ILTS Mathematics (208) Exam Secrets Study Guide: ILTS Test Review for the Illinois Licensure Testing System

I was pretty excited to use this book to review math that I haven't done in years, so I could be better prepared to take the 9-12 math endorsement test in IL. (For the record, I aced the ACT math and Calculus - but that was 30 years ago. Also taught logic. Yay me, whatever.) It's my COVID social-distancing project.Not even 30 pages into the first book, I've found three errors in examples the author(s) use(s). Wow. Makes it hard to trust the material to come.The terrifying example that led me to write this review is found on pg 25, where the author tries to demonstrate formal reasoning. Author presents the following:"If a quadrilateral has four congruent sides, it is a rhombus.If a shape is a rhombus, then the diagonals are perpendicular.A shape is a quadrilateral.Therefore, the diagonals are perpendicular.This example employs the chain rule, shown below:p->qq->rptherefore, r"Good grief! That's an invalid argument. Two things are obvious.1. "a shape is a quadrilateral" is not the same as "p".2. "If a shape is a quadrilateral, then it has perpendicular diagonals" is a false conditional. The antecedent can be true when the consequent is false. Draw a rectangle or a non-trapezoidal quadrilateral. Ta-freakin-da. Any conditional with a T antecedent and a F consequent is F.One must hope the author forgot to write "a shape is a quadrilateral with congruent sides" as the step before their deduction, but then that means the book was not proofread closely.The inductive proof on p.22 is a MESS. Not only is it false that "the sum of the natural numbers is equal to n^2," but the proof that follows is incoherent anyway. (I again assume lack of editorial oversight?)The "proof" that follows appears to right the ship a little, because at least it is for the true claim that "the sum of odd natural numbers = n^2". However it is a banana pants proof. It appears to involve an unstated (and unnecessary) step of adding 1 to both sides...yikes. At this point, though, why not violate Occam's Razor, too.FYI, it is true that you can use induction to prove that the sum of odd natural numbers equals n^2, but to do that you simply use the common understanding that an odd number n is (2n-1). (1st odd number is 1, 2nd odd number is 3, etc.) That way, in your induction step you get k^2 + [2(k + 1) - 1] = (k+1)^2. That is true.Then in a systems problem on p.28, they forget which variable represents which element of a story problem, so if you didn't feel comfortable with systems, you'd think YOU were wrong, when THEY are wrong. The guide flips which variable represents which % solution (mid-sentence, mind you), so it gets the amounts wrong.Can I have my money back?

I enjoyed the secrets at the start, and I am now working my way through the various problems after those secrets! I'm very excited for the help this will bring me on my journey to becoming a math teacher

Helped me pass the exam on my first try!! Comes in 2 thin books, very concise, yet covers all the material on the exam.