Difference between revisions of "1984 AHSME Problems"
m (→Problem 21) |
Made in 2016 (talk | contribs) |
||
(35 intermediate revisions by 9 users not shown) | |||
Line 1: | Line 1: | ||
+ | {{AHSME Problems | ||
+ | |year = 1984 | ||
+ | }} | ||
==Problem 1== | ==Problem 1== | ||
<math> \frac{1000^2}{252^2-248^2} </math> equals | <math> \frac{1000^2}{252^2-248^2} </math> equals | ||
− | <math> \mathrm{(A) \ } | + | <math> \mathrm{(A) \ }62500 \qquad \mathrm{(B) \ }1000 \qquad \mathrm{(C) \ } 500\qquad \mathrm{(D) \ }250 \qquad \mathrm{(E) \ } \frac{1}{2} </math> |
[[1984 AHSME Problems/Problem 1|Solution]] | [[1984 AHSME Problems/Problem 1|Solution]] | ||
Line 10: | Line 13: | ||
If <math> x, y </math>, and <math> y-\frac{1}{x} </math> are not <math> 0 </math>, then | If <math> x, y </math>, and <math> y-\frac{1}{x} </math> are not <math> 0 </math>, then | ||
− | < | + | <cmath> \frac{x-\frac{1}{y}}{y-\frac{1}{x}} </cmath> |
+ | equals | ||
<math> \mathrm{(A) \ }1 \qquad \mathrm{(B) \ }\frac{x}{y} \qquad \mathrm{(C) \ } \frac{y}{x}\qquad \mathrm{(D) \ }\frac{x}{y}-\frac{y}{x} \qquad \mathrm{(E) \ } xy-\frac{1}{xy} </math> | <math> \mathrm{(A) \ }1 \qquad \mathrm{(B) \ }\frac{x}{y} \qquad \mathrm{(C) \ } \frac{y}{x}\qquad \mathrm{(D) \ }\frac{x}{y}-\frac{y}{x} \qquad \mathrm{(E) \ } xy-\frac{1}{xy} </math> | ||
Line 24: | Line 28: | ||
==Problem 4== | ==Problem 4== | ||
− | + | A rectangle intersects a circle as shown: <math>AB = 4</math>, <math>BC = 5</math> and <math>DE = 3</math>. Then <math>EF</math> equals | |
+ | [[File:AHSME-1984-Q4.jpg]] | ||
− | {{ | + | <math> \mathrm{(A) \ }6 \qquad \mathrm{(B) \ }7 \qquad \mathrm{(C) \ }\frac{20}{3} \qquad \mathrm{(D) \ }8 \qquad \mathrm{(E) \ }9 </math> |
− | |||
[[1984 AHSME Problems/Problem 4|Solution]] | [[1984 AHSME Problems/Problem 4|Solution]] | ||
Line 39: | Line 43: | ||
==Problem 6== | ==Problem 6== | ||
− | In a certain school, there are | + | In a certain school, there are three times as many boys as girls and nine times as many girls as teachers. Using the letters <math>b, g, t</math> to represent the number of boys, girls and teachers, respectively, then the total number of boys, girls and teachers can be represented by the [[expression]] |
− | <math> \mathrm{(A) \ }31b \qquad \mathrm{(B) \ }\frac{ | + | <math> \mathrm{(A) \ }31b \qquad \mathrm{(B) \ }\frac{37}{27}b \qquad \mathrm{(C) \ } 13g \qquad \mathrm{(D) \ }\frac{37}{27}g \qquad \mathrm{(E) \ } \frac{37}{27}t </math> |
[[1984 AHSME Problems/Problem 6|Solution]] | [[1984 AHSME Problems/Problem 6|Solution]] | ||
==Problem 7== | ==Problem 7== | ||
− | When Dave walks to school, he averages <math> 90 </math> steps per minute, | + | When Dave walks to school, he averages <math> 90 </math> steps per minute, each of his steps <math> 75 </math> cm long. It takes him <math> 16 </math> minutes to get to school. His brother, Jack, going to the same school by the same route, averages <math> 100 </math> steps per minute, but his steps are only <math> 60 </math> cm long. How long does it take Jack to get to school? |
