1969 AHSME Problems
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
Problem 1
When is added to both the numerator and denominator of the fraction , the value of the fraction is changed to . Then equals:
Problem 2
If an item is sold for dollars, there is a loss of based on the cost. If, however, the same item is sold for dollars, there is a profit of based on the cost. The ratio of is:
Problem 3
If , written in base , is , the integer immediately preceding , written in base , is:
Problem 4
Let a binary operation on ordered pairs of integers be defined by . Then, if and represent identical pairs, equals:
Problem 5
If a number , diminished by four times its reciprocal, equals a given real constant , then, for this given , the sum of all such possible values of is
Problem 6
The area of the ring between two concentric circles is square inches. The length of a chord of the larger circle tangent to the smaller circle, in inches, is:
Problem 7
If the points and lie on the graph of , and , then equals:
Problem 8
Triangle is inscribed in a circle. The measure of the non-overlapping minor arcs , and are, respectively, . Then one interior angle of the triangle is:
Problem 9
The arithmetic mean (ordinary average) of the fifty-two successive positive integers beginning at 2 is:
Problem 10
The number of points equidistant from a circle and two parallel tangents to the circle is:
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Let be the number of ways dollars can be changed into dimes and quarters, with at least one of each coin being used. Then equals:
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Solution The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.