You can find some really good resources for math test prep in the used bookstores in a college town. Some examples that I like are: (1) Humongous Book of ______________ Problems (fill in the blank with your math topic); (2) the REA Problem Solvers series;
and (3) the Schaum's Outlines. If you don't live near a college town it might be worth a Saturday trip just to buy books. Alternately, all of these are available (used) through the Amazon Marketplace sellers at really low prices.
You should preview each title of these book series that you might be considering to be sure you like the authors style. Each one is different. You may like one series' treatment of Pre-Calc but prefer a different series for Calculus.
So how do you use these books ?
They are an alternate resource for explanations of basic concepts and problem solving techniques. You should use them as 'hint mills' and sources of problems to...
You'd think that, "If I'm paying for tutoring, he should be answering MY questions. Not the other way around."
While I can sympathize with the general sentiment, I'd say,"you're way off base there!"
I think that the tutor/teacher/coach should never ask the student directly,"Do you understand __________ ?" Not knowing the subject matter, how would the student know/evaluate/determine if they understood or not ? Generally they can't, that's why the need
a tutor. Rather than ask about specific content, directly, I ask questions to determine if the student understands the material and how the pieces fit together. Sometimes that's five or six questions.
Here's my general GAME PLAN: Find out where they are. Tell them, show them, then see what they heard and saw.
When your tutor's asking you questions, he/she is probably working the same kind of plan. You can help them help you by always providing the syllabus...
0. Many STEM problems involve manipulation of a set of constrained equations. Identify the set for the problem you are solving.
1. The numbers don't matter; so, ... plan on always deriving the formula or mathematical expression for your answer, first.
2. Never operate on or write dimensionless numbers in a derivation or problem solution.
3. VARIABLE = Quantity x [Units]. This is always true, even if its not presented this way in introductory courses.
4. Only variables with the same units can be added (or subtracted).
5. The result of multiplying two variables is has units that are the product of the multiplier and multiplicand:
VARIABLE_1 x VARIABLE_2 = Quantity_1 x Quantity_2 x [Units_1 x Units_2] .
Sometimes, units in the numerator(denominator) of one variable will cancel out units in the denominator(numerator) of the other.
6. For details, Google "Dimensional Analysis". That's what I'm talking about!
7. Corrects answers come from derivation...
Work is force times distance: handling your calculator is just as much work as is figuring out what to write down. You will have more time to figure out what to write down if you wait until you've worked out solutions to all the problem you know how to work,
before you use the calculator to compute numerical values. Picking up the calculator, putting it down, making the context shift in your mind,.., all take time away from the work that's earning you points on that test. So just do it once. I will say it again:
deal with the numbers only once!
It's simple. I can help you more, and more quickly, if I can identify your problem areas in advance. So scan in a couple of graded tests and homework assignments and attach those to your email. I can get an ideal of how your teacher grades and how you may
be missing the mark. Make sure your writing is legible on the scanned document. Sooner is better than later.