− | <math> \mathrm{(A) \ }14 \frac{2}{9} \text{minutes} \qquad \mathrm{(B) \ }15 \text{minutes}\qquad \mathrm{(C) \ } 18 \text{minutes}\qquad \mathrm{(D) \ }20 \text{minutes} \qquad \mathrm{(E) \ } 22 \frac{2}{9} \text{minutes} </math> | + | <math> \mathrm{(A) \ }14 \frac{2}{9} \text{ minutes} \qquad \mathrm{(B) \ }15 \text{ minutes}\qquad \mathrm{(C) \ } 18 \text{ minutes}\qquad \mathrm{(D) \ }20 \text{ minutes} \qquad \mathrm{(E) \ } 22 \frac{2}{9} \text{ minutes} </math> |
[[1984 AHSME Problems/Problem 7|Solution]] | [[1984 AHSME Problems/Problem 7|Solution]] | ||
==Problem 8== | ==Problem 8== | ||
− | Figure <math> ABCD </math> is a [[trapezoid]] with <math> AB||DC </math>, <math> AB=5 </math>, <math> BC=3\sqrt{2} </math>, <math> \angle BCD=45^\circ </math> | + | Figure <math> ABCD </math> is a [[trapezoid]] with <math> AB||DC </math>, <math> AB=5 </math>, <math> BC=3\sqrt{2} </math>, <math> \angle BCD=45^\circ </math> and <math> \angle CDA=60^\circ </math>. The length of <math> DC </math> is |
+ | |||
+ | [[File:AHSME-1984-Q8.jpg]] | ||
<math> \mathrm{(A) \ }7+\frac{2}{3}\sqrt{3} \qquad \mathrm{(B) \ }8 \qquad \mathrm{(C) \ } 9 \frac{1}{2} \qquad \mathrm{(D) \ }8+\sqrt{3} \qquad \mathrm{(E) \ } 8+3\sqrt{3} </math> | <math> \mathrm{(A) \ }7+\frac{2}{3}\sqrt{3} \qquad \mathrm{(B) \ }8 \qquad \mathrm{(C) \ } 9 \frac{1}{2} \qquad \mathrm{(D) \ }8+\sqrt{3} \qquad \mathrm{(E) \ } 8+3\sqrt{3} </math> | ||
Line 67: | Line 73: | ||
==Problem 10== | ==Problem 10== | ||
− | Four [[complex numbers]] lie at the [[vertices]] of a [[square]] in the [[complex plane]]. Three of the numbers are <math> 1+2i, -2+i </math> | + | Four [[complex numbers]] lie at the [[vertices]] of a [[square]] in the [[complex plane]]. Three of the numbers are <math> 1+2i, {-2}+i </math> and <math> {-1}-2i </math>. The fourth number is |
− | <math> \mathrm{(A) \ }2+i \qquad \mathrm{(B) \ }2-i \qquad \mathrm{(C) \ } 1-2i \qquad \mathrm{(D) \ }-1+2i \qquad \mathrm{(E) \ } -2-i </math> | + | <math> \mathrm{(A) \ }2+i \qquad \mathrm{(B) \ }2-i \qquad \mathrm{(C) \ } 1-2i \qquad \mathrm{(D) \ }{-1}+2i \qquad \mathrm{(E) \ } {-2}-i </math> |
[[1984 AHSME Problems/Problem 10|Solution]] | [[1984 AHSME Problems/Problem 10|Solution]] | ||
==Problem 11== | ==Problem 11== | ||
− | A calculator has a key that replaces the displayed entry with its [[Perfect square|square]], and another key which replaces the displayed entry with its [[reciprocal]]. Let <math> y </math> be the final result when one starts with | + | A calculator has a key that replaces the displayed entry with its [[Perfect square|square]], and another key which replaces the displayed entry with its [[reciprocal]]. Let <math> y </math> be the final result when one starts with an entry <math> x\not=0 |
</math> and alternately squares and reciprocates <math> n </math> times each. Assuming the calculator is completely accurate (e.g. no roundoff or overflow), then <math> y </math> equals | </math> and alternately squares and reciprocates <math> n </math> times each. Assuming the calculator is completely accurate (e.g. no roundoff or overflow), then <math> y </math> equals | ||
Line 84: | Line 90: | ||
If the [[sequence]] <math> \{a_n\} </math> is defined by | If the [[sequence]] <math> \{a_n\} </math> is defined by | ||
− | < | + | <cmath>a_1=2,</cmath> |
