
Multiply same-base terms by adding exponents and divide by subtracting exponents. Raise powers by multiplying exponents, invert negative exponents, and treat zero and fractional exponents as one or radicals.
Practice applying exponent rules to algebraic expressions by distributing outer exponents, combining like bases, and using multiplication and division of exponents to simplify expressions involving x, y, and z.
In this section, we will review the basic rules of radicals and exponents applicable to radicals. Then, we will solve exponent and radical problems that are similar to the SAT.
Practice simplifying radicals by decomposing square roots (for example sqrt(8) = 2 sqrt(2)), combining like terms, and applying foil to multiply and simplify expressions with radicals.
Practice simplifying radicals and combining like terms, using identities such as (x+y)(x−y)=x^2−y^2, to evaluate and simplify expressions with square roots and coefficients.
In this section, we will review the basic rules for adding and subtracting polynomials and solve problems similar to the SAT.
Practice adding and subtracting polynomials by distributing negatives, lining up like terms, and summing coefficients across corresponding variables.
Explore factoring techniques for algebraic expressions by selecting appropriate factor pairs to match given signs and products. Apply the zero-product property to solve for x.
Explore dividing polynomials by a monomer using the distribution law and long division, apply exponent rules, and interpret quotients and remainders with sat-style examples.
Master SAT-type polynomial division and factoring using long division to find quotients and remainders. Explore factoring x^2 − y^2, identifying roots, and applying distribution and foil to build accurate solutions.
This is a quick review of problems on the math sections 3 and 4 of the SAT test that include exponents, radicals and polynomials. Each concept will consist of a review of the rules. Then, you will practice the basics, including the typical questions that all students must be able to answer comfortably. Once you have finished covering the fundamentals, you will be ready to solve problems that are similar to the SAT. The majority of the SAT-type questions are similar to the practice SAT tests provided by the College Board, but with different numbers. You will see all of the solutions in a pdf format as well as a video solution with my comments and tips on the best ways to solve these problems. Since this course is designed for those of you who are already adept at solving math problems, it is a condensed version of a longer course that I teach in my group class and one-on-one sessions. Please note that there is a no calculator section, so be sure to review your basic arithmetic on your own time if need be. You don't want to lose time for having to stop and think about basic addition and multiplication problems.