Advanced Math Summary

SAT Math · Axiom Academy

Recap, Strategy Tips, and Common Traps Quadratic Equations (28% of advanced math) Factoring, quadratic formula, and completing the square. You know when to use each method and can solve any quadratic quickly. Polynomial Operations & Factoring Add, subtract, multiply polynomials. Factor by grouping, difference of squares, sum/difference of cubes. Recognize patterns instantly. Simplify by factoring, find LCD to add/subtract, solve rational equations, and identify extraneous solutions. Convert between radicals and exponents, simplify radical expressions, rationalize denominators, and solve radical equations. Exponential Functions (20% of advanced math) Growth and decay models with real-world applications. Doubling time, half-life, compound interest. Understand why exponentials matter. Function Notation & Composition Master f(x) notation, evaluate compositions f(g(x)), apply transformations, and find inverses. Solve line-parabola systems, circle-line systems. Use discriminant to determine number of solutions before solving. Recognize perfect squares, difference of squares, and other patterns hidden in complex expressions. This is how you solve hard problems fast. Add, subtract, multiply complex numbers. Use the conjugate trick. Master the powers of i cycle. Look for structure first. Before computing, scan for patterns. Perfect squares, difference of squares, GCF. Quadratics almost always factor. Spend 10 seconds looking for factors. If you find them, solve in 20 seconds.

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