- Beth & Tim Manners

# Holy Polynomials: SAT Advanced Math Tips

Updated: Sep 20, 2019

**US News**: “The Passport to Advanced Math subsection of the SAT, which includes 16 questions out of 58 total, or 28 percent, is perhaps the most complex part of the math section. While this can be intimidating to students, taking the time to study and ensuring you know your formulas will help you greatly … One thing worth noting about Passport to Advanced Math is its emphasis on equation simplification … For success on Passport to Advanced Math, you must know how to move variables within an equation without making errors, as well as the rules for the quadratic equation. You should also be comfortable with factoring before you sit for the SAT.”

“While you may be very comfortable solving equations or expressions in certain forms, you should also be prepared to move between different forms fluidly. To practice this fluidity, you can do something as simple as setting aside 10 minutes each day to work with equations and expressions in multiple forms … Get comfortable adding, subtracting, multiplying and dividing polynomial expressions. The addition or subtraction of polynomial expressions is relatively easy – you simply combine like terms, such as 2x and 5x or -1 and 3. When dealing with subtraction, it is important to remember to reverse the sign in each term prior to adding the expressions; for example, -10y would become 10y.”

“For multiplication, remember to use the FOIL method – first, outside, inside, last. You should also ensure that you multiply each term in the second polynomial by each term in the first polynomial … When working with exponents in Passport to Advanced Math, remember that when simplifying expressions, you either need the same base or the same exponent in most cases. It can be helpful to recall that the ‘core’ exponent rules follow a similar pattern … For division, if the bases to be divided are different, but the exponent is the same, you divide the bases before raising them to the exponent. If the bases and the exponents are different, you calculate each term separately and then divide the results.”