1989 AHSME Problems
- 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
A square is cut into three rectangles along two lines parallel to a side, as shown. If the perimeter of each of the three rectangles is 24, then the area of the original square is
In the figure, is an isosceles trapezoid with side lengths , , and . The point is on and is the midpoint of hypotenuse in right triangle . Then
Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is 20 toothpicks high and 10 toothpicks wide, then the number of toothpicks used is
If and the triangle in the first quadrant bounded by the coordinate axes and the graph of has area , then
In , , , , is an altitude, and is a median. Then
For how many integers between and does factor into the product of two linear factors with integer coefficients?
Mr. and Mrs. Zeta want to name their baby Zeta so that its monogram (first, middle, and last initials) will be in alphabetical order with no letter repeated. How many such monograms are possible?
Consider the sequence defined recursively by (any positive integer), and , . For which of the following values of must ?
Let , , , and be positive integers with , , and . If , the largest possible value for is
The traffic on a certain east-west highway moves at a constant speed of 60 miles per hour in both directions. An eastbound driver passes 20 west-bound vehicles in a five-minute interval. Assume vehicles in the westbound lane are equally spaced. Which of the following is closest to the number of westbound vehicles present in a 100-mile section of highway?
Two strips of width 1 overlap at an angle of as shown. The area of the overlap (shown shaded) is
In , , , , and is on with . Find the ratio of .
A lattice point is a point in the plane with integer coordinates. How many lattice points are on the line segment whose endpoints are (3,17) and (48,281)? (Include both endpoints of the segment in your count.)
The perimeter of an equilateral triangle exceeds the perimeter of a square by cm. The length of each side of the triangle exceeds the length of each side of the square by cm. The square has perimeter greater than 0. How many positive integers are NOT a possible value for ?
The set of all numbers x for which is a rational number is the set of all:
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths , , and . What is the area of the triangle?