Chapter 1: Review
By the end of Chapter 1, you should be able to:
From Section 1.2:
From Section 1.3:
From Section 1.4:
From Section 1.5:
From Section 1.6:
From Section 1.2:
- Identify and give an example of numbers contained in each subset of the Real Numbers.
- Identify and use the properties of the Real Numbers.
From Section 1.3:
- Simplify a mathematical expression
- Evaluate a mathematical expression
- Model a situation using an algebraic expression.
From Section 1.4:
- Solve algebraic equations
- Create equations to model situations.
From Section 1.5:
- Solve inequalities and compound inequalities.
- Visually represent (graph) inequalities and compound inequalities on a number line.
- Create inequalities and compound inequalities to model situations.
From Section 1.6:
- Solve absolute value equations and inequalities.
- Create absolute value equations and inequalities to model situations.
Make sure you are familiar with all of the following definitions:
From Section 1.2:
From Section 1.3:
From Section 1.4:
From Section 1.5:
From Section 1.6:
Absolute Value: the distance a real number x is away from zero. Extraneous Solution: a solution found from an original equation that is not a solution to the original equation.
From Section 1.2:
- Constant: a value that does not change
- Variable: a symbol (usually a letter) that represents one or more numbers.
- Algebraic Expression: A mathematical phrase that contains one or more variables
From Section 1.3:
- Simplify: combine all like terms and reduce the expression to the smallest number of terms possible.
- Evaluate: substitute a number in for each variable and simplify the expression using the order of operations.
- Term: a number, variable, or the product of a number and one or more variables. Terms are separated by addition/subtraction.
- Coefficient: the numerical factor of a term.
- Constant Term: a term with no variables
- Like Terms: two or more terms with the same variables raised to the same power
From Section 1.4:
- Equation: a statement that two expressions are equal (=).
- Solution of an Equation: a value, or values of the variable that make the equation true.
- Inverse Operations: operations that “undo” each other (addition and subtraction, multiplication and division, etc.).
- Identity: an equation that is true for EVERY possible value of the variable.
- Literal Equation: an equation that uses at least two different letters as variables. With literal equations, the solution of the equation is “in terms of” the other variable(s).
From Section 1.5:
- Inequality: a relationship between two expressions when one expression is greater than (>), greater than or equal to (≥), less than (<), or less than or equal to (≤) the other expression.
- Compound Inequality: two inequalities that are joined with the word and or the word or.
From Section 1.6:
- Absolute Value: the distance a real number x is away from zero.
- Extraneous Solution: a solution found from an original equation that is not a solution to the original equation.