Mathematics
High School Mathematics
Who this is for
Middle and high school students working through the standard mathematics sequence — pre-algebra through precalculus — including students taking a course a year early and students repeating one they did not pass.
It is also for the student who is doing fine on homework and losing points on tests. That gap is almost never carelessness; it is usually a procedure that works when you already know which procedure to use.
High School Mathematics
Pre-Algebra, Algebra I & II, Geometry, Trigonometry, and Precalculus
$60/hr online · $90/hr in person
What usually goes wrong
Each mathematics course builds strictly on the one before it. Gaps do not disappear when the semester ends; they become the reason the next course feels impossibly hard.
- Fractions and negative signs. The single most common cause of wrong answers in Algebra II, and it is almost always a habit from three years earlier.
- Solving versus simplifying. Students who cannot say which one a problem is asking for apply the rules of the other, and the work looks reasonable the whole way down.
- Function notation. f(x) read as multiplication rather than as a machine with an input makes every later transformation arbitrary.
- The graph and the equation as separate objects. They are one object. Until they are, half of precalculus is memorization.
- Word problems. Not a reading problem — a translation problem. Most students can solve the equation they could not write down.
- Calculator dependence. A calculator is fine once you can estimate the answer. Before that, it hides the error instead of catching it.
Topics covered
The sequence below is one continuous track rather than four separate courses, which is why it lives on a single page. Where a student actually needs to start is often a year or two earlier than the course they are enrolled in, and that is worth finding out first.
Pre-Algebra
Numbers, variables, equations, and problem-solving habits.
- Integers, fractions, decimals, and percent
- Ratios, rates, and proportional reasoning
- Order of operations and the properties of arithmetic
- Variables, expressions, and one- and two-step equations
- Introduction to the coordinate plane
Algebra I & II
Functions, equations, modeling, and mathematical reasoning.
- Linear equations, inequalities, and systems
- Slope, intercepts, and the equation of a line
- Exponents, radicals, and polynomial arithmetic
- Factoring and quadratic equations, including the quadratic formula
- Rational expressions and rational equations
- Exponential and logarithmic functions
- Function notation, domain and range, and transformations
- Sequences and series
Geometry & Trigonometry
Relationships, proofs, spatial reasoning, and periodic models.
- Angles, parallel lines, triangles, and quadrilaterals
- Congruence, similarity, and geometric proof
- The Pythagorean theorem and the distance formula
- Circles, arcs, and sectors
- Area, surface area, and volume
- Right-triangle trigonometry — sine, cosine, and tangent
- The unit circle and radian measure
- Trigonometric graphs, identities, and equations
- The laws of sines and cosines
Precalculus
Functions, transformations, and preparation for calculus.
- Polynomial and rational functions, including end behavior and asymptotes
- Composite and inverse functions
- Exponential and logarithmic modeling
- Analytic trigonometry and trigonometric identities
- Vectors, polar coordinates, and parametric equations
- Conic sections
- An introduction to limits
How I teach high school math
Engineering mindset. My engineering background shapes how I teach math: equations are models of real systems, not isolated symbols. When students learn what the math actually represents, they stop guessing which formula to use and start building solutions logically.
Find the upstream gap first. If Algebra II is going badly, the fix is often in fractions or signed numbers. Working the current chapter harder does not repair the thing underneath it, and the next chapter will ask for it again.
Write the problem down properly. Almost every problem a student calls impossible is a problem they have not yet written down correctly. Setup is most of the work, and it is the part that is teachable.
Graph it. A sketch turns an abstract equation into something with shape and direction, and it makes a wrong answer obvious before the arithmetic is checked.
Estimate before calculating. Knowing roughly what the answer should be is what catches a sign error, a misplaced decimal, or a calculator in the wrong mode.
Say it out loud. A student who can explain why a step is allowed can reconstruct it under exam pressure. A student who has only seen it done cannot.
Who this is not a fit for
- Statistics, including AP Statistics. It is a genuinely different course and not one I offer.
- Calculus III, multivariable calculus, and Linear Algebra — none are offered at any level.
- Anyone who needs homework completed rather than taught.
- Anyone looking for someone to sit an online quiz or test on their behalf.
- Competition preparation as a specialty. Sessions follow your course and syllabus.
Common questions
Do you tutor middle schoolers?
Yes, where the course is pre-algebra or algebra. The sequence on this page starts before high school on purpose, because that is where most of the gaps that surface later actually begin.
My student is behind grade level. Is that still a fit?
Yes, and it is worth saying so in your first message. We start where the understanding actually stops rather than where the syllabus says it should, and then work forward to the current course. That is slower for a few sessions and considerably faster after that.
Do you follow our teacher's method?
Yes. Send the syllabus, the textbook, or a photo of the notes and I will work the material in advance so we use the notation and the approach your student is graded on. A second method taught in parallel is a good way to lose marks.
Is AP Calculus covered here?
No — that has its own page, at the same High School & Test Prep rate. This page ends at precalculus, which is what AP Calculus assumes you already have.
Does math work online?
Yes. Sessions run on a digital whiteboard, which for mathematics is closer to sitting beside someone than a video call suggests — and you keep the board and the recording afterwards.
What do I keep afterwards?
The full video recording and a high-resolution whiteboard PDF, organized by course in your own folder. More on how sessions run →
Related subjects
- Calculus →Where this sequence leads. AP Calculus AB and BC assume the algebra and trigonometry on this page are automatic rather than effortful.
- Physics →Usually the first course that spends this math instead of teaching it, which is where a shaky foundation shows up first.
- Chemistry →Often on the same schedule, and the course where weak exponents and logarithms surface as a chemistry problem rather than a math one.
“Ben is actively tutoring my son in High School Algebra II with active realization in significant improvement after just a few sessions. Ben is provided the class syllabus and proactively uses it to complete problems himself ahead of time, so that he is familiar with the current course module of instruction; this active prep significantly adds value to the tutor session. We appreciate his preparation and delivery of instruction via a caring and patient demeanor.”
Build the foundation.
Send the course name, the textbook, and what you are working toward. I will tell you where I think the real gap is before anything is scheduled.
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