If you want to set your kid to succeed at spelling tests per se (and he doesn’t have enough past reading/writing experience to know the words already), you could get a list of likely words a few months in advance and put them into some kind of spaced repetition system (whether electronic or based on paper flash cards).

You’ll pay back your initial time investment within a month or two, and you’ll end up with a dramatic improvement to efficiency and long-term retention, as well as teaching a useful tool/skill that can be put to good effect if the kid ever needs to memorize trivia for med school or bar quizzes.

Trying to cram-learn a new list of miscellaneous things every week is a fool’s game. The key to human memory is connections, context, and repeated exposure, not brute-force effort.

Personally I always just read science fiction books hidden in my lap during spelling time in school, and my teachers gave up on trying to get me to study lists of words I already knew how to spell. My older brother’s strategy was to just do poorly on spelling tests because he thought it was a waste of time: never seemed to hurt him, and decades later he can spell as well as anyone. YMMV.