Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "User:Azjps/sandbox"

m (asy testing)
(Progress Table)
Line 1: Line 1:
−
<center><asy>
+
{| class="wikitable"
−
defaultpen(fontsize(11pt));
+
|-
−
size(250);
+
| style="background:#66ff66" | [[1983 AIME]] - || [[1983 AIME Problems|Problems]] - || [[1983 AIME Answer Key|Key]] - || [[1983 AIME Problems/Problem 1|1]] - || [[1983 AIME Problems/Problem 2|2]] - || [[1983 AIME Problems/Problem 3|3]] - || [[1983 AIME Problems/Problem 4|4]] - || [[1983 AIME Problems/Problem 5|5]] - || [[1983 AIME Problems/Problem 6|6]] - || [[1983 AIME Problems/Problem 7|7]] - || [[1983 AIME Problems/Problem 8|8]] - || [[1983 AIME Problems/Problem 9|9]] - || [[1983 AIME Problems/Problem 10|10]] - || [[1983 AIME Problems/Problem 11|11]] - || [[1983 AIME Problems/Problem 12|12]] - || [[1983 AIME Problems/Problem 13|13]] - || [[1983 AIME Problems/Problem 14|14]] - || [[1983 AIME Problems/Problem 15|15]] - ||
−
real Radius = 4;
+
|-
−
pair O=(0,0), A=(Radius,0), B=A*expi(pi/3), C=((63^.5-3^.5)/2,0), D=C*expi(pi/3);
+
| style="background:#66ff66" | [[1984 AIME]] - || [[1984 AIME Problems|Problems]] - || [[1984 AIME Answer Key|Key]] - || [[1984 AIME Problems/Problem 1|1]] - || [[1984 AIME Problems/Problem 2|2]] - || [[1984 AIME Problems/Problem 3|3]] - || [[1984 AIME Problems/Problem 4|4]] - || [[1984 AIME Problems/Problem 5|5]] - || [[1984 AIME Problems/Problem 6|6]] - || [[1984 AIME Problems/Problem 7|7]] - || [[1984 AIME Problems/Problem 8|8]] - || [[1984 AIME Problems/Problem 9|9]] - || [[1984 AIME Problems/Problem 10|10]] - || [[1984 AIME Problems/Problem 11|11]] - || [[1984 AIME Problems/Problem 12|12]] - || [[1984 AIME Problems/Problem 13|13]] - || [[1984 AIME Problems/Problem 14|14]] - || [[1984 AIME Problems/Problem 15|15]] - ||
−
draw(Circle(O,Radius));
+
|-
−
dot(O);
+
| style="background:#66ff66" | [[1985 AIME]] - || [[1985 AIME Problems|Problems]] - || [[1985 AIME Answer Key|Key]] - || [[1985 AIME Problems/Problem 1|1]] - || [[1985 AIME Problems/Problem 2|2]] - || [[1985 AIME Problems/Problem 3|3]] - || [[1985 AIME Problems/Problem 4|4]] - || [[1985 AIME Problems/Problem 5|5]] - || [[1985 AIME Problems/Problem 6|6]] - || [[1985 AIME Problems/Problem 7|7]] - || [[1985 AIME Problems/Problem 8|8]] - || [[1985 AIME Problems/Problem 9|9]] - || [[1985 AIME Problems/Problem 10|10]] - || [[1985 AIME Problems/Problem 11|11]] - || [[1985 AIME Problems/Problem 12|12]] - || [[1985 AIME Problems/Problem 13|13]] - || [[1985 AIME Problems/Problem 14|14]] - || [[1985 AIME Problems/Problem 15|15]] - ||
−
draw(B--O); draw(C--A);
+
|-
−
pair F=(C+(0.5*3^0.5,0.5)), G=(D+(0.5*3^0.5,0.5));
+
| style="background:#66ff66" | [[1986 AIME]] - || [[1986 AIME Problems|Problems]] - || [[1986 AIME Answer Key|Key]] - || [[1986 AIME Problems/Problem 1|1]] - || [[1986 AIME Problems/Problem 2|2]] - || [[1986 AIME Problems/Problem 3|3]] - || [[1986 AIME Problems/Problem 4|4]] - || [[1986 AIME Problems/Problem 5|5]] - || [[1986 AIME Problems/Problem 6|6]] - || [[1986 AIME Problems/Problem 7|7]] - || [[1986 AIME Problems/Problem 8|8]] - || [[1986 AIME Problems/Problem 9|9]] - || [[1986 AIME Problems/Problem 10|10]] - || [[1986 AIME Problems/Problem 11|11]] - || [[1986 AIME Problems/Problem 12|12]] - || [[1986 AIME Problems/Problem 13|13]] - || [[1986 AIME Problems/Problem 14|14]] - || [[1986 AIME Problems/Problem 15|15]] - ||
−
draw(C--D--G--F);
+
|-
−
draw(O--C--F--cycle,linewidth(1));
+
