Algebra Class: Expressions and Operations

Study Notes

Algebraic Expressions

Algebraic expressions consist of numbers, symbols, and variables representing one or more operations.
Example: In the expression 7x + 8, both the variable x and the number 8 are part of the expression.

Coefficient

A coefficient is a numerical factor that multiplies a variable within an expression.
In the expression 7x + 8, the coefficient is 7.

Constant

A constant is a specific numerical value that remains unchanged.
In the expression 7x + 8, the constant term is 8.

Dependent Variable

The dependent variable in a function is determined by the value of the independent variable.
Its value changes in response to modifications of the independent variable.

Expression

An expression signifies that two mathematical quantities or operations are equivalent.
Example: 3 * 5 = 7 + 8 demonstrates that both sides yield the same value.

Equivalent Expression

Equivalent expressions yield the same result or value despite having different appearances.
Example: Both 4 * 4 and 9 + 7 equal 16.

Evaluate

Evaluating an expression involves substituting variables with numbers and performing the operations to simplify.
For instance, replacing 'a' in 4 + a when a = 2 results in 4 + 2 = 6.

Exponent

An exponent indicates how many times a number (the base) is multiplied by itself.
For example, in ( x^3 ), the exponent is 3, denoting ( x \times x \times x ).

Formula

A formula is a mathematical statement or equation that expresses a rule or relationship between variables.
An example is the area of a rectangle, represented by A = l * w, where l is the length and w is the width.

Independent Variable

The independent variable is the input value in a function that influences the dependent variable's output.
It is the variable that stands alone and isn't affected by other variables in the equation.

Inequality

An inequality is a mathematical statement that compares two non-equal expressions using symbols, such as >, <, or ≠.
Inequalities demonstrate relational differences between quantities.

Description

Test your knowledge of algebraic expressions and the fundamental operations associated with them. This quiz will help reinforce your understanding of terms like coefficients and constants through flashcards. Prepare to strengthen your algebra skills!