On Tuesday, November 18, BEAM students (and thousands of 8th graders across the country) participated in the AMC 8. Taken by the strongest 8th grade mathematicians nationwide, the AMC 8 is both challenging and fun.
The AMC 8 is 25 multiple-choice questions, administered over 40 minutes. When the contest ended, students got to request solutions to the problems they didn't understand, making sure that the day was a learning opportunity as well! Most of the solutions were presented by Lynn, our Director of Programs, but Ezelle (an 8th grader) practically jumped out of her seat when it was time to discuss problem #18. Here's the problem she was so excited to solve:
Here's how Ezelle solved it:
- You know the top row has to grow 24 over 4 terms, so each number must be 6 more than the prior number. That gives you 1, 7, 13, 19, 25.
- You know the bottom row has to grow by 64 over 4 terms, so each number must be 16 more than the prior number. That gives you 17, 33, 49, 65, 81.
- Now, to get to X, you only have solve the middle column.
- You know the middle column has to grow from 13 to 49, which is 36 over 4 terms, so each number must be 9 more than the number above. That gives you 13, 22, 31, 40, 49.
- X is in the middle square of the middle column, so X must be 31.
When asked how she figured it out, Ezelle credited a favorite class from last summer, Cory's class titled "Integer Sequences", for teaching her how to think about sequences and series. Nice work, Ezelle! (And a hat tip to Cory, as well!)
You can find the full list of 2015 questions and solutions here. We promise more updates when we get students results back!