| style="background:#66ff66" | [[1987 AIME]] - || [[1987 AIME Problems|Problems]] - || [[1987 AIME Answer Key|Key]] - || [[1987 AIME Problems/Problem 1|1]] - || [[1987 AIME Problems/Problem 2|2]] - || [[1987 AIME Problems/Problem 3|3]] - || [[1987 AIME Problems/Problem 4|4]] - || [[1987 AIME Problems/Problem 5|5]] - || [[1987 AIME Problems/Problem 6|6]] - || [[1987 AIME Problems/Problem 7|7]] - || [[1987 AIME Problems/Problem 8|8]] - || [[1987 AIME Problems/Problem 9|9]] - || [[1987 AIME Problems/Problem 10|10]] - || [[1987 AIME Problems/Problem 11|11]] - || [[1987 AIME Problems/Problem 12|12]] - || [[1987 AIME Problems/Problem 13|13]] - || [[1987 AIME Problems/Problem 14|14]] - || [[1987 AIME Problems/Problem 15|15]] - ||
−
picture p = new picture;
+
|-
−
draw(p,Circle(C,0.15));
+
| style="background:#66ff66" | [[1988 AIME]] - || [[1988 AIME Problems|Problems]] - || [[1988 AIME Answer Key|Key]] - || [[1988 AIME Problems/Problem 1|1]] - || [[1988 AIME Problems/Problem 2|2]] - || [[1988 AIME Problems/Problem 3|3]] - || [[1988 AIME Problems/Problem 4|4]] - || [[1988 AIME Problems/Problem 5|5]] - || [[1988 AIME Problems/Problem 6|6]] - || [[1988 AIME Problems/Problem 7|7]] - || [[1988 AIME Problems/Problem 8|8]] - || [[1988 AIME Problems/Problem 9|9]] - || [[1988 AIME Problems/Problem 10|10]] - || [[1988 AIME Problems/Problem 11|11]] - || [[1988 AIME Problems/Problem 12|12]] - || [[1988 AIME Problems/Problem 13|13]] - || [[1988 AIME Problems/Problem 14|14]] - || [[1988 AIME Problems/Problem 15|15]] - ||
−
clip(p,O--C--F--cycle);
+
|-
−
add(p);
+
| style="background:#66ff66" | [[1989 AIME]] - || [[1989 AIME Problems|Problems]] - || [[1989 AIME Answer Key|Key]] - || [[1989 AIME Problems/Problem 1|1]] - || [[1989 AIME Problems/Problem 2|2]] - || [[1989 AIME Problems/Problem 3|3]] - || [[1989 AIME Problems/Problem 4|4]] - || [[1989 AIME Problems/Problem 5|5]] - || [[1989 AIME Problems/Problem 6|6]] - || [[1989 AIME Problems/Problem 7|7]] - || [[1989 AIME Problems/Problem 8|8]] - || [[1989 AIME Problems/Problem 9|9]] - || [[1989 AIME Problems/Problem 10|10]] - || [[1989 AIME Problems/Problem 11|11]] - || [[1989 AIME Problems/Problem 12|12]] - || [[1989 AIME Problems/Problem 13|13]] - || [[1989 AIME Problems/Problem 14|14]] - || [[1989 AIME Problems/Problem 15|15]] - ||
−
p = new picture;
+
|-
−
draw(p,Circle(D,0.15));
+
| style="background:#66ff66" | [[1990 AIME]] - || [[1990 AIME Problems|Problems]] - || [[1990 AIME Answer Key|Key]] - || [[1990 AIME Problems/Problem 1|1]] - || [[1990 AIME Problems/Problem 2|2]] - || [[1990 AIME Problems/Problem 3|3]] - || [[1990 AIME Problems/Problem 4|4]] - || [[1990 AIME Problems/Problem 5|5]] - || [[1990 AIME Problems/Problem 6|6]] - || [[1990 AIME Problems/Problem 7|7]] - || [[1990 AIME Problems/Problem 8|8]] - || [[1990 AIME Problems/Problem 9|9]] - || [[1990 AIME Problems/Problem 10|10]] - || [[1990 AIME Problems/Problem 11|11]] - || [[1990 AIME Problems/Problem 12|12]] - || [[1990 AIME Problems/Problem 13|13]] - || [[1990 AIME Problems/Problem 14|14]] - || [[1990 AIME Problems/Problem 15|15]] - ||
−
clip(p,O--D--C--cycle);
+
|-
−
add(p);
+
| style="background:#66ff66" | [[1991 AIME]] - || [[1991 AIME Problems|Problems]] - || [[1991 AIME Answer Key|Key]] - || [[1991 AIME Problems/Problem 1|1]] - || [[1991 AIME Problems/Problem 2|2]] - || [[1991 AIME Problems/Problem 3|3]] - || [[1991 AIME Problems/Problem 4|4]] - || [[1991 AIME Problems/Problem 5|5]] - || [[1991 AIME Problems/Problem 6|6]] - || [[1991 AIME Problems/Problem 7|7]] - || [[1991 AIME Problems/Problem 8|8]] - || [[1991 AIME Problems/Problem 9|9]] - || [[1991 AIME Problems/Problem 10|10]] - || [[1991 AIME Problems/Problem 11|11]] - || [[1991 AIME Problems/Problem 12|12]] - || [[1991 AIME Problems/Problem 13|13]] - || [[1991 AIME Problems/Problem 14|14]] - || [[1991 AIME Problems/Problem 15|15]] - ||
−
clip(currentpicture,B+(0,1)--O-(0.2,0.2)--A+(1,0)--cycle);
+
|-
−
