June 2021- Lower Semifinals

Learn Bases, and Oh, the Places You'll Go!

100

What is the largest digit that can appear in a Base-5 number?

4

200

What is 21₃ in base 10?

7

300

Write 257 in base 11. 

214₁₁

400

Convert 177₈ to base 5. 

1002₅​​​​

Gee-I'm-A-Tree!

100

What is the hypotenuse of a right triangle with side lengths 8 and 15?

17

200

What is the area of a regular hexagon with side length 2?

6sqrt3

300

A cylinder has a radius of R and a height that is equal to 2 times the radius minus three. If R=4, what is the volume of the cylinder? (exact answer)

80pi

400

What is the sum of ALL interior angles of a 7 sided polygon?

900

Number Theory

100

What is the largest prime number who's perfect square ends in 5?

5

200

How many factors does 252 have?

18 factors

300

What is the next term in the following series?

5, 6, 9, 14, 21...

30

400

The product of a non-zero rational number and an irrational number is always what?

- Rational

- Irrational

- Rational OR Irrational

Irrational

Algebra (I'm out of creative titles, sorry)

100

Solve the following system of equations for B:

3A+2B=14

5A+7B=40

50/11

200

Solve:

x²(x+3)(x+4) when X=2

120

300

Simplify the following expression:

8x² + 5x - 3x² - 9x + 14

5x² - 4x + 14

400

The sum of two numbers is 27 and product is 182. The numbers are:

13 and 14