Math Team

Number Theory

100

What is the greatest common factor of 1005 and 2021?

1

200

The sum of 10 consecutive even integers is 450; find the largest integer.

54

300

Find two numbers whose product is 1,000,000 such that neither number contains a zero.

64 and 15,625

Geometry

100

What is the sum of the angles of a triangle?

180

200

An equilateral triangle has perimeter P and area A . If A = 2sqrt(3)P, then what is the side length of the triangle

24

300

) We begin with an equilateral triangle. We divide each side into three segments of equal length, and add an equilateral triangle to each side using the middle third as a base. We then repeat this to get a third figure. Given that the perimeter of the first figure is 12, what is the perimeter of the third figure?

64/3

Algebra

100

Solve the following equation for x: |4x-5| = 2x+1

x=3 and x=2/3

200

The vertex of the parabola y = x²-16x+k is on the x-axis. What is the value of k ?

64

300

Bryan has a part-time job delivering packages. He is paid a flat rate of $9.50 per hour. Caleb works at a competitor that pays its employees $2 per hour plus $3 per delivery. How many deliveries would Caleb have to make in 40 hours to earn the same pay as Bryan for a a 40 hour work week

100

Trigonometry and Complex Numbers

100

sin²(x) + cos²(x) = ?

1

200

Simplify (i²⁰²¹+i²⁰²²+i²⁰²³+i²⁰²⁴)²⁰²¹

0

300

Triangle ABC has a right triangle at C. If sin(A) = 2/3, then find the exact value of sin(B)*cos(A)*tan²(B)

25/36

Pre-Calculus

100

A circle is defined by equation x² +y² -2x -8y +10 = 0. Find the distance between the origin and the center of this circle.

sqrt (17)

200

If a$b = a^b +b. Determine the value of (4$5) - (5$4)

400

300

Find the largest value of 𝑥 for which x2+y2 = x+y has a solution, if 𝑥 and 𝑦 are real.

(1+sqrt(2))/2