label("\(x\)",(O+C)/2,S);
+
| [[1992 AIME]] - || [[1992 AIME Problems|Problems]] - || [[1992 AIME Answer Key|Key]] - || [[1992 AIME Problems/Problem 1|1]] - || [[1992 AIME Problems/Problem 2|2]] - || [[1992 AIME Problems/Problem 3|3]] - || [[1992 AIME Problems/Problem 4|4]] - || [[1992 AIME Problems/Problem 5|5]] - || [[1992 AIME Problems/Problem 6|6]] - || [[1992 AIME Problems/Problem 7|7]] - || [[1992 AIME Problems/Problem 8|8]] - || [[1992 AIME Problems/Problem 9|9]] - || [[1992 AIME Problems/Problem 10|10]] - || [[1992 AIME Problems/Problem 11|11]] - || [[1992 AIME Problems/Problem 12|12]] - || [[1992 AIME Problems/Problem 13|13]] - || [[1992 AIME Problems/Problem 14|14]] - || [[1992 AIME Problems/Problem 15|15]] - ||
−
label("\(x\)",(D+C)/2,NE);
+
|-
−
label("\(1\)",(F+C)/2,SE);
+
| [[1993 AIME]] - || [[1993 AIME Problems|Problems]] - || [[1993 AIME Answer Key|Key]] - || [[1993 AIME Problems/Problem 1|1]] - || [[1993 AIME Problems/Problem 2|2]] - || [[1993 AIME Problems/Problem 3|3]] - || [[1993 AIME Problems/Problem 4|4]] - || [[1993 AIME Problems/Problem 5|5]] - || [[1993 AIME Problems/Problem 6|6]] - || [[1993 AIME Problems/Problem 7|7]] - || [[1993 AIME Problems/Problem 8|8]] - || [[1993 AIME Problems/Problem 9|9]] - || [[1993 AIME Problems/Problem 10|10]] - || [[1993 AIME Problems/Problem 11|11]] - || [[1993 AIME Problems/Problem 12|12]] - || [[1993 AIME Problems/Problem 13|13]] - || [[1993 AIME Problems/Problem 14|14]] - || [[1993 AIME Problems/Problem 15|15]] - ||
−
label("\(4\)",(O+F)/2,NW);
+
|-
−
label("\(150^{\circ}\)",C+(-0.08,0.08),NW);
+
| [[1994 AIME]] - || [[1994 AIME Problems|Problems]] - || [[1994 AIME Answer Key|Key]] - || [[1994 AIME Problems/Problem 1|1]] - || [[1994 AIME Problems/Problem 2|2]] - || [[1994 AIME Problems/Problem 3|3]] - || [[1994 AIME Problems/Problem 4|4]] - || [[1994 AIME Problems/Problem 5|5]] - || [[1994 AIME Problems/Problem 6|6]] - || [[1994 AIME Problems/Problem 7|7]] - || [[1994 AIME Problems/Problem 8|8]] - || [[1994 AIME Problems/Problem 9|9]] - || [[1994 AIME Problems/Problem 10|10]] - || [[1994 AIME Problems/Problem 11|11]] - || [[1994 AIME Problems/Problem 12|12]] - || [[1994 AIME Problems/Problem 13|13]] - || [[1994 AIME Problems/Problem 14|14]] - || [[1994 AIME Problems/Problem 15|15]] - ||
−
label("\(60^{\circ}\)",D+(0,-0.15),S);
+
|-
−
</asy></center>
+
| [[1995 AIME]] - || [[1995 AIME Problems|Problems]] - || [[1995 AIME Answer Key|Key]] - || [[1995 AIME Problems/Problem 1|1]] - || [[1995 AIME Problems/Problem 2|2]] - || [[1995 AIME Problems/Problem 3|3]] - || [[1995 AIME Problems/Problem 4|4]] - || [[1995 AIME Problems/Problem 5|5]] - || [[1995 AIME Problems/Problem 6|6]] - || [[1995 AIME Problems/Problem 7|7]] - || [[1995 AIME Problems/Problem 8|8]] - || [[1995 AIME Problems/Problem 9|9]] - || [[1995 AIME Problems/Problem 10|10]] - || [[1995 AIME Problems/Problem 11|11]] - || [[1995 AIME Problems/Problem 12|12]] - || [[1995 AIME Problems/Problem 13|13]] - || [[1995 AIME Problems/Problem 14|14]] - || [[1995 AIME Problems/Problem 15|15]] - ||
−
 
+
|-
−
By the [[Law of Cosines]] on the bolded triangle,
+
| [[1996 AIME]] - || [[1996 AIME Problems|Problems]] - || [[1996 AIME Answer Key|Key]] - || [[1996 AIME Problems/Problem 1|1]] - || [[1996 AIME Problems/Problem 2|2]] - || [[1996 AIME Problems/Problem 3|3]] - || [[1996 AIME Problems/Problem 4|4]] - || [[1996 AIME Problems/Problem 5|5]] - || [[1996 AIME Problems/Problem 6|6]] - || [[1996 AIME Problems/Problem 7|7]] - || [[1996 AIME Problems/Problem 8|8]] - || [[1996 AIME Problems/Problem 9|9]] - || [[1996 AIME Problems/Problem 10|10]] - || [[1996 AIME Problems/Problem 11|11]] - || [[1996 AIME Problems/Problem 12|12]] - || [[1996 AIME Problems/Problem 13|13]] - || [[1996 AIME Problems/Problem 14|14]] - || [[1996 AIME Problems/Problem 15|15]] - ||
