1968 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
Let units be the increase in circumference of a circle resulting from an increase in units in the diameter. Then equals:
Problem 2
The real value of such that divided by equals is:
Problem 3
A straight line passing through the point is perpendicular to the line . Its equation is:
Problem 4
Define an operation for positive real numbers as . Then equals:
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
In this diagram, not drawn to scale, Figures and are equilateral triangular regions with respective areas of and square inches. Figure is a square region with area square inches. Let the length of segment be decreased by % of itself, while the lengths of and remain unchanged. The percent decrease in the area of the square is:
Problem 32
Problem 33
Problem 34
Problem 35
In this diagram the center of the circle is , the radius is inches, chord is parallel to chord . ,,, are collinear, and is the midpoint of . Let (sq. in.) represent the area of trapezoid and let (sq. in.) represent the area of rectangle Then, as and are translated upward so that increases toward the value , while always equals , the ratio becomes arbitrarily close to:
Solution The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.