Intermediate Algebra Summary

ACT Math · Axiom Academy

SUMMARY Intermediate Algebra & Functions Summary You just covered nine core topic areas — quadratics, polynomials, systems, functions, logs and exponentials, exponential models, sequences and series, matrices, and complex numbers. Here's the full arc in one place. Quadratics have three solving tools — factoring, completing the square, the quadratic formula — and the discriminant b^2-4ac tells you how many real solutions to expect before you solve anything. A function is a machine with a rule: evaluating substitutes, domain restricts the input side, range restricts the output side, and composition runs the inside function first. Exponentials and logarithms are the same relationship read two ways — — and every log property (product, quotient, power) is an exponent rule in disguise. Arithmetic sequences add a common difference d ; geometric sequences multiply by a common ratio r — always test differences first, then ratios, before picking a formula. Matrices and complex numbers are both mechanical: matrix operations are element-by-element bookkeeping, and every complex-number rule reduces to the one fact i^2=-1 . Core Concept Quadratic Equations Every quadratic ax^2+bx+c=0 can be solved by factoring (fast, when the numbers cooperate), completing the square (the derivation itself), or the quadratic formula (works every time). The discriminant b^2-4ac predicts the outcome before you solve: positive means two real solutions, zero means one repeated solution, negative means none.

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