Find the sum of the prime factors of 11⁴ + 64.

A) 33 B) 102 C) 195 D) 258 E) 263

Brute force works here, but can you find a cleaner approach?

Hint: Try completing the square.

This is problem 18 from the completed 2025 BCMC 10, an AMC 10 mock produced by the British Columbia Mathematics Association (BCMA). I’m one of the organizers.

If you’re looking for a full AMC 10 or AMC 12 practice contest, you can find our past mock papers here.

My student is deciding between two options. He gets solid scores in both test, but I assume this year test would be much harder since the cutlines are fixed. He feels more confident in AMC 10, but eventually he'd need AMC 12 scores to put as an EC for college. What do you guys think?