− | + | <cmath>a_{n+1}=a_n+2n \qquad (n \geq 1),</cmath> | |
− | < | ||
− | + | then <math> a_{100} </math> equals | |
− | |||
− | |||
<math> \mathrm{(A) \ }9900 \qquad \mathrm{(B) \ }9902 \qquad \mathrm{(C) \ } 9904 \qquad \mathrm{(D) \ }10100 \qquad \mathrm{(E) \ } 10102 </math> | <math> \mathrm{(A) \ }9900 \qquad \mathrm{(B) \ }9902 \qquad \mathrm{(C) \ } 9904 \qquad \mathrm{(D) \ }10100 \qquad \mathrm{(E) \ } 10102 </math> | ||
Line 127: | Line 130: | ||
==Problem 17== | ==Problem 17== | ||
− | A [[right triangle]] <math> ABC </math> with [[hypotenuse]] <math> AB </math> has side <math> AC=15 </math>. [[Altitude]] <math> CH </math> divides <math> AB </math> into segments <math> AH </math> and <math> HB </math>, with <math> HB=16 </math>. The [[area]] of <math> \triangle ABC </math> is: | + | A [[right triangle]] <math> ABC </math> with [[hypotenuse]] <math> AB </math> has side <math> AC=15 </math>. [[Altitude]] <math> CH </math> divides <math> AB </math> into segments <math> AH </math> and <math> HB </math>, with <math> HB=16 </math>. The [[area]] of <math> \triangle ABC </math> is |
+ | |||
+ | [[File:AHSME-1984-Q17.jpg]] | ||
<math> \mathrm{(A) \ }120 \qquad \mathrm{(B) \ }144 \qquad \mathrm{(C) \ } 150 \qquad \mathrm{(D) \ }216 \qquad \mathrm{(E) \ } 144\sqrt{5} </math> | <math> \mathrm{(A) \ }120 \qquad \mathrm{(B) \ }144 \qquad \mathrm{(C) \ } 150 \qquad \mathrm{(D) \ }216 \qquad \mathrm{(E) \ } 144\sqrt{5} </math> | ||
Line 134: | Line 139: | ||
==Problem 18== | ==Problem 18== | ||
− | A point <math> (x, y) </math> is to be chosen in the [[coordinate plane]] so that it is equally distant from the [[x-axis]], the [[y-axis]], and the [[line]] <math> x+y=2 </math>. Then <math> x </math> is | + | A point <math> (x, y) </math> is to be chosen in the [[coordinate plane]] so that it is equally distant from the [[x-axis|<math>x</math>-axis]], the [[y-axis|<math>y</math>-axis]], and the [[line]] <math> x+y=2 </math>. Then <math> x </math> is |
− | <math> \mathrm{(A) \ }\sqrt{2}-1 \qquad \mathrm{(B) \ }\frac{1}{2} \qquad \mathrm{(C) \ } 2-\sqrt{2} \qquad \mathrm{(D) \ }1 \qquad \mathrm{(E) \ } \text{ | + | <math> \mathrm{(A) \ }\sqrt{2}-1 \qquad \mathrm{(B) \ }\frac{1}{2} \qquad \mathrm{(C) \ } 2-\sqrt{2} \qquad \mathrm{(D) \ }1 \qquad \mathrm{(E) \ } \text{not uniquely determined} </math> |
[[1984 AHSME Problems/Problem 18|Solution]] | [[1984 AHSME Problems/Problem 18|Solution]] | ||
==Problem 19== | ==Problem 19== | ||
− | A box contains <math> 11 </math> balls, numbered <math> 1, 2, 3, | + | A box contains <math> 11 </math> balls, numbered <math> 1, 2, 3,\ldots,11 </math>. If <math> 6 </math> balls are drawn simultaneously at random, what is the [[probability]] that the sum of the numbers on the balls drawn is odd? |
<math> \mathrm{(A) \ }\frac{100}{231} \qquad \mathrm{(B) \ }\frac{115}{231} \qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ }\frac{118}{231} \qquad \mathrm{(E) \ } \frac{6}{11} </math> | <math> \mathrm{(A) \ }\frac{100}{231} \qquad \mathrm{(B) \ }\frac{115}{231} \qquad \mathrm{(C) \ } \frac{1}{2} \qquad \mathrm{(D) \ }\frac{118}{231} \qquad \mathrm{(E) \ } \frac{6}{11} </math> | ||
Line 148: | Line 153: | ||