−
<cmath>\begin{align*}
+
|-
−
4^2 &= x^2 + 1^2 - 2 \cdot x \cdot 1 \cos 150^{\circ}\\
+
| style="background:#66ff66" | [[1997 AIME]] - || [[1997 AIME Problems|Problems]] - || [[1997 AIME Answer Key|Key]] - || [[1997 AIME Problems/Problem 1|1]] - || [[1997 AIME Problems/Problem 2|2]] - || [[1997 AIME Problems/Problem 3|3]] - || [[1997 AIME Problems/Problem 4|4]] - || [[1997 AIME Problems/Problem 5|5]] - || [[1997 AIME Problems/Problem 6|6]] - || [[1997 AIME Problems/Problem 7|7]] - || [[1997 AIME Problems/Problem 8|8]] - || [[1997 AIME Problems/Problem 9|9]] - || [[1997 AIME Problems/Problem 10|10]] - || [[1997 AIME Problems/Problem 11|11]] - || [[1997 AIME Problems/Problem 12|12]] - || [[1997 AIME Problems/Problem 13|13]] - || [[1997 AIME Problems/Problem 14|14]] - || [[1997 AIME Problems/Problem 15|15]] - ||
−
0 &= x^2 + \sqrt{3}x - 15 \\
+
|-
−
x &= \boxed{\frac{3\sqrt{7}-\sqrt{3}}{2}}
+
| style="background:#66ff66" | [[1998 AIME]] - || [[1998 AIME Problems|Problems]] - || [[1998 AIME Answer Key|Key]] - || [[1998 AIME Problems/Problem 1|1]] - || [[1998 AIME Problems/Problem 2|2]] - || [[1998 AIME Problems/Problem 3|3]] - || [[1998 AIME Problems/Problem 4|4]] - || [[1998 AIME Problems/Problem 5|5]] - || [[1998 AIME Problems/Problem 6|6]] - || [[1998 AIME Problems/Problem 7|7]] - || [[1998 AIME Problems/Problem 8|8]] - || [[1998 AIME Problems/Problem 9|9]] - || [[1998 AIME Problems/Problem 10|10]] - || [[1998 AIME Problems/Problem 11|11]] - || [[1998 AIME Problems/Problem 12|12]] - || [[1998 AIME Problems/Problem 13|13]] - || [[1998 AIME Problems/Problem 14|14]] - || [[1998 AIME Problems/Problem 15|15]] - ||
−
\end{align*}
+
|-
−
</cmath>
+
| style="background:#66ff66" | [[1999 AIME]] - || [[1999 AIME Problems|Problems]] - || [[1999 AIME Answer Key|Key]] - || [[1999 AIME Problems/Problem 1|1]] - || [[1999 AIME Problems/Problem 2|2]] - || [[1999 AIME Problems/Problem 3|3]] - || [[1999 AIME Problems/Problem 4|4]] - || [[1999 AIME Problems/Problem 5|5]] - || [[1999 AIME Problems/Problem 6|6]] - || [[1999 AIME Problems/Problem 7|7]] - || [[1999 AIME Problems/Problem 8|8]] - || [[1999 AIME Problems/Problem 9|9]] - || [[1999 AIME Problems/Problem 10|10]] - || [[1999 AIME Problems/Problem 11|11]] - || [[1999 AIME Problems/Problem 12|12]] - || [[1999 AIME Problems/Problem 13|13]] - || [[1999 AIME Problems/Problem 14|14]] - || [[1999 AIME Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2000 AIME I]] - || [[2000 AIME I Problems|Problems]] - || [[2000 AIME I Answer Key|Key]] - || [[2000 AIME I Problems/Problem 1|1]] - || [[2000 AIME I Problems/Problem 2|2]] - || [[2000 AIME I Problems/Problem 3|3]] - || [[2000 AIME I Problems/Problem 4|4]] - || [[2000 AIME I Problems/Problem 5|5]] - || [[2000 AIME I Problems/Problem 6|6]] - || [[2000 AIME I Problems/Problem 7|7]] - || [[2000 AIME I Problems/Problem 8|8]] - || [[2000 AIME I Problems/Problem 9|9]] - || [[2000 AIME I Problems/Problem 10|10]] - || [[2000 AIME I Problems/Problem 11|11]] - || [[2000 AIME I Problems/Problem 12|12]] - || [[2000 AIME I Problems/Problem 13|13]] - || [[2000 AIME I Problems/Problem 14|14]] - || [[2000 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2000 AIME II]] - || [[2000 AIME II Problems|Problems]] - || [[2000 AIME II Answer Key|Key]] - || [[2000 AIME II Problems/Problem 1|1]] - || [[2000 AIME II Problems/Problem 2|2]] - || [[2000 AIME II Problems/Problem 3|3]] - || [[2000 AIME II Problems/Problem 4|4]] - || [[2000 AIME II Problems/Problem 5|5]] - || [[2000 AIME II Problems/Problem 6|6]] - || [[2000 AIME II Problems/Problem 