Here's a big tip for any science tutor.
Expand your range. You can't be an expert in everything, but as long as you have a lot of depth in one arena, it pays to work on breadth.
Think of a redwood tree. The tree seems to be focused single-mindedly on growing straight up and being the tallest tree in the forest. The mighty Sequoia sempervirens doesn't waste a lot of energy growing side branches.
And yet, if you look under the surface, every redwood sends out roots that may extend as far out as a football field. You should be the same in your science learning.
For example, I'm a biologist. But I'm making a point of teaching myself calculus and physics. You never know when you'll find something useful in another field that helps you shed light on a topic in your own field. This extra breadth is especially useful for a science tutor. Being able to explain something new to a student in terms of something they already know is an age-old technique that stays in vogue because it's so effective.
I'm even using this technique on myself, as this video will show. I'm using my personal experience with biking to become more skilled in calculus and physics.
This video just shows a very simplified version of a basic concept, but it helped me understand some things that had been perplexing me for years. It's a start.
In the book Mindhacker, Ron and Marty Hale-Evans suggest that one should try to "polyspecialize." I'm not sure how successful I'll ever be at becoming a polyspecialist, but I can see the immediate value of their suggestion. Pick two or three subjects that really interest you, and learn more about them than 90% of the human population.
If you can do that, you'll actually have the means to learn a lot more. You'll have built yourself a framework for hanging up new information. But more importantly, a lot of cognitive research suggests that you learn better and more thoroughly when you connect seemingly unrelated ideas and knowledge.
Which brings me back to the whole point of this post. A science tutor should learn things that are loosely related to his or her field. It will make you smarter. It will make your students smarter.
Biologists make extensive use of probability and statistics. So I must learn calculus.