==Problem 20== | ==Problem 20== | ||
− | The number of the distinct solutions | + | The number of the distinct solutions of the [[equation]] <math> |{x-|2x+1|}|=3 </math> is |
− | |||
− | <math> |x-|2x+1||=3 </math> is | ||
<math> \mathrm{(A) \ }0 \qquad \mathrm{(B) \ }1 \qquad \mathrm{(C) \ } 2 \qquad \mathrm{(D) \ }3 \qquad \mathrm{(E) \ } 4 </math> | <math> \mathrm{(A) \ }0 \qquad \mathrm{(B) \ }1 \qquad \mathrm{(C) \ } 2 \qquad \mathrm{(D) \ }3 \qquad \mathrm{(E) \ } 4 </math> | ||
Line 159: | Line 162: | ||
The number of triples <math> (a, b, c) </math> of [[Natural numbers|positive integers]] which satisfy the simultaneous [[Equation|equations]] | The number of triples <math> (a, b, c) </math> of [[Natural numbers|positive integers]] which satisfy the simultaneous [[Equation|equations]] | ||
− | < | + | <cmath> ab+bc=44,</cmath> |
− | + | <cmath> ac+bc=23,</cmath> | |
− | < | ||
is | is | ||
Line 170: | Line 172: | ||
==Problem 22== | ==Problem 22== | ||
− | Let <math> a </math> and <math> c </math> be fixed [[Natural numbers|positive numbers]]. For each [[real number]] <math> t </math> let <math> (x_t, y_t) </math> be the [[vertex]] of the [[parabola]] <math> y=ax^2+bx+c </math>. If the set of the vertices <math> (x_t, y_t) </math> for all real | + | Let <math> a </math> and <math> c </math> be fixed [[Natural numbers|positive numbers]]. For each [[real number]] <math> t </math> let <math> (x_t, y_t) </math> be the [[vertex]] of the [[parabola]] <math> y=ax^2+bx+c </math>. If the set of the vertices <math> (x_t, y_t) </math> for all real values of <math> t </math> is graphed on the [[Cartesian plane|plane]], the [[graph]] is |
− | <math> \mathrm{(A) \ } \text{a straight line} \qquad \mathrm{(B) \ } \text{a parabola} \qquad \mathrm{(C) \ } \text{part, but not all, of a parabola} \qquad \mathrm{(D) \ } \text{one branch of a hyperbola} \qquad | + | <math> \mathrm{(A) \ } \text{a straight line} \qquad \mathrm{(B) \ } \text{a parabola} \qquad \mathrm{(C) \ } \text{part, but not all, of a parabola} \qquad \mathrm{(D) \ } \text{one branch of a hyperbola} \qquad \mathrm{(E) \ } \text{none of these} </math> |
[[1984 AHSME Problems/Problem 22|Solution]] | [[1984 AHSME Problems/Problem 22|Solution]] | ||
Line 191: | Line 193: | ||
==Problem 25== | ==Problem 25== | ||
− | The total [[area]] of all the [[faces]] of a [[Rectangular prism|rectangular solid]] is <math> 22\text{cm}^2 </math>, and the total length of all its [[edges]] is <math> 24\text{cm} </math>. Then the length in cm of any one of its [[Diagonal#Polyhedra|interior diagonals]] is | + | The total [[area]] of all the [[faces]] of a [[Rectangular prism|rectangular solid]] is <math> 22 \ \text{cm}^2 </math>, and the total length of all its [[edges]] is <math> 24 \ \text{cm} </math>. Then the length in cm of any one of its [[Diagonal#Polyhedra|interior diagonals]] is |
− | <math> \mathrm{(A) \ }\sqrt{11} \qquad \mathrm{(B) \ }\sqrt{12} \qquad \mathrm{(C) \ } \sqrt{13}\qquad \mathrm{(D) \ }\sqrt{14} \qquad \mathrm{(E) \ } \text{ | + | <math> \mathrm{(A) \ }\sqrt{11} \qquad \mathrm{(B) \ }\sqrt{12} \qquad \mathrm{(C) \ } \sqrt{13}\qquad \mathrm{(D) \ }\sqrt{14} \qquad \mathrm{(E) \ } \text{not uniquely determined} </math> |
