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!)
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.
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.
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.
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.
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!
Properties of exponents (and some radicals).
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.
Transformations; quadratics; completing the square; vertex form; quadratic formula; discriminant; i (complex number); powers of i; factored form
Inequalities; linear programming; absolute value; piecewise functions
Solving problems using the math we know. Rate*Time = Total; train problems; open box problem; painting problems; mixture problems
More about functions! Parent functions; Domain and range; asymptotes; inverses; vertical line test; horizontal line test; one-to-one functions
Exponential functions, y=a^x. Interest (simple interest and compound interest; where does e come into this? continuous compounting, Pe^(rt); half-life problems.
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
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
Polynomials; degree; leading term; constant term; multiplying polynomials; dividing polynomials
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