sat的知识点总结.docVIP

Algebra Concept Powers of Numbers Roots of numbers 2. Powers Exponents, roots, and real number line. Raising numbers to powers can have surprising effects on the size or sign of the base number. This is one of the test-makers` favourite areas! The impact of raising a number to an exponent depends on the region on the number line where the number and exponent fall. Here are the four regions you need to consider; Less than -1 Between -1 and 0 Between 0 and 1 Greater than 1 As with exponents, the root of a number can bear a surprising relationship to the size and sign of the number. Here are our observations you should remember. If n1 , (the higher the roots, the higher the value.) The square root of any negative number is an imaginary number, not a real number. Remember: you won`t encounter any imaginary numbers on the SAT. Every positive number has two square roots: a negative number and a positive number (with the same absolute value). The same holds true for all other even-numbered roots of positive numbers. Every negative number has exactly one cube root, and that root is a negative number. The same holds true for all other odd-numbered roots of negative numbers. Every positive number has only one cube root, and that root is always a positive number. The same holds true for all other odd-numbered root of positive numbers. The Operation Rule of Radicals Combining Radicals Addition and Subtraction: if a term under a radical is being added to or subtracted from a term under a different radical, you cannot combine the two terms under the same radical. Multiplication and Division: terms under different radicals can be combined under a common radical if one term is multiplied or divided by the other, but only if the root is the same. Simplifying Radicals On the SAT, always look for the possibility of simplifying radicals by moving part of what`s inside the radical to the outside. Check inside your square-root radicals for factors that are squares of nice tidy numbers (