[[1984 AHSME Problems/Problem 25|Solution]] | [[1984 AHSME Problems/Problem 25|Solution]] | ||
==Problem 26== | ==Problem 26== | ||
− | In the [[obtuse triangle]] <math> ABC | + | In the [[obtuse triangle]] <math> ABC </math>, <math> AM=MB </math>, <math> MD\perp BC </math>, <math> EC\perp BC </math>. If the [[area]] of <math> \triangle ABC </math> is <math> 24 </math>, then the area of <math> \triangle BED </math> is |
− | <math> \mathrm{(A) \ }9 \qquad \mathrm{(B) \ }12 \qquad \mathrm{(C) \ } 15 \qquad \mathrm{(D) \ }18 \qquad \mathrm{(E) \ } \text{ | + | [[File:AHSME-1984-Q26.jpg]] |
+ | |||
+ | <math> \mathrm{(A) \ }9 \qquad \mathrm{(B) \ }12 \qquad \mathrm{(C) \ } 15 \qquad \mathrm{(D) \ }18 \qquad \mathrm{(E) \ } \text{not uniquely determined} </math> | ||
[[1984 AHSME Problems/Problem 26|Solution]] | [[1984 AHSME Problems/Problem 26|Solution]] | ||
==Problem 27== | ==Problem 27== | ||
− | In <math> \triangle ABC </math>, <math> D </math> is on <math> AC </math> and <math> F </math> is on <math> BC </math>. Also, <math> AB\ | + | In <math> \triangle ABC </math>, <math> D </math> is on <math> AC </math> and <math> F </math> is on <math> BC </math>. Also, <math> AB\perp AC </math>, <math> AF\perp BC </math>, and <math> BD=DC=FC=1 </math>. Find <math> AC </math>. |
+ | |||
+ | [[File:AHSME-1984-Q27.jpg]] | ||
<math> \mathrm{(A) \ }\sqrt{2} \qquad \mathrm{(B) \ }\sqrt{3} \qquad \mathrm{(C) \ } \sqrt[3]{2} \qquad \mathrm{(D) \ }\sqrt[3]{3} \qquad \mathrm{(E) \ } \sqrt[4]{3} </math> | <math> \mathrm{(A) \ }\sqrt{2} \qquad \mathrm{(B) \ }\sqrt{3} \qquad \mathrm{(C) \ } \sqrt[3]{2} \qquad \mathrm{(D) \ }\sqrt[3]{3} \qquad \mathrm{(E) \ } \sqrt[4]{3} </math> | ||
Line 227: | Line 233: | ||
==Problem 30== | ==Problem 30== | ||
For any [[complex number]] <math> w=a+bi </math>, <math> |w| </math> is defined to be the [[real number]] <math> \sqrt{a^2+b^2} </math>. If <math> w=\cos40^\circ+i\sin40^\circ </math>, then | For any [[complex number]] <math> w=a+bi </math>, <math> |w| </math> is defined to be the [[real number]] <math> \sqrt{a^2+b^2} </math>. If <math> w=\cos40^\circ+i\sin40^\circ </math>, then | ||
+ | <math> |w+2w^2+3w^3+...+9w^9|^{-1} </math> equals | ||
− | <math> | + | <math> \mathrm{(A) \ }\frac{1}{9}\sin40^\circ \qquad \mathrm{(B) \ }\frac{2}{9}\sin20^\circ \qquad \mathrm{(C) \ } \frac{1}{9}\cos40^\circ \qquad \mathrm{(D) \ }\frac{1}{18}\cos20^\circ \qquad \mathrm{(E) \ } \text{none of these} </math> |
− | + | [[1984 AHSME Problems/Problem 30|Solution]] | |
− | |||
− | |||
− | |||
− | ==See | + | == See also == |
− | *[[ | + | * [[AMC 12 Problems and Solutions]] |
+ | * [[Mathematics competition resources]] | ||
− | + | {{AHSME box|year=1984|before=[[1983 AHSME]]|after=[[1985 AHSME]]}} | |
− | + | {{MAA Notice}} |
Latest revision as of 14:00, 19 February 2020
1984 AHSME (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
| ||
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 |
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 See also
Problem 1
equals
Problem 2
If , and
are not
, then
equals
Problem 3
Let be the smallest nonprime integer greater than
with no prime factor less than
