Math Competitions

 

 

This is an annual competition held at your high school every March or April. In 2001-2002, it was held on March 26 and April 9. It is open for students who perform well on the American Mathematics Contest 10 or the American Mathematics Contest 12. It contains 15 challenging questions with answers being integers from 0 to 999. 3 hours are given for this contest. More information can be found here.

 

Sample Problem

 

What is the largest 2-digit prime factor of ?

 

 

This is an annual competition held at your high school every February. It is open for any student in grade 10 or below. In 2001-2002, it was held on February 12 and February 27. It contains 25 multiple choice questions. 75 minutes are given for this contest. More information can be found here.

 

Sample Problem

 

What is the maximum number for the possible points of intersection of a circle and a triangle?

 

 

This is an annual competition held at your high school every February. In 2001-2002, it was held on February 12 and  February 27. It contains 25 multiple choice questions. 75 minutes are given for this contest. More information can be found here.

 

Sample Problem

 

Let f be a function satisfying for all positive real numbers x and y. If , what is the value of ?

 

American Regions Math League

 

This is an annual competition held simultaneously at San Jose State University, University of Iowa, and Penn State every June. It contains an individual round, with 8 questions, 10 minutes per pair. There is also a relay round, a team round, and a power (proof) round. In 2001-2002, it will be held on May 31 and June 1. More information can be found here.

 

Sample Problem

 

The measure of the vertex angle of isosceles triangle ABC is  and the sides of the triangle are , , and . Compute the area of .

 

Bay Area Math Meet

 

This is an annual competition held at University of San Francisco every April. More information can be found here.

 

Sample Problem

 

Find the probability that a number from the set  is divisible by 7 or 11 (or both).

 

Bay Area Math Olympiad

 

This is a competition held annually at your high school every February. In 2001-2002, it will be held on February 26. More information can be found here.

 

Sample Problem

 

Let JHIZ be a rectangle, and let A and C be points on sides ZI and ZJ, respectively. The perpendicular from A to CH intersects line HI at X, and the perpendicular from C to AH intersects line HJ at Y. Prove that X, Y and Z are collinear (lie on the same line).

 

California Math League

 

This is a competition held six times per year at your high school. There is one in October, one in November, one in December, one in January, one in February, and one in March. In 2001-2002, they will be held on October 30, December 4, January 8, February 5, March 5, and April 9. More information can be found here.

 

Sample Problem

 

If i represents the imaginary unit, what is the ordered pair of real numbers (a, b) for which ?

 

 

Department of Energy Math Competition

This is an annual competition held at the Lawrence Livermore Labs every May. More information can be found here.

 

Sample Problem

 

What two integers, neither containing any zeros, when multiplied together, will give exactly 1,000,000,000?

 

Hokubei Mainichi Math Competition

 

This competition is held annually in January at Santa Teresa High School. There is a Junior division for students in grades 7-9 and a Senior division for students in grades 10-12.

 

Sample Problem

 

Coming soon hopefully

 

 

This competition is held annually in July, in a different country each year. A country can send six students to the International Mathematical Olympiad each year. In the United States, these people will are among the top twelve students in the USA Mathematical Olympiad. More information can be found here.

 

Sample Problem

 

Let a, b, c, d be integers with . Suppose that . Prove that  is not prime.

 

 

This competition is held four times per year at your high school. The dates are in November, January, February, and March. In 2001-2002, they will be held on October 22, November 26, January 21, and February 25. More information can be found here.

 

Sample Problem

 

A quadrilateral inscribed in a circle has side lengths 17, 99, 19, and 97. Find the area of the circle.

 

Polya

 

This is an annual competition held at Castilleja School every October or November. In 2001-2002, it will be held on November 17. More information can be found here.

 

Sample Problem

 

Find all integers n > 3 such that n – 3 divides evenly into .

 

College of Creative Studies Math Competition

 

This is an annual competition held annually at your high school. The first round is a preliminary round held in October. For students who perform well on this preliminary round, there is an advanced round held in November. More information can be found here.

 

Sample Problem

 

Preliminary round: An equilateral triangle is inscribed in a circle of radius 2 inches. What is the area of the triangle?

Advanced round: A number is said to be rational if it can be expressed as the ratio of two integers. Prove that the tangent of  degrees is not rational.

 

Santa Clara High School Math Contest

 

This is an annual competition held at Santa Clara University every November. More information can be found here.

 

Sample Problem

 

In how many ways can the numbers 1, 2, 3, 4, 5, 6 be arranged as a sequence u, v, w, x, y, z such that u + x = v + y = w + z?

 

Santa Clara Valley Math Field Day

 

This is an annual competition held at San Jose State University every March. In 2001-2002, it will be held on March 23. There are seven divisions for competition: Algebra I, Geometry, Algebra II, Open (Trigonometry and Precalculus), Calculus, Leapfrog, and Discovery Quest. For the first five of these, you must be currently enrolled in a class covering those topics to enter.

 

Sample Problem

 

Algebra I: Find the domain of the following equation: .

Geometry: A square and an equilateral triangle have equal perimeters. The area of the triangle is 93 square inches. Expressed in inches what is the diagonal of the square?

Algebra II: Simplify .

Open: What is the center of an ellipse whose equation is ?

Calculus: What is the value of ?

Leap Frog: What is the smallest natural number with exactly 24 divisors?

Discovery Quest: Hopefully coming soon

 

 

This is an annual competition held at Stanford University every February. More information can be found here.

 

Sample Problem

 

Advanced Topics: Evaluate .

Algebra: Find all solutions to .

Calculus: Let . If , then find .

Geometry: In a triangle the sum of squares of medians is 96. What is the maximum possible value of the sum of the medians?

General: How many permutations of 123456 have exactly one number in the correct place?

 

 

This is an annual competition which is held in Massachusetts in May each year. In 2001-2002, it will be held on May 2-5. It is open to all students who perform well on the American Invitational Mathematics Examination. More information can be found here.

 

Sample Problem

 

Prove that the average of the numbers  is cot 1.

 

USA Mathematical Talent Search

 

This contest is held four times per year. You get the questions with about a month to solve them, using whatever references you want, as long as those references are not other people. Due dates are in October, November, January, and March. In 2001-2002, these due dates are October 8, November 25, January 6, and March 17. More information can be found here.

 

Sample Problem

 

We define the repetition number of a positive integer n to be the number of distinct digits of n when written in base 10. Prove that each integer has a multiple which has a repetition number less than or equal to 2.