Pre-calculus Contents A
The set of real numbers
Rational numbers
Irrational numbers
The real number line and relations
I
nterval definition and notation
Distance and absolute value
Properties of the real numbers
Order of operations
Absolute value equations
Linear Inequalities
Absolute value inequalities
Algebraic expressions
Expanding algebraic expression by removing parentheses
The binomial expansion algorithm
Factoring and expanding algebraic expressions, rules for transforming algebraic expressions
Factoring quadratic trinomials
Factoring polynomials
Rational expressions
Solving complex rational expressions
Imaginary and Complex Numbers
Addition and subtraction of complex numbers
Multiplication and division of complex numbers
Polar or trigonometric notation of complex numbers
Multiplication and division of complex numbers in the polar form
Exponentiation and root extraction of complex numbers in the polar form
Powers and roots of complex numbers, use of de Moivre’s formulas
Euler’s formula, relationship between trigonometric functions and the complex exponential function
Linear equation in one variable
Solving linear equations
Linear equation in one variable, examples
Linear Inequalities
Solving inequalities
Properties of inequalities
Examples of solving single linear inequalities
Solving compound (double) inequalities
Equations with Rational Expressions
Solving rational equations
Rational equations - Linear equations
Rational Inequalities
Method of solving rational inequalities
The graph of the translated equilateral (or rectangular) hyperbola
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