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Algebra 2
This course picks up where linear equations leave off: inequalities, systems of equations, radicals and finally quadratic equations, the gateway to most of high school math. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.
Before you start: Algebra 1: factoring, rational expressions and linear equations.
Unit 1 Inequalities
- 1 Solving linear inequalities What an inequality is, how to write its solutions in interval notation, and how to solve linear inequalities without forgetting to flip the sign. 12 min
- 2 Compound inequalities Inequalities joined by "and" or "or", how to solve them, how to graph the solution, and how to handle three-part inequalities. 11 min
- 3 Product and rational inequalities How to solve inequalities involving a product or a quotient with a sign chart, and why you can't multiply both sides by the denominator. 13 min
- 4 Absolute value equations and inequalities Absolute value as distance, and how to solve absolute value equations and inequalities, including checking for extraneous solutions. 13 min
Unit 2 Systems of equations
- 5 Systems of linear equations, graphing and substitution What a system of two linear equations is, what its solution looks like on a graph, and how to solve it by substitution. 12 min
- 6 Elimination and Cramer's rule Solving systems by elimination, using determinants and Cramer's rule, and recognizing systems with no solution or infinitely many solutions. 13 min
- 7 Word problems with systems of equations How to turn a word problem into a system of two equations: tickets, mixtures, coins, interest and motion with a current. 12 min
Unit 3 Radicals and rational exponents
- 8 Radicals and nth roots Square roots, cube roots and nth roots, principal roots, when a root is a real number, simplifying the index and comparing radicals. 12 min
- 9 Multiplying, dividing and simplifying radicals The product and quotient rules for radicals, simplifying square roots and higher roots, radicals with different indices, powers of radicals and roots of roots. 13 min
- 10 Adding radicals and rationalizing denominators Like radicals, adding and subtracting radical expressions, multiplying binomials with radicals, conjugates, and rationalizing the denominator. 13 min
- 11 Rational exponents What a fractional exponent means, how it connects to radicals, and how the laws of exponents make radical expressions easier to simplify. 11 min
Unit 4 Quadratic equations
- 12 Solving quadratic equations Standard form, solving by square roots, by factoring and by completing the square, the quadratic formula and what the discriminant tells you. 15 min
- 13 Sum and product of the roots How the roots of a quadratic relate to its coefficients, how to factor any quadratic using its roots, and how to build an equation from given roots. 12 min
- 14 Polynomial and rational equations Solving cubic and quartic equations by factoring, by synthetic division and as quadratics in form, and solving rational equations that lead to quadratics. 14 min
Unit 5 Quadratic inequalities
- 15 Quadratic inequalities Solving quadratic inequalities with the graph of a parabola or with test intervals, including the special cases of a zero or negative discriminant. 13 min
- 16 Polynomial and rational inequalities, and systems Solving higher-degree polynomial inequalities and rational inequalities with quadratic factors using sign charts, and solving systems of quadratic inequalities. 14 min