7|7]] - || [[2000 AIME II Problems/Problem 8|8]] - || [[2000 AIME II Problems/Problem 9|9]] - || [[2000 AIME II Problems/Problem 10|10]] - || [[2000 AIME II Problems/Problem 11|11]] - || [[2000 AIME II Problems/Problem 12|12]] - || [[2000 AIME II Problems/Problem 13|13]] - || [[2000 AIME II Problems/Problem 14|14]] - || [[2000 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2001 AIME I]] - || [[2001 AIME I Problems|Problems]] - || [[2001 AIME I Answer Key|Key]] - || [[2001 AIME I Problems/Problem 1|1]] - || [[2001 AIME I Problems/Problem 2|2]] - || [[2001 AIME I Problems/Problem 3|3]] - || [[2001 AIME I Problems/Problem 4|4]] - || [[2001 AIME I Problems/Problem 5|5]] - || [[2001 AIME I Problems/Problem 6|6]] - || [[2001 AIME I Problems/Problem 7|7]] - || [[2001 AIME I Problems/Problem 8|8]] - || [[2001 AIME I Problems/Problem 9|9]] - || [[2001 AIME I Problems/Problem 10|10]] - || [[2001 AIME I Problems/Problem 11|11]] - || [[2001 AIME I Problems/Problem 12|12]] - || [[2001 AIME I Problems/Problem 13|13]] - || [[2001 AIME I Problems/Problem 14|14]] - || [[2001 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2001 AIME II]] - || [[2001 AIME II Problems|Problems]] - || [[2001 AIME II Answer Key|Key]] - || [[2001 AIME II Problems/Problem 1|1]] - || [[2001 AIME II Problems/Problem 2|2]] - || [[2001 AIME II Problems/Problem 3|3]] - || [[2001 AIME II Problems/Problem 4|4]] - || [[2001 AIME II Problems/Problem 5|5]] - || [[2001 AIME II Problems/Problem 6|6]] - || [[2001 AIME II Problems/Problem 7|7]] - || [[2001 AIME II Problems/Problem 8|8]] - || [[2001 AIME II Problems/Problem 9|9]] - || [[2001 AIME II Problems/Problem 10|10]] - || [[2001 AIME II Problems/Problem 11|11]] - || [[2001 AIME II Problems/Problem 12|12]] - || [[2001 AIME II Problems/Problem 13|13]] - || [[2001 AIME II Problems/Problem 14|14]] - || [[2001 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2002 AIME I]] - || [[2002 AIME I Problems|Problems]] - || [[2002 AIME I Answer Key|Key]] - || [[2002 AIME I Problems/Problem 1|1]] - || [[2002 AIME I Problems/Problem 2|2]] - || [[2002 AIME I Problems/Problem 3|3]] - || [[2002 AIME I Problems/Problem 4|4]] - || [[2002 AIME I Problems/Problem 5|5]] - || [[2002 AIME I Problems/Problem 6|6]] - || [[2002 AIME I Problems/Problem 7|7]] - || [[2002 AIME I Problems/Problem 8|8]] - || [[2002 AIME I Problems/Problem 9|9]] - || [[2002 AIME I Problems/Problem 10|10]] - || [[2002 AIME I Problems/Problem 11|11]] - || [[2002 AIME I Problems/Problem 12|12]] - || [[2002 AIME I Problems/Problem 13|13]] - || [[2002 AIME I Problems/Problem 14|14]] - || [[2002 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2002 AIME II]] - || [[2002 AIME II Problems|Problems]] - || [[2002 AIME II Answer Key|Key]] - || [[2002 AIME II Problems/Problem 1|1]] - || [[2002 AIME II Problems/Problem 2|2]] - || [[2002 AIME II Problems/Problem 3|3]] - || [[2002 AIME II Problems/Problem 4|4]] - || [[2002 AIME II Problems/Problem 5|5]] - || [[2002 AIME II Problems/Problem 6|6]] - || [[2002 AIME II Problems/Problem 7|7]] - || [[2002 AIME II Problems/Problem 8|8]] - || [[2002 AIME II Problems/Problem 9|9]] - || [[2002 AIME II Problems/Problem 10|10]] - || [[2002 AIME II Problems/Problem 11|11]] - || [[2002 AIME II Problems/Problem 12|12]] - || [[2002 AIME II Problems/Problem 13|13]] - || [[2002 AIME II Problems/Problem 14|14]] - || [[2002 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2003 AIME I]] - || [[2003 AIME I Problems|Problems]] - || [[2003 AIME I Answer Key|Key]] - || [[2003 AIME I Problems/Problem 1|1]] - || [[2003 AIME I Problems/Problem 2|2]] - || [[2003 AIME I Problems/Problem 3|3]] - || [[2003 AIME I Problems/Problem 4|4]] - || [[2003 