1. SAT Algebra
May 3rd, 2010 by Marty Rafson
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Back in Algebra 1, all students were assigned problems such as (x + y)2. At that time most
students were advised to write the (x + y) twice, and then multiply. Many teachers, when
multiplying polynomials, employ the FOIL pneumonic device. “First”, “Outers”, “Inners”,
“Last”. This would give us x2 + xy + xy + y2. Simplification yields x2 + 2xy + y2. The 2xy is
referred to as the “middle term”. Some teachers, perhaps when the students reach the Algebra 2
level, ask the students to memorize this form. Every time we square a binomial we are going to
get two identical middle terms from the “outers” and the “inners”. Of course, the less adept math
students will look at (x + y)2 and merely get x2 + y2. The writers of the SAT, the Educational
Testing Service, know how to test students to be sure that they know about the existence of the
middle term.
Problem: “If a2 +b2 = 13 and ab = 7, find the value of (a + b)2.” If you memorized how to square
a binomial, you will instantly write down a2 + 2ab + b2 (of course, if you are not confident with
this, you can write down a + b twice and “FOIL” it). Note how the given information perfectly
fits this form. We are given that the first term plus the last term, a2 +b2 has a value of 13. Now,
examine the middle term. If ab = 7 then 2ab must have a value of 14. Thus, the value of the given
expression is 13 + 14, or 27.
Knowing how to multiply polynomials is a must in any algebra course and is important to
practice for the SAT. Specifically, knowing how to square (x + y) quickly can be a great asset on
the SAT.
Tags: SAT Math, SAT Prep, SAT Preparation
Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and
curriculum developer for 30 years. He has been a high school math teacher for 36 years and a
math department chairman for 25 years. He was also an adjunct professor at City College of New
York School of Education.
This entry was posted by Marty Rafson on Monday, May 3rd, 2010 at 10:25 am and is filed under SAT Prep Info.
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