Math Reasoning Notes

Math Reasoning Notes, Problem Sets, Playlists

We'll be working through a lot of notes and problems during class. This is where you get the file to print.

Notes 01

These notes are about the distributive property. Since you won't be able to do anything else well if you can't use it properly, it seems like a good place to start, right?

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

These notes are about factoring, mostly trinomials, but a little more interesting as well. Factoring is too important to risk not being amazing at it. There are a LOT of factoring problems in these notes. We won't do all of them in class.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 03

These notes are about fractions! We're going to add, subtract, multiply, and divide. Also, we're not using just numbers here. We're also working with binomials and trinomials. Someday you might think of this as working with rational expressions but I'd rather you get good at it than worry about what it's called.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 04

These notes are about factoring again! First we talk about the ac-method, which is kind of the ultimate in factoring ease at the price of speed. Then we solve some equations by factoring; talk a little about using our calculators to do the same. Finally I casually mention a difference of cubes, which we're going to just memorize for now.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 05

These notes are about solving some equations and then solving some systems of linear equations. We also use the calculator a lot in this set of notes.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 06

These notes are about the properties of exponents. We also cover a little bit about radicals.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 07

These notes are about lines and linear functions. We write equations, work with slope, find intersections, do some graphing, and get a little bit into circles.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 08

These notes are about quadratic functions! Quadratics are all over the place in pretty much every course beyond Geometry, so we need to be amazing at them. If you really learn to deal with them, they'll help you deal with a whole lot of other things.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 09

These notes are about inequalities, absolute values, and piecewise functions. Understanding these concepts gives you a huge advantage over people who never bother since they're ideas that come up again and again.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 10

These notes are about problems that have lots of words. People fear problems with words, but you have to push through that or you won't be successful.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 11

These notes are about functions. There are a whole bunch of parent functions to memorize--make some note cards! Domain and range are discussed. We talk a little about increasing and decreasing just because we can. Finally we dig into inverses for a bit.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 12

These notes are about exponential functions. We talk about transformations and changing up the base. We also talk about simple interest and compound interest. We modify compound interest to get continuous compound interest and figure out what e is all about. Finally we talk a little bit about half-life.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 13

These notes are about logs (or logarithms, more properly). We go through what logs are, how to work with them, their properties, using them to solve equations, common logs, and natural logs. Logs seem to terrify some students, but they're honestly just not that bad. If you know your exponents and you're confident in your algebra skills you'll be fine!

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 14

These notes are about spreadsheets, really. We learn how to use a bunch of built-in features and how to enter our own formulas. The ability to use a spreadsheet is quite prized in certain circles and this should get you started on your way. We take a bunch of averages; make a spreadsheet that can calculate grades; investigate the Fibonacci sequence; learn a little about modular arithmetic; look at the Collatz Conjecture; and learn some things about cellular automata by investigating the diffusion of a technology through a population and playing a little bit of The Game of Life.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 15

These notes are about sequences and series! We talk about explicit and recursive sequences. Finding formulas for the nth term is highlighted--as well as the connections to lines and exponential functions. We work a little bit on the calculator and a little bit in spreadsheets. We talk about summing up a sequence to get a series; finding sums of finite arithmetic and geometric series as well as infinite geometric series. Finally we revisit some recursive sequences and take a look at two interesting applications.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 16

These notes cover a little bit about polynomials. We go over adding, subtracting, multiplying, and dividing them. We also look at a few typical problems that you can solve about polynomials.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.

Notes 17

These notes cover some of the basics of right triangle trigonometry that you should have picked up along the way in a geometry course. You'll definitely be doing some trig in Algebra II and then a ton in Precalculus/Math Analysis. We review the basics of similar triangles. Using the Pythagorean theorem to find missing sides of a right triangle. Review SOH-CAH-TOA. How to change your calculator from radians to degrees and back. How to evaluate trig functions on your calculator. Inverse sine, cosine, and tangent to find acute angles. Solving for missing sides and angles of right triangles. Angle of depression and angle of elevation. We also solve my favorite indirect measurement problem at the end.

Here's a link to the Problem Sets for these notes.

Here's a link to a YouTube playlist of videos about these notes.