Algebra Fundamentals Quiz

Fundamental Concepts

• Algebra is a branch of mathematics that uses symbols to represent numbers and quantities. These symbols, often letters, allow expressing mathematical relationships and solving for unknowns.
• Variables are symbols that stand for unknown numerical values.
• Constants are fixed numerical values in an algebraic expression.
• Expressions are combinations of variables, constants, and mathematical operators (like +,-,*,/).
• Equations are expressions where two expressions are set equal to each other. Solving equations involves finding the values of the variables that make the equation true.
• Inequalities represent relationships where one expression is greater than, less than, greater than or equal to, or less than or equal to another expression.

Basic Operations

• Addition and subtraction of algebraic terms: Combine like terms (terms with the same variable raised to the same power).
• Multiplication and division of algebraic terms: Apply the rules of exponents (e.g., x² * x³ = x⁵).
• Order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Solving Equations

• Linear equations (equations of the form ax + b = 0):
  • Isolate the variable term on one side of the equation.
  • Perform inverse operations (addition, subtraction, multiplication, division) to solve for the variable.
• Quadratic equations (equations of the form ax² + bx + c = 0):
  • Factoring: Express the equation as a product of factors equal to zero.
  • Quadratic formula: A general formula for solving quadratic equations.
• Systems of equations: Multiple equations with multiple variables. Solutions involve finding values that satisfy all equations.

Linear Equations

• Slope-intercept form (y = mx + b): Represents a linear relationship where 'm' is the slope and 'b' is the y-intercept.
• Point-slope form: Used to find the equation of a line given a point and the slope.

Polynomials

• Polynomials are algebraic expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. The exponents of the variables are whole numbers.
• Evaluating polynomials: Substituting values for variables and calculating the result.
• Adding, subtracting, multiplying, and dividing polynomials.

Exponents and Radicals

• Rules governing exponents: Such as the product rule, quotient rule, power rule, and zero exponent.
• Working with radicals (square roots, cube roots, etc.)
• Rational exponents and simplifying radical expressions.

Factoring

• Common factors: Identifying and factoring out common terms from expressions.
• Difference of squares: A special factoring case.
• Trinomials: Factoring quadratic expressions.

Functions

• Definition of a function: A relationship where each input has exactly one output.
• Domain and range: The set of possible input values (domain) and the set of possible output values (range) of a function.
• Function notation: Expressing functions using f(x), g(x), etc.

Inequalities

• Solving linear inequalities: Similar to solving equations, but with attention to the direction of the inequality sign.
• Graphing inequalities: Representing solutions on a number line or coordinate plane.
• Combining inequalities.