AIME I Problems/Problem 5|5]] - || [[2003 AIME I Problems/Problem 6|6]] - || [[2003 AIME I Problems/Problem 7|7]] - || [[2003 AIME I Problems/Problem 8|8]] - || [[2003 AIME I Problems/Problem 9|9]] - || [[2003 AIME I Problems/Problem 10|10]] - || [[2003 AIME I Problems/Problem 11|11]] - || [[2003 AIME I Problems/Problem 12|12]] - || [[2003 AIME I Problems/Problem 13|13]] - || [[2003 AIME I Problems/Problem 14|14]] - || [[2003 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2003 AIME II]] - || [[2003 AIME II Problems|Problems]] - || [[2003 AIME II Answer Key|Key]] - || [[2003 AIME II Problems/Problem 1|1]] - || [[2003 AIME II Problems/Problem 2|2]] - || [[2003 AIME II Problems/Problem 3|3]] - || [[2003 AIME II Problems/Problem 4|4]] - || [[2003 AIME II Problems/Problem 5|5]] - || [[2003 AIME II Problems/Problem 6|6]] - || [[2003 AIME II Problems/Problem 7|7]] - || [[2003 AIME II Problems/Problem 8|8]] - || [[2003 AIME II Problems/Problem 9|9]] - || [[2003 AIME II Problems/Problem 10|10]] - || [[2003 AIME II Problems/Problem 11|11]] - || [[2003 AIME II Problems/Problem 12|12]] - || [[2003 AIME II Problems/Problem 13|13]] - || [[2003 AIME II Problems/Problem 14|14]] - || [[2003 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2004 AIME I]] - || [[2004 AIME I Problems|Problems]] - || [[2004 AIME I Answer Key|Key]] - || [[2004 AIME I Problems/Problem 1|1]] - || [[2004 AIME I Problems/Problem 2|2]] - || [[2004 AIME I Problems/Problem 3|3]] - || [[2004 AIME I Problems/Problem 4|4]] - || [[2004 AIME I Problems/Problem 5|5]] - || [[2004 AIME I Problems/Problem 6|6]] - || [[2004 AIME I Problems/Problem 7|7]] - || [[2004 AIME I Problems/Problem 8|8]] - || [[2004 AIME I Problems/Problem 9|9]] - || [[2004 AIME I Problems/Problem 10|10]] - || [[2004 AIME I Problems/Problem 11|11]] - || [[2004 AIME I Problems/Problem 12|12]] - || [[2004 AIME I Problems/Problem 13|13]] - || [[2004 AIME I Problems/Problem 14|14]] - || [[2004 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2004 AIME II]] - || [[2004 AIME II Problems|Problems]] - || [[2004 AIME II Answer Key|Key]] - || [[2004 AIME II Problems/Problem 1|1]] - || [[2004 AIME II Problems/Problem 2|2]] - || [[2004 AIME II Problems/Problem 3|3]] - || [[2004 AIME II Problems/Problem 4|4]] - || [[2004 AIME II Problems/Problem 5|5]] - || [[2004 AIME II Problems/Problem 6|6]] - || [[2004 AIME II Problems/Problem 7|7]] - || [[2004 AIME II Problems/Problem 8|8]] - || [[2004 AIME II Problems/Problem 9|9]] - || [[2004 AIME II Problems/Problem 10|10]] - || [[2004 AIME II Problems/Problem 11|11]] - || [[2004 AIME II Problems/Problem 12|12]] - || [[2004 AIME II Problems/Problem 13|13]] - || [[2004 AIME II Problems/Problem 14|14]] - || [[2004 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2005 AIME I]] - || [[2005 AIME I Problems|Problems]] - || [[2005 AIME I Answer Key|Key]] - || [[2005 AIME I Problems/Problem 1|1]] - || [[2005 AIME I Problems/Problem 2|2]] - || [[2005 AIME I Problems/Problem 3|3]] - || [[2005 AIME I Problems/Problem 4|4]] - || [[2005 AIME I Problems/Problem 5|5]] - || [[2005 AIME I Problems/Problem 6|6]] - || [[2005 AIME I Problems/Problem 7|7]] - || [[2005 AIME I Problems/Problem 8|8]] - || [[2005 AIME I Problems/Problem 9|9]] - || [[2005 AIME I Problems/Problem 10|10]] - || [[2005 AIME I Problems/Problem 11|11]] - || [[2005 AIME I Problems/Problem 12|12]] - || [[2005 AIME I Problems/Problem 13|13]] - || [[2005 AIME I Problems/Problem 14|14]] - || [[2005 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2005 AIME II]] - || [[2005 AIME II Problems|Problems]] - || [[2005 AIME II Answer Key|Key]] - || [[2005 AIME II Problems/Problem 1|1]] - || [[2005 AIME II