1980 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
- 31 See also
The largest whole number such that seven times the number is less than is
The degree of as a polynomial in is
If the ratio of to is , what is the ratio of to ?
In the adjoining figure, CDE is an equilateral triangle and ABCD and DEFG are squares. The measure of is
If and are perpendicular diameters of circle , in , and , then the length of divided by the length of is
A positive number satisfies the inequality if and only if
Sides and of convex polygon have lengths 3,4,12, and 13, respectively, and is a right angle. The area of the quadrilateral is
How many pairs of non-zero real numbers satisfy the equation
A man walks miles due west, turns to his left and walks 3 miles in the new direction. If he finishes a a point from his starting point, then is
The number of teeth in three meshed gears , , and are , , and , respectively. (The teeth on all gears are the same size and regularly spaced.) The angular speeds, in revolutions per minutes of , , and are in the proportion
If the sum of the first terms and the sum of the first terms of a given arithmetic progression are and , respectively, then the sum of first terms is:
The equations of and are and , respectively. Suppose makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does , and that has 4 times the slope of . If is not horizontal, then is
A bug (of negligible size) starts at the origin on the coordinate plane. First, it moves one unit right to . Then it makes a counterclockwise and travels a unit to . If it continues in this fashion, each time making a degree turn counterclockwise and traveling half as far as the previous move, to which of the following points will it come closest?
If the function is defined by satisfies for all real numbers except , then is
A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly dollars where is a positive integer. The smallest value of is
Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron.
Given that , for how many integers is an integer?
If , , , and , then equals
Let and be three parallel chords of a circle on the same side of the center. The distance between and is the same as the distance between and . The lengths of the chords are , and . The radius of the circle is
A box contains pennies, nickels, and dimes. Six coins are drawn without replacement, with each coin having an equal probability of being chosen. What is the probability that the value of coins drawn is at least cents?
In triangle , , is the midpoint of side , and is a point on side such that ; and intersect at . The ratio of the area of triangle to the area of quadrilateral is
For each real number , let be the minimum of the numbers , and . Then the maximum value of is
Line segments drawn from the vertex opposite the hypotenuse of a right triangle to the points trisecting the hypotenuse have lengths and , where is a real number such that . The length of the hypotenuse is
For some real number , the polynomial is divisible by . Which of the following numbers is closest to ?
In the non-decreasing sequence of odd integers each odd positive integer appears times. It is a fact that there are integers , and such that for all positive integers , , where denotes the largest integer not exceeding . The sum equals
Four balls of radius are mutually tangent, three resting on the floor and the fourth resting on the others. A tetrahedron, each of whose edges have length , is circumscribed around the balls. Then equals
The sum equals
The polynomial is not divisible by if equals
How many ordered triples (x,y,z) of integers satisfy the system of equations below?
A six digit number (base 10) is squarish if it satisfies the following conditions:
(i) none of its digits are zero;
(ii) it is a perfect square; and
(iii) the first of two digits, the middle two digits and the last two digits of the number are all perfect squares when considered as two digit numbers.
How many squarish numbers are there?
|1980 AHSME (Problems • Answer Key • Resources)|
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