Algebra

Linear equations in one variable

Constants and variables; linear equations in one variable; the solution of an equation; the properties of equality (addition, subtraction, multiplication, and division); solving linear equations, including equations with fractions; and equations with no solution or infinitely many solutions.

Absolute value equations

The absolute value of a number; solving absolute value equations; isolating the absolute value before solving; equations with no solution; and the equality of absolute values.

Linear inequalities in one variable

Linear inequalities in one variable; solving linear inequality; solution in graph-number line, interval notation, set-builder notation, addition, subtraction, multiplication and division properties of inequality; compound inequalities, union, intersection, or, and operations; absolute value equations and absolute value inequalities.

Absolute value inequalities

Solving absolute value inequalities using the four formulas; isolating the absolute value; no-solution and all-real-number cases; and writing solutions in set-builder and interval notation and on the number line.

Linear equations in two variables

Linear equations in two variable; graphing; x- and y- intercepts; horizontal and vertical lines; slope of a line; parallel and perpendicular lines; equations of lines; standard for, slope-intercept form, and point-slope form; relation, domain and range; and functions.

System of linear equations and inequalities

Solving system of linear equations by graphical method, substitution method and addition method; and applications.

Polynomials

Integer exponents; scientific notation; addition and subtraction of polynomials and polynomial functions; multiplication of polynomials; division of polynomials; greatest common factor; factoring by grouping; factoring trinomials; factoring binomials; and solving equations by zero product rule.

Rational expressions and rational equations

rational expressions; rational functions; multiplication of rational expressions; division of rational expressions; addition of rational expressions; subtraction of rational expressions; complex fractions; solving rational equations; applications of rational equations; applications of proportions and variations.

Radicals and complex numbers

nth root; rational exponents; simplifying radical expressions; addition of radicals; subtraction of radicals; multiplication of radicals; division of radicals; rationalization; solving radical equations; and complex numbers.

Quadratic equations and functions

Solving quadratic equation using the square root property; solving quadratic equation by completing the square; quadratic formula; equations in quadratic form; graphs of quadratic functions; vertex of a parabola; polynomial and rational inequalities.

Exponential and logarithmic functions

Algebra of functions; compositions; inverse functions; exponential functions; logarithmic functions; properties of logarithms; the irrational number e; change of base; logarithmic equations and exponential equations.

Practice questions

Practice problems with full step-by-step solutions covering absolute value, inequalities, linear equations, polynomials, radicals, quadratics, and exponential and logarithmic functions.