents. In order to make a profit of $ , he must sell:
Problem 2
A refrigerator is offered at sale at $250.00 less successive discounts of 20% and 15%. The sale price of the refrigerator is:
Problem 3
The factors of the expression are:
Problem 4
The roots of are:
Problem 5
If , the value of is:
Problem 6
Charles has quarters and Richard has quarters. The difference in their money in dimes is:
Problem 7
The fraction reduces to:
Problem 8
The value of at the intersection of and is:
Problem 9
The number of ounces of water needed to reduce ounces of shaving lotion containing % alcohol to a lotion containing % alcohol is:
Problem 10
The number of revolutions of a wheel, with fixed center and with an outside diameter of feet, required to cause a point on the rim to go one mile is:
Problem 11
A running track is the ring formed by two concentric circles. It is feet wide. The circumference of the two circles differ by about:
Problem 12
The diameters of two circles are inches and inches respectively. The ratio of the area of the smaller to the area of the larger circle is:
Problem 13
A triangle and a trapezoid are equal in area. They also have the same altitude. If the base of the triangle is 18 inches, the median of the trapezoid is:
Problem 14
Given the larger of two circles with center and radius and the smaller with center and radius . Draw . Which of the following statements is false?
Problem 15
A circular piece of metal of maximum size is cut out of a square piece and then a square piece of maximum size is cut out of the circular piece. The total amount of metal wasted is:
Problem 16
Adams plans a profit of % on the selling price of an article and his expenses are % of sales. The rate of markup on an article that sells for $ is:
Problem 17
A man has part of $ invested at % and the rest at %. If his annual return on each investment is the same, the average rate of interest which he realizes of the $4500 is:
Problem 18
One of the factors of is:
Problem 19
In the expression , the values of and are each decreased %; the value of the expression is:
Problem 20
If , then becomes:
Problem 21
If , the value of is:
Problem 22
The logarithm of to the base is:
Problem 23
The equation has:
Problem 24
If are positive integers less than , then if:
Problem 25
In a geometric progression whose terms are positive, any term is equal to the sum of the next two following terms. then the common ratio is:
Problem 26
The base of a triangle is inches. Two lines are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal areas. The length of the parallel closer to the base is:
Problem 27
The radius of the first circle is inch, that of the second inch, that of the third inch and so on indefinitely. The sum of the areas of the circles is:
Problem 28
In , sides and are opposite and respectively. bisects and meets at . Then if and the correct proportion is:
Problem 29
The number of significant digits in the measurement of the side of a square whose computed area is square inches to the nearest ten-thousandth of a square inch is:
Problem 30
A house worth $ is sold by Mr. A to Mr. B at a % loss. Mr. B sells the house back to Mr. A at a % gain. The result of the two transactions is:
Problem 31
The rails on a railroad are feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in:
Problem 32
Each angle of a rectangle is trisected. The intersections of the pairs of trisectors adjacent to the same side always form:
Problem 33
The perimeter of an isosceles right triangle is . Its area is:
Problem 34
If one side of a triangle is inches and the opposite angle is , then the diameter of the circumscribed circle is:
Problem 35
If , then equals:
Problem 36
Determine so that is divisible by . The obtained value, , is an exact divisor of:
Problem 37
The base of an isosceles triangle is inches and one of the equal sides is inches. The radius of the circle through the vertices of the triangle is:
Problem 38
If and , then is:
Problem 39
The product, is equal to:
Problem 40
The negation of the statement "all men are honest," is:
Problem 41
A girls' camp is located rods from a straight road. On this road, a boys' camp is located rods from the girls' camp. It is desired to build a canteen on the road which shall be exactly the same distance from each camp. The distance of the canteen from each of the camps is:
Problem 42
The centers of two circles are inches apart. The smaller circle has a radius of inches and the larger one has a radius of inches. The length of the common internal tangent is:
Problem 43
If the price of an article is increased by percent , then the decrease in percent of sales must not exceed in order to yield the same income. The value of is:
Problem 44
In solving a problem that reduces to a quadratic equation one student makes a mistake only in the constant term of the equation and obtains and for the roots. Another student makes a mistake only in the coefficient of the first degree term and find and for the roots. The correct equation was:
Problem 45
The lengths of two line segments are units and units respectively. Then the correct relation between them is:
Problem 46
Instead of walking along two adjacent sides of a rectangular field, a boy took a shortcut along the diagonal of the field and saved a distance equal to the longer side. The ratio of the shorter side of the rectangle to the longer side was:
Problem 47
If , then the correct relationship is:
Problem 48
If the larger base of an isosceles trapezoid equals a diagonal and the smaller base equals the altitude, then the ratio of the smaller base to the larger base is:
Problem 49
The coordinates of and are and respectively. The value of that makes as small as possible is:
Problem 50
One of the sides of a triangle is divided into segments of and units by the point of tangency of the inscribed circle. If the radius of the circle is , then the length of the shortest side of the triangle is:
See also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by 1952 AHSC |
Followed by 1954 AHSC | |
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The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.