The Johnson
Family Homestead

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Educational
Services
Math Help Subsection
Over the years, GW has taught mathematics from the 7th grade all the way to college algebra
and trigonometry, and even a little college calculus, at a variety of institutions. Math is a weak subject
for many students, whether still in high school, or those entering college. It is possible for even the
weakest student to become good in math, but it takes work, selfdiscipline, and determination. Some good
“cheat sheet” learning aids may also greatly help, and that is what GW provides here.
The first is a 4page text file that explains how to pass a math course. It has a good list of what, and
what not, to do. For a downloadable copy, click here.
Another is a little onepage cheat sheet with some fundamentals for algebra on it, including the basic
“sign pattern” for +/ signed numbers, and the rules of exponents and radicals. For a copy,
click here.
The “oddities that are useful” handout includes a table of squares and cubes for numbers from 1 to 20
(useful for handcalculating radical expressions), a table of the first 20 prime numbers up to 100
(useful for both factoring and common denominators), and two fractional approximations to the number “pi”.
For a copy, click here.
One of the most common shortfalls many students have is linear equations in 2 dimensions (and the related
straight line xy graphs). For a “cheat sheet” that includes all the equations and formulas for this topic,
and all the odd cases one must remember, click here.
Many students have difficulties with polynomials, whether multiplying or factoring them. For a good
cheat sheet on this topic that includes one quadratic factoring technique not yet commonly found in
textbooks, click here. For solving equations in that class of polynomials known as
quadratics, there is a really handy onepage cheat sheet arranged in a convenient “dropthrough” checklist
form. (It even includes the only two known practical factoring formulas for cubics.)
To obtain it, click here.
Many students have difficulties with expressions or equations having radicals in them, meaning square roots,
cube roots, and worse. There actually is method to this madness. For a good cheat sheet,
click here.
Lots of students really hate fractions, especially the ones with letters in them. A fraction with a letter
(variable) in its denominator is a “rational expression”. For a good cheat sheet on handling these things
in equations, click here.
There are a set of quadratics that describe figures on the graph plane known as “conics”. The keys to this
topic are recognizing the type of figure from the form of its equation, and vice versa, plus how to put
those equations into their standard forms, in order to actually recognize them. For a good cheat sheet,
click here.
One topic that many find difficult is solving systems of equations in multiple variables, such as two equations
in two unknowns, three equations in three unknowns, etc. There are five algebraic techniques for doing this.
Two are analytical, the other three are based on manipulating matrices (arrays of numbers). For a good
cheat sheet on solving systems of two equations in two unknowns by any of these methods,
click here. For a cheat sheet on solving systems of 3 equations in 3 unknowns,
click here. One of the matrix methods in the 3D systems handout can be easily used for
systems of any size (10 equations in 10 variables, etc.).