MMPC-I Algebra1
1.
If there are n points in the plane no three of which are c1inear and they determine 351
lines, n is equal to?
2.
The number of integers between 1 and 250 (inclusive) that are not divisible by 2 nor by 7
but are divisible by 5 is?
3.
The

MMPC-I Geometry Problems
1.
A right circular cone has height h and base radius. r. Find the area of the cone
(excluding area of the base).
2.
A regular hexagon is inscribed in one circle and circumscribed about another.
Find the ratio of the areas of the

CIMC Practice Problems
1.
Joey is standing at a corner of the rectangular field shown. He walks the perimeter of the
field 5 times. How many meters does Joey walk?
2.
If a + b = 9 - c and a + b = 5 + c, what is the value of c?
3.
Ophelia is paid $51 for t

The Online Math Open Fall Contest
Official Solutions
October 18 - 29, 2013
Acknowledgements
Contest Directors
Evan Chen
Head Problem Writers
Evan Chen
Michael Kural
David Stoner
Problem Contributors, Proofreaders, and Test Solvers
Ray Li
Calvin Deng

MMPC2 Geo2
1.
Given a rectangle ABCD with AC length e and four circles centers A, B, C, D and
radii a, b, c, d respectively, satisfying a+c=b+d<e. Prove you can inscribe a circle
inside the quadrilateral whose sides are the two outer common tangents to th

MATHCOUN TS
1988-89
I State Competition I
40/40 Sprint Round
Name
DO NOT BEGIN UNTIL YOU ARE
INSTRUCTED TO DO $0.
This section of the contest consists of 40
questions. You will have 40 minutes to
complete all the questions. Calculators,
slide rules, boo

32nd United States of America Mathematical Olympiad
Recommended Marking Scheme
May 1, 2003
Remark: The general philosophy of this marking scheme follows that of IMO 2002. This scheme
encourages complete solutions. Partial credits will be given under more

2014 COMC Problems
1.
In triangle ABC, there is a point D on side BC such that BA = AD = DC. Suppose BAD
= 80. Determine the size of ACB.
2.
The equations x2 - a = 0 and 3x4 - 48 = 0 have the same real solutions. What is the value
of a?
3.
A positive inte

2014 DCDS Problems
1.
Bill owed his parents $150. He paid t hem 50% of his debt after a week, 20% of t he
remaining debt the following week, and 40% of the remaining debt (following the first
two payments) one week later. How much more does Bill still owe

AMC 10/12 Practice
1.
What is the smallest positive odd integer n such that the product
21/723/72(2n+1)/7
is greater than 1000? (In the product the denominators of the exponents are all sevens,
and the numerators are the successive odd integers from 1 to

Math IIB/III/IIIAB Placement Test
Spring 2015 February 28 & March 1, 2015
Please staple the placement test along with your answers and the Admit Card. Indicate any
schedule preferences on the Admit Card. The placement test will be posted on the web as
Wee

MATHCOUNTS
2015
Mock State Competition
Sprint Round
Problems 1-30
_
Name _
School _
Chapter_
DO NOT BEGIN UNTIL YOU HAVE SET YOUR TIMER TO FORTY MINUTES.
This section of the competition consists of 30 problems. You will have 40 minutes to complete all the

AHSME Triangles #1
1.
[61 : 8] Let the two base angles of a triangle be A and B, with B larger than A. The
altitude to the base divides the vertex angle C into two parts, C1 and C2, with C2 adjacent
to side a. Then:
(A) C1 + C2 = A + B
(B) Cl - C2 = B - A

Mass Point Geometry Problem Set 1
1.
In ABC, D is the midpoint of BC and E is the trisection point of AC nearer A. Let G =
BE AD. Find AG : GD and BG : GE.
2.
In ABC, D is on AB and E is on BC. Let F = AE CD. AD = 3, DB = 2, BE = 3 and
EC = 4 Find EF : FA

Euclid Practice #1
1.
2.
The equations x2 + 5x + 6 = 0 and x2 + 5x 6 = 0 each have integer solutions whereas
only one of the equations in the pair x2 + 4x + 5 = 0 and x2 + 4x 5 = 0 has integer
solutions.
(a)
Show that if x2 + px + q = 0 and x2 + px q = 0