************************************* MathMagic Cycle 4: Level 10-12 Regular ************************************* MATH CHAIN A math chain is a series of operations which keeps generating the same result. Start with any number you want and perform the indicated operations to fill in the spaces. When you fill in the [ ] it will be the number you started with. For a greater challenge, start with a number less than 3. [___] -3 = ___ x 6 = ___ + 12 = ___ /6 = ___ + 1 = [___] x 4 = ___ + 8 = ___ /4 = ___ - 2 = [___] + 36 = ___ - 28 = ___ x 4 = ____ - 32 = ____ /4 = [___] Exercise I A) Do the Chain for [ 3 ]. Then do it for [ -2 ]. B) Will the results in [___] always be the same. Explain. C) Is it true for any number x. Prove it! D) Does the chain work in reverse? Start on the end and try it. Explain your results. E) Make your own math chain with at least 3 [___] 's. *************************************** MathMagic Cycle 4: Level 10-12 Advanced *************************************** MORE THAN ONE... EXERCISE I In a pet shop, one section had fish, parrots, and ferrets. When I counted heads of animals, there were 28. When I counted feet, there were 20. How could this be? How many of each type of animal were there? EXERCISE II Find the point(s) of intersection of x^2 + y^2 + 4x - 2y = 5 and x^2 + y^2 + 6x + 4y = 19. ( Substitution may be useful--be creative!) ***********************************