Overview
This review covers core algebra topics from intervals and equations to functions, graphing, exponents, scientific notation, and systems of equations.
Intervals and Absolute Value
- Intervals can be written in set-builder notation and graphed on a number line.
- Absolute value means the distance of a number from zero; |a| is always non-negative.
Tables, Graphs, and Functions
- Complete tables of values and graph equations like y = x² + 1, y = 3x + 1, and y = 2|x + 4|.
- The domain of a function is the set of all possible x-values; the range is the set of all possible y-values.
- Relations are functions if each x-value corresponds to exactly one y-value.
Solving Linear Equations and Word Problems
- Solve linear equations by isolating the variable on one side.
- Translate word problems into equations (e.g., perimeter, discount, allowances) and solve for unknowns.
- Set up and solve average and age-related problems algebraically.
Algebraic Formulas and Manipulations
- Solve formulas for a specified variable (e.g., solve A = P + Prt for t).
- Simplify expressions; eliminate negative exponents and use exponent rules.
- Convert numbers between scientific and decimal notations.
Graphs and Equation Forms
- Write equations in slope-intercept form (y = mx + b) for graphing.
- Find the equation of a line given two points or a point and a condition (parallel or perpendicular).
- Graph quadratic functions and compare transformations.
Systems of Equations
- Solve linear systems using substitution or elimination.
- Set up systems from word problems involving tickets, mixtures, ages, coins, and rates.
- Solutions give the values satisfying all equations in the system.
Key Terms & Definitions
- Interval notation — Describes a set of numbers between two endpoints.
- Absolute value — The non-negative value of a number (distance from zero).
- Domain — All possible input (x) values for a function.
- Range — All possible output (y) values for a function.
- Slope-intercept form — Line equation y = mx + b, where m is slope, b is y-intercept.
- System of equations — A set of equations to be solved together.
- Scientific notation — Writing numbers as a × 10ⁿ for large/small values.
Action Items / Next Steps
- Practice solving all sample equations and word problems.
- Complete tables and graph all given equations as requested.
- Review definition and identification of functions, domain, and range.
- Convert numbers between scientific and decimal notations.
- Prepare to explain and apply exponent rules.