# Math Reasoning Notes and Videos

Math Reasoning was a pretty amazing course that I taugth for a couple of years. It was meant to bridge the gap between Algebra 1 from middle school and Honors Algebra II in high school, where the expectation and rigor are far greater. There’s a tacit assumption that students working on these notes have taken Algebra 1 but that they weren’t amazing at it. This page is a work in progress. (But the links to the notes and playlists work!)

## Notes 01

The distributive property applied to polynomials. (You’ve got to move beyond FOIL if you’re going to excel!) Also, how to use your TI-Nspire CXII CAS to expand products.

## Notes 02

Factoring, the opposite of distributing! Looking for the GCF. Factoring with a leading coefficient of 1 by educated guessing and pattern recognition. Factoring with prime leading coefficient using educated guessing and pattern recognition. Factoring with composite leading coefficient, educated guessing and pattern recognition. Basically a st of 277 factoring problems.

## Notes 03

How comfortable you are with fractions will go a long way to determining how well you do in Algebra II and beyond. In these notes we simplify fractions; add & subtract fractions; multiply & divide fractions.

## Notes 04

More techniques of factoring! Using the ac-method. If a quadratic factors you can basically always use the ac-method, so if the pattern recognition hasn’t been working great for you, this is the one to focus on! Also, factoring a sum and difference of cubes using formulas.

## Notes 05

Solving some simple equations. Solving systems of linear equations using calculators, subsitution, elimination (linear combinations), and symmetry. Using your calculator to solve a system of equations. Solving a system of three equations in three unknowns. Introducing the idea of a matrix to solve a system of equations. Also, here’s a link to a set of problems that are associated with these notes. Not sure why that particular document exists!

## Notes 06

Properties of exponents (and some radicals).

## Notes 07

Lines and linear functions. Evaluating linear functions. Point-slope form; slope-intercept form; standard form; general form. x- and y-intercepts of a linear function. Parallel and perpendicular lines (and the relationship of their slopes). Distance between a point and a line. Graphing linear functions. Equation of a circle. Circle through three points.

## Notes 08

Transformations; quadratics; completing the square; vertex form; quadratic formula; discriminant; i (complex number); powers of i; factored form

## Notes 09

Inequalities; linear programming; absolute value; piecewise functions

## Notes 10

Solving problems using the math we know. Rate*Time = Total; train problems; open box problem; painting problems; mixture problems

## Notes 11

More about functions! Parent functions; Domain and range; asymptotes; inverses; vertical line test; horizontal line test; one-to-one functions

## Notes 12

Exponential functions, y=a^x. Interest (simple interest and compound interest; where does e come into this? continuous compounting, Pe^(rt); half-life problems.

## Notes 13

logarithms; inverses of exponentials; log of a in base b; bacon an eggs; logs are are BAE; common logs; properties of logs (product to sum; quotient to difference; exponent becomes coefficient; change of base); expanding and condensing log expressions; solving equations with logs; domain and range for log functions; naural logs; base e

## Notes 14

Three fun ideas in these notes: Fibonacci sequece, Collatz Conjecture, and The Game of Life

## Notes 15

Sequences and Series; arithmetic sequences vs. linear functions; geometric sequences vs. exponential functions; finding an expression for the nth term; recurssive formulas; sequences on your TI-Nspire; sums of sequences; series; number of terms in a sequence; sum of finite arithmetic series; sum of geometric series; sum of infinite geometric series; revisiting the Collatz conjucture; Lotka-Volterra model

## Notes 16

Polynomials; degree; leading term; constant term; multiplying polynomials; dividing polynomials

## Notes 17

Right triangle trig; Pythagorean Theorem; sine, cosine, and tangent; SOHCAHTOA; changing radians to degrees on calculator; evaluating trig functions on your calculator; solving right triangles; inverse trig functions to find angles; solving problems in context