Lial's intermediate algebra book. Linear equations through quadratics, exponentials and logs, conic sections, and sequences.
A brief review of the foundational arithmetic and algebra needed to enter Intermediate Algebra: variables and algebraic expressions, operations on real numbers, and exponents and the order of operations.
Solving linear equations in one variable, formulas, percent and ratio applications, linear inequalities including compound inequalities, and absolute value equations and inequalities.
The rectangular coordinate system, graphing linear equations, slope and equations of lines, linear inequalities in two variables, and an introduction to functions including basic graphs and transformations.
Solving systems of linear equations by graphing, substitution, and elimination; applications of systems; and systems of three linear equations.
Exponent rules including negative exponents, scientific notation, polynomial structure and operations, multiplying polynomials, dividing polynomials, and an introduction to polynomial functions.
Factoring polynomials using the greatest common factor, grouping, trinomial techniques, and special forms; using factoring to solve quadratic equations and applications.
Simplifying rational expressions, multiplying and dividing rational expressions, finding the least common denominator, adding and subtracting rational expressions, simplifying complex fractions, solving rational equations, applications, and variation.
Square roots and higher roots, rational exponents, simplifying radicals, operations on radicals, rationalizing denominators, solving equations involving radicals, and complex numbers.
Solving quadratic equations by factoring, the square root property, completing the square, and the quadratic formula; equations in quadratic form; quadratic inequalities; quadratic functions and their graphs; applications.
One-to-one functions and inverse functions; exponential functions and their graphs; logarithmic functions and their graphs; properties of logarithms; exponential and logarithmic equations; applications.
The conic sections — parabolas, ellipses, hyperbolas — in standard form; nonlinear systems of equations.
Sequences and series notation, arithmetic sequences and series, geometric sequences and series, and the binomial theorem.