Problems/Problem 2|2]] - || [[2005 AIME II Problems/Problem 3|3]] - || [[2005 AIME II Problems/Problem 4|4]] - || [[2005 AIME II Problems/Problem 5|5]] - || [[2005 AIME II Problems/Problem 6|6]] - || [[2005 AIME II Problems/Problem 7|7]] - || [[2005 AIME II Problems/Problem 8|8]] - || [[2005 AIME II Problems/Problem 9|9]] - || [[2005 AIME II Problems/Problem 10|10]] - || [[2005 AIME II Problems/Problem 11|11]] - || [[2005 AIME II Problems/Problem 12|12]] - || [[2005 AIME II Problems/Problem 13|13]] - || [[2005 AIME II Problems/Problem 14|14]] - || [[2005 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2006 AIME I]] - || [[2006 AIME I Problems|Problems]] - || [[2006 AIME I Answer Key|Key]] - || [[2006 AIME I Problems/Problem 1|1]] - || [[2006 AIME I Problems/Problem 2|2]] - || [[2006 AIME I Problems/Problem 3|3]] - || [[2006 AIME I Problems/Problem 4|4]] - || [[2006 AIME I Problems/Problem 5|5]] - || [[2006 AIME I Problems/Problem 6|6]] - || [[2006 AIME I Problems/Problem 7|7]] - || [[2006 AIME I Problems/Problem 8|8]] - || [[2006 AIME I Problems/Problem 9|9]] - || [[2006 AIME I Problems/Problem 10|10]] - || [[2006 AIME I Problems/Problem 11|11]] - || [[2006 AIME I Problems/Problem 12|12]] - || [[2006 AIME I Problems/Problem 13|13]] - || [[2006 AIME I Problems/Problem 14|14]] - || [[2006 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2006 AIME II]] - || [[2006 AIME II Problems|Problems]] - || [[2006 AIME II Answer Key|Key]] - || [[2006 AIME II Problems/Problem 1|1]] - || [[2006 AIME II Problems/Problem 2|2]] - || [[2006 AIME II Problems/Problem 3|3]] - || [[2006 AIME II Problems/Problem 4|4]] - || [[2006 AIME II Problems/Problem 5|5]] - || [[2006 AIME II Problems/Problem 6|6]] - || [[2006 AIME II Problems/Problem 7|7]] - || [[2006 AIME II Problems/Problem 8|8]] - || [[2006 AIME II Problems/Problem 9|9]] - || [[2006 AIME II Problems/Problem 10|10]] - || [[2006 AIME II Problems/Problem 11|11]] - || [[2006 AIME II Problems/Problem 12|12]] - || [[2006 AIME II Problems/Problem 13|13]] - || [[2006 AIME II Problems/Problem 14|14]] - || [[2006 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2007 AIME I]] - || [[2007 AIME I Problems|Problems]] - || [[2007 AIME I Answer Key|Key]] - || [[2007 AIME I Problems/Problem 1|1]] - || [[2007 AIME I Problems/Problem 2|2]] - || [[2007 AIME I Problems/Problem 3|3]] - || [[2007 AIME I Problems/Problem 4|4]] - || [[2007 AIME I Problems/Problem 5|5]] - || [[2007 AIME I Problems/Problem 6|6]] - || [[2007 AIME I Problems/Problem 7|7]] - || [[2007 AIME I Problems/Problem 8|8]] - || [[2007 AIME I Problems/Problem 9|9]] - || [[2007 AIME I Problems/Problem 10|10]] - || [[2007 AIME I Problems/Problem 11|11]] - || [[2007 AIME I Problems/Problem 12|12]] - || [[2007 AIME I Problems/Problem 13|13]] - || [[2007 AIME I Problems/Problem 14|14]] - || [[2007 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2007 AIME II]] - || [[2007 AIME II Problems|Problems]] - || [[2007 AIME II Answer Key|Key]] - || [[2007 AIME II Problems/Problem 1|1]] - || [[2007 AIME II Problems/Problem 2|2]] - || [[2007 AIME II Problems/Problem 3|3]] - || [[2007 AIME II Problems/Problem 4|4]] - || [[2007 AIME II Problems/Problem 5|5]] - || [[2007 AIME II Problems/Problem 6|6]] - || [[2007 AIME II Problems/Problem 7|7]] - || [[2007 AIME II Problems/Problem 8|8]] - || [[2007 AIME II Problems/Problem 9|9]] - || [[2007 AIME II Problems/Problem 10|10]] - || [[2007 AIME II Problems/Problem 11|11]] - || [[2007 AIME II Problems/Problem 12|12]] - || [[2007 AIME II Problems/Problem 13|13]] - || [[2007 AIME II Problems/Problem 14|14]] - || [[2007 AIME II Problems/Problem 15|15]] - ||
 +
|-
 +
