AAJ Math Geniuses Competition - Final Round

Divide and Conquer!"Numerations & Operations"

100

Evaluate: 2⁵-5²

7

200

The ratio of boys to girls in a class is 8:2. 

If there are 40 students in total, how many girls are there?

8 Girls.

300

Find the sum of the first 5 terms of an arithmetic sequence where the first term is 5 and the common difference is 5:

75

400

Calculate the modulus function for Z = 12 + 5i :

13

500

The ratio of boys to girls in a class is 8:2. 

If there are 40 students in total, how many girls are there?

8 girls

X Marks the Spot!"Algebra"

100

find f(0) for f(x)=3^2x+3+3 :

30

200

If 3X + 7 = 2X + 15

Find X :

8

300

What is the domain for the function: 

f(x) = Ln (3X-6)

X > 2

(2, + Infinity)

400

If A+B=13, and A x B = 42, 

Then: A²+B²=

85

500

Find the value of X: 

9^2x+2 = 27⁸

5

Game of Cones!"Geometry"

100

A rectangular prism has a length of 5, width of 2, and height of 10. What is its volume?

100

200

A square has a perimeter of 40. What is its area?

100

300

A cone has a radius of 3 and a height of 4. What is its slant height?

5

400

What is the exact distance between the points (-2, 5) and (4, -3) on the coordinate plane?

10

500

A cone and a cylinder have the exact same base radius and the exact same volume. If the height of the cylinder is 10, what is the height of the cone?

30

Angle Management!"Trigonometry"

100

In an equilateral triangle the measure of each angle is equal to:

60^o

200

If the two legs of a right triangle are perfectly equal in length, what is the exact tangent of either acute angle?

45^o

300

Sin²(17)+Cos²(17) = ?

1

400

In a right angle triangle, if the opposite side of an angle is equal to 12 and the adjacent side is equal to 5, calculate the Sine of that angle:

(12/13)

500

Simplify the following trigonometric identity completely: 

2Tan(x) . 3Cot(x) . 4Sec(x) . 5Cos(x)=?

120