I have tutored and helped many students with Algebra 1, and I am very experienced with the maths involved, due to using it extensively throughout high school and university-level maths courses.
Algebra 2 is one of the subjects I tutor most often, and it's also one of my favorite subjects to tutor. It expands on some topics from algebra 1, and introduces some new topics, which are also seen in precalculus.
If students struggled in algebra 1, then they often run into trouble with the more advanced math and new concepts in algebra 2. I try to catch them up on their previously covered algebra, while also helping them to understand the new material.
Calculus is the study of rates-of-change. It is a very interesting subject, but can also be very difficult for a lot of students. This is due to the math involved being very different to previous maths courses, thus it can feel very abstract.
It is here that students are introduced to some advanced mathematical concepts such as limits, differentiation and integration.
I haven't studied chemistry beyond the 12th-grade level, but I did have a very solid understanding of high school chemistry, and I am proficient enough to help students at that level. I have a strong physics background, which helps, as a lot of chemistry concepts have their roots in physics.
I have tutored several chemistry students, and it's a subject I really enjoy teaching. There are many real-life applications, and plenty of interesting topics, such as chemical reactions (e.g., dropping cesium into water!).
I studied discrete math in high school and performed very well in the course, and continued my study of it throughout university. I have also tutored students in discrete math.
I tutor many students in elementary math at the tutoring center I work at - most of the students we get are elementary math, or academic reading. I've tutored children from 6 years old and up, in basic arithmetic (addition, subtraction, multiplication, division), fractions, decimals, percentages, and problem solving.
A lot of geometry concepts are second nature to me by now, due to using them extensively in other math courses. I've helped many students with geometry at the tutoring center I work at, and also helped older students to review key geometry concepts and formulas (such as for the SAT).
There are a lot of theorems and formulas in geometry, but there's also simple ways to remember said theorems/formulas.
I graduated from university in Australia with a Bachelor of Science degree, with a double major in physics and mathematics. I taught myself logic when a student needed help with it. I found it quite easy once I realized it's a lot like algebra - most of the mathematical symbols and equations are analogous to algebra symbols and equations.
It's a relatively simple topic, and is often about translating words and phrases into mathematical symbols. A lot of logic problems can just be solved using common sense.
Physics is my passion. It describes how the world around us works, and it is the foundation of the other sciences (chemistry, biology, etc., have their roots in physics).
I love talking about and teaching physics, as it can be applied to (and describe) many common real-life situations. For example: the next time you hear an ambulance siren approaching you, listen for how the pitch of the siren drops as the ambulance passes you - this is known as the Doppler effect.
I played poker online for a living for almost four years, earning a modest income from it (I averaged about $30/hr). I have a solid maths background along with a very solid understanding of poker fundamentals.
Prealgebra helps to prepare the mind of a student for the concepts that they will tackle in algebra. For this reason, many students struggle with it, as it introduces many seemingly foreign concepts, but a solid understanding of prealgebra can help greatly when moving into algebra 1.
Precalculus is an extension of algebra 2. It covers some of the same topics (in slightly more detail and difficulty), while also exploring many interesting new topics that will be applied in calculus. It can also include trigonometry.
While it is not a necessary precursor to calculus (it generally doesn't involve much/any actual calculus), it will certainly help prepare most students. Even students who don't go on to take calculus can still gain a greater understanding of mathematics and problem-solving skills from precalc.
Probability is an interesting subject that has many real-life, day-to-day uses (eg. in playing poker), as well as more advanced applications (eg. quantum physics). It is a measure or estimation of the chance that an event will happen.
I studied some basic statistics in high school, mostly involving discrete variables such as binomial probability, combinations and permutations, and tree diagrams.
I took several statistics courses at university, dealing with more complex stats and continuous random variables, such as the normal distribution (and the normal approximations), and discrete random variables like the Poisson distribution.
I also have a solid understanding of probability and expected value, due to playing poker for several years, and also just due to having a somewhat natural sense for chance and the law of large numbers.
Trigonometry is all about triangles and trigonometric functions (sine, cosine, tangent). It's a very interesting subject, and is extremely useful in many other fields of study (calculus and physics especially, and any fields that require the use of them).