| style="background:#66ff66" | [[2008 AIME I]] - || [[2008 AIME I Problems|Problems]] - || [[2008 AIME I Answer Key|Key]] - || [[2008 AIME I Problems/Problem 1|1]] - || [[2008 AIME I Problems/Problem 2|2]] - || [[2008 AIME I Problems/Problem 3|3]] - || [[2008 AIME I Problems/Problem 4|4]] - || [[2008 AIME I Problems/Problem 5|5]] - || [[2008 AIME I Problems/Problem 6|6]] - || [[2008 AIME I Problems/Problem 7|7]] - || [[2008 AIME I Problems/Problem 8|8]] - || [[2008 AIME I Problems/Problem 9|9]] - || [[2008 AIME I Problems/Problem 10|10]] - || [[2008 AIME I Problems/Problem 11|11]] - || [[2008 AIME I Problems/Problem 12|12]] - || [[2008 AIME I Problems/Problem 13|13]] - || [[2008 AIME I Problems/Problem 14|14]] - || [[2008 AIME I Problems/Problem 15|15]] - ||
 +
|-
 +
| [[2008 AIME II]] - || [[2008 AIME II Problems|Problems]] - || [[2008 AIME II Answer Key|Key]] - || [[2008 AIME II Problems/Problem 1|1]] - || [[2008 AIME II Problems/Problem 2|2]] - || [[2008 AIME II Problems/Problem 3|3]] - || [[2008 AIME II Problems/Problem 4|4]] - || [[2008 AIME II Problems/Problem 5|5]] - || [[2008 AIME II Problems/Problem 6|6]] - || [[2008 AIME II Problems/Problem 7|7]] - || [[2008 AIME II Problems/Problem 8|8]] - || [[2008 AIME II Problems/Problem 9|9]] - || [[2008 AIME II Problems/Problem 10|10]] - || [[2008 AIME II Problems/Problem 11|11]] - || [[2008 AIME II Problems/Problem 12|12]] - || [[2008 AIME II Problems/Problem 13|13]] - || [[2008 AIME II Problems/Problem 14|14]] - || [[2008 AIME II Problems/Problem 15|15]] - ||
 +
|}

Revision as of 17:06, 19 June 2008

1983 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1984 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1985 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1986 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1987 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1988 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1989 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1990 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1991 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1992 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1993 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1994 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1995 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1996 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1997 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1998 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
1999 AIME - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2000 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2000 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2001 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2001 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2002 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2002 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2003 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2003 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2004 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2004 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2005 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2005 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2006 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2006 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2007 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2007 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2008 AIME I - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
2008 AIME II - Problems - Key - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 -
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=User:Azjps/sandbox&oldid=26677"