. Then
Problem 4
A rectangle intersects a circle as shown: ,
and
. Then
equals
Problem 5
The largest integer for which
is
Problem 6
In a certain school, there are three times as many boys as girls and nine times as many girls as teachers. Using the letters to represent the number of boys, girls and teachers, respectively, then the total number of boys, girls and teachers can be represented by the expression
Problem 7
When Dave walks to school, he averages steps per minute, each of his steps
cm long. It takes him
minutes to get to school. His brother, Jack, going to the same school by the same route, averages
steps per minute, but his steps are only
cm long. How long does it take Jack to get to school?
Problem 8
Figure is a trapezoid with
,
,
,
and
. The length of
is
Problem 9
The number of digits in (when written in the usual base
form) is
Problem 10
Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are and
. The fourth number is
Problem 11
A calculator has a key that replaces the displayed entry with its square, and another key which replaces the displayed entry with its reciprocal. Let be the final result when one starts with an entry
and alternately squares and reciprocates
times each. Assuming the calculator is completely accurate (e.g. no roundoff or overflow), then
equals
Problem 12
If the sequence is defined by
then equals
Problem 13
equals
Problem 14
The product of all real roots of the equation is
Problem 15
If , then one value for
is
Problem 16
The function satisfies
for all real numbers
. If the equation
has exactly four distinct real roots, then the sum of these roots is
Problem 17
A right triangle with hypotenuse
has side
. Altitude
divides
into segments
and
, with
. The area of
is
Problem 18
A point is to be chosen in the coordinate plane so that it is equally distant from the
-axis, the
-axis, and the line
. Then
is
Problem 19
A box contains balls, numbered
. If
balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?
Problem 20
The number of the distinct solutions of the equation is
Problem 21
The number of triples of positive integers which satisfy the simultaneous equations
is
Problem 22
Let and
be fixed positive numbers. For each real number
let
be the vertex of the parabola
. If the set of the vertices
for all real values of
is graphed on the plane, the graph is
Problem 23
equals
Problem 24
If and
are positive real numbers and each of the equations
and
has real roots, then the smallest possible value of
is
Problem 25
The total area of all the faces of a rectangular solid is , and the total length of all its edges is
. Then the length in cm of any one of its interior diagonals is
Problem 26
In the obtuse triangle ,
,
,
. If the area of
is
, then the area of
is
Problem 27
In ,
is on
and
is on
. Also,
,
, and
. Find
.
Problem 28
The number of distinct pairs of integers such that
and
is
Problem 29
Find the largest value for for pairs of real numbers
which satisfy
.
Problem 30
For any complex number ,
is defined to be the real number
. If
, then
equals
See also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by 1983 AHSME |
Followed by 1985 AHSME | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.