# 0: Preliminary Topics for College Algebra

- Page ID
- 38164

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

- 0.1: Review - Real Numbers: Notation and Operations
- Sets of Real Numbers. Inequality notation. Set builder and interval notation. Definition and notation for the union and intersection of intervals. Order of operations. Substitution and evaluation of expressions.

- 0.2: Review - whole number exponents
- Whole number exponent manipulation. Includes the Power Rule, Quotient Rule, Zero Exponent Rule, Negative Exponent Rule, and Power of a Product and/or Quotient. Also includes using the exponent rules "in reverse" (see Section on Graphs of Exponential Functions for more examples and exercises).

- 0.3: Review - Radicals (Square Roots)
- Square root evaluation and simplification. Use of the product and quotient rules. Performing multiplication, division, addition, and subtraction on expressions containing square roots and simplifying the result. Rationalizing monomial and binomial denominators that contain square roots.

- 0.4: Review - Rational Exponents
- Introduction to nth root radicals. Translation between radical form and rational exponent form. Operations on expressions containing rational exponents.

- 0.5: Review - Factoring
- Factoring - GCF; 4 terms by grouping 2 terms; trinomials with leading coefficient of 1; trinomials with leading coefficient not 1 using two different methods - the reverse FOIL method and the AC grouping method; Perfect square trinomials; Difference of squares; 4 terms by grouping 3 terms; sum and difference of cubes; difference of powers of 6; use the GCF of terms with rational or negative exponents.

- 0.6: Review - Rational Expressions
- Simplifying rational expressions, adding, subtracting, multiplying and dividing. Simplifying complex fractions. Domain restrictions.

- 0.7: Review - Solving Linear Equations
- Review of how to solve linear equations. Includes descriptions of equations as conditional, an identity and a contradiction. Solve formulas for a variable.

- 0.8: Review - Linear Inequalities in One Variable
- Solve linear inequalities and compound linear inequalities.