Level 4: Solve the following 5 problems:

The tale of twelve drummers drumming: All of the twelve drumming drummers have decorated the heads of their snare drums. A typical snare drum has a diameter of 14 inches.   1. Drummer #8 decorated his drum head with two circles. The areas of the two circles are shown. Which of the numbered expressions is equivalent to the difference of these areas? The green circle is the drum head. 1) (3x - 1) (2x + 1) 2) (6x - 1) (x + 1) 3) (3x + 1) (2x - 1) 4) (6x + 1) (x - 1)         2. Drummer # 4 has decorated his drum head (as shown at the right) with a graphic image and a square. Find the area of the square if the equation of the circle is x² + y² = 49. The green circle is the drum head.     3. Drummer #1 says that the decorative circle on his drum head has the equation x² + y² - 2x - 4y - 11 = 0. Which of the following diagrams depicts his decorated drum head? The green circle is the drum head. 1) 2) 3) 4)         4. Drummer #12 has artistically placed a picture of a fractal (specifically a Julia set) on his drum head. Fractals work with complex numbers (z) on a repeating basis. The function for a Julia set may be f (z) = z² + (1 + i). The green circle is the drum head. Using this function, determine which of the numbered choices will be the simplification of f (2 + i). 1) 3 + 2i 2) 1 + 3i 3) 4 + 5i 4) 4 + i           5. Drummer #6 has decorated his drum in a symmetrical circular pattern. R and r represent radii of the circles as shown where R = 2r. The area of the viewable green portion of the drum head (the largest circle) is . a) Find R. b) Find r. The green circle is the drum head.

This is the END of LEVEL 4:
Read carefully!!
Multiply 10 times the sum of the answers to question #5. Multiply this result by the product of the remaining answers.

To obtain your LEVEL 4 CERTIFICATE: Place this answer in the address below (following the capital letters "HCERT"), and type the address into your browser to find the certificate.

http://mathbits.com/caching/holiday/HCERT__________.pdf