All of
Michael’s current tutoring subjects are listed at the left. You
can read more about
Michael’s qualifications in specific subjects below.
ACT Math
The ACT Math covers topics from Pre-Algebra, Algebra, Geometry, and Trigonometry.
If you are in Pre-Calc, you have most likely seen all the information before.
While the test is certainly checking for content knowledge, it also checks for a certain level of ability to manipulate the material.
Though a calculator is allowed, all questions are designed to be done without, and usually with less effort or the same as typing into the calculator. Time should be set aside for practicing problems both ways.
Unless the problem indicates in some manner that you will be rounding, all answers will be exactly one of the options. If you are even a little off, it is probably not the answer.
Algebra 2
College Level: Intermediate Algebra
High School Level: Algebra II
Algebra 2 is typically taken after Geometry, but can be taken beforehand. Check with your counselor beforehand either way before doing either, however. A large focus here is placed on parent graphs, how you can translate them, and how their corresponding equations would look. Factoring techniques are covered in depth, and quite often, a deeper look will be taken at Trigonometry, beyond SOHCAHTOA, to accommodate ACT test questions.
ASVAB
I have done tutoring for the ASVAB Math portion, which I would compare to the SAT, or the ACT without the Trigonometry, both of which I have also done tutoring.
There are two math portions on this test: Arithmetic Reasoning and Mathematics Knowledge. The Arithmetic Reasoning portion contains word problems, while the Mathematics Knowledge portion contains algebra and geometry problems, which may or may not start off as a word problem.
Currently, no calculator is allowed, so mental calculations, and tricks for simplifying are very useful.
Calculus
Calc I: Take the formula for slope from your algebra and geometry classes, change the notation, and see what happens when the 'run' is taken to be infinitely small.
This derivative will then be used for practical applications: minimizing outputs, maximizing outputs, related rates, etc... Anything from your Alg I, Alg II, and Geom is fair game for working out a problem.
A lot of time will be spent learning the rules for finding the derivative of a function by means of: Power Rule, Product Rule, Quotient rule, and Chain Rule. Be very comfortable using rational exponents rather than radical symbols, and keep a sheet of trig identities at hand.
Calc II: Here is where you mainly learn about anti-derivatives and integrals. There will be a variety of techniques for finding the anti-derivative and integrating: Substitution, Partial Fractions, Integration By Parts, Tabular Integration, etc... Again, anything from previous math courses is fair game, and keep a sheet of trig identities handy. Typical applications are for finding the area and volume of an object.
Geometry
Most of a student's difficulty comes from writing proofs. Think of it as writing an argumentative paper, and having to cite your sources.
With the 'Given' typically as your introduction, make your argument with any supporting definitions, postulates, and/or theorems available to you at that time, and end it with what you want to 'prove' as your conclusion.
Your particular geometry text book is your source for citing, unless other material is given by your instructor. You can only cite references covered to date. No peeking ahead.
Beyond proof writing, while it may be other geometric concepts causing issues, it is probably number concepts, algebra skills, and/or mental calculations that need to be worked on.
Precalculus
A further look is taken at parent graphs, how they can be translated, and the domain and range of functions are more closely kept track of.
Main things to look for when determining the domain of a function: division by zero, square rooting (or any even root) of a number.
Anything learned in previous math classes is fair game at any point, and more time will be spent on special classes of functions, and identities: logarithmic, exponential, trigonometric, rational, etc...
Become very comfortable using rational exponents rather than radical symbols, and do not rely too much on the calculator for calculations which should be done mentally.