Check out these problems from the 2006 AMC 8.
#17 – This is an excellent probability problem that deals with how the sum of odd numbers are created.
#20 – This counting problem looks at a single elimination tournament and the number of games won/lost by different competitors. It takes a good bit of logic to get to the solution:
#22 – This is also a good logic problem involving numbers:
#24 – Another logic problem involving multiplication:
#21 – This is a good example of a counting problem masking itself as a geometry problem. There is a very nice application of combination theory that makes it very simple:
#22 – This problem deals with analyzing the relative cost of an item. It is actually a great example of a very real world problem.
#23 – The geometry problem combines concepts about isosceles right triangles, circles and area. I always enjoy problems that combine multiple shapes like this:
#25 – This is one of my all-time favorite AMC 8 problems. It always takes me a little while to grasp what turns out to be a very simple concepts about the relationship between the square and the circle:
#22 – This is a good probability problem that uses a very common math competition problem solving skill – use an example to solve the problem. In this case, allowing 8 people to attend the party makes for a very simple solution. I have also included algebraic solution as well.
#24 – A very common method of solving Geometry problems is to use information about the area of a triangle or quadrilateral to find the height of the shape. This problem is a great example of that.
#25 – This Geometry problem brings together multiple concepts all at once. It looks at overlapping squares, 45-45-90 triangles and area of circles. Check out my solution:
I will add some more 2003 videos later. For now check out number 20:
#20 – Measures of angles on a clock are common competition problems. There are some nice formulas that can be used, but I prefer to make sure the why’s behind the formula’s are undestood. Here is my solution:
#20 – This is a good example of using a tessallation to simplify a Geometry problem. If you watch the whole video you can also see it solved using the midsegment theorem.
#24 – The math needed to solve this problem is pretty simple. The hard part is interpreting the problem. Check out my interpretation:
#25 – This is a pretty classic problem involving fractions.
#20 – This is an example of one of my favorite types of problems that show up on the AMC 8. It is essentially a logic problem. I like to draw a diagram to help me decipher who goes where. Here is my solution:
#24 – In my experience, this problem gives students as much trouble as any former AMC 8 problem. I have found the best technique to solve it is to create an example that systematically uses the given information.
#25 – I have always thought this was a weird problem for the AMC 8. You can use some logic to make it easier.
Number 19 – This problem looks at the area of a curved region. My favorite part of this problem is the result is unexpected. Here is the solution:
Number 25 – This is another geometry problem. It is a great example of an important technique when solving competition geometry problems. Often, the properties of the drawing are generalized so a simple example can be used to solve the problem. In this case, picking easy sides to the rectangles so that the area is 72 is very effective. Here is the solution: