Questions and Answers
What is the opposite of any number b?
What is the reciprocal of a nonzero number b?
What consists of numbers, operations, and grouping symbols?
Numerical expression
What represents repeated multiplication of the same factor?
Signup and view all the answers
What is the exponent in a power?
Signup and view all the answers
What is the base of a power?
Signup and view all the answers
What is a variable?
Signup and view all the answers
What is an algebraic expression?
Signup and view all the answers
What are the parts of an expression that are added together called?
Signup and view all the answers
What is a variable term?
Signup and view all the answers
What is a constant term?
Signup and view all the answers
What is a coefficient?
Signup and view all the answers
What are like terms?
Signup and view all the answers
What are equivalent expressions?
Signup and view all the answers
What is an identity?
Signup and view all the answers
What is an equation?
Signup and view all the answers
What is a linear equation in one variable?
Signup and view all the answers
What is the solution of an equation in one variable?
Signup and view all the answers
What are equivalent equations?
Signup and view all the answers
What is a formula?
Signup and view all the answers
What does it mean to solve for a variable?
Signup and view all the answers
What is a verbal model?
Signup and view all the answers
What is a linear inequality in one variable?
Signup and view all the answers
What is the solution of an inequality in one variable?
Signup and view all the answers
What is the graph of an inequality in one variable?
Signup and view all the answers
What is a compound inequality?
Signup and view all the answers
What are equivalent inequalities?
Signup and view all the answers
Study Notes
Algebra 2 Definitions
- The opposite or additive inverse of any number b is represented as -b.
- The reciprocal, also called the multiplicative inverse of a nonzero number b, is 1/b.
- A numerical expression includes numbers, operations, and grouping symbols.
- A power indicates repeated multiplication of the same factor.
- An exponent indicates the number of times the base is used in a power.
- The base of a power is the factor that is multiplied in repeated multiplication.
- A variable is a letter used to represent numbers.
- An algebraic expression consists of numbers, variables, operations, and grouping and is often referred to as a variable expression.
- Terms of an expression are the individual parts that are added together within that expression.
- A variable term contains a variable part.
- A constant term contains only a number and lacks a variable part.
- A coefficient is the number in front of a variable in a term.
- Like terms have the same variable parts, including constant terms.
- Equivalent expressions yield the same result for all variable values.
- An identity equates two equivalent expressions.
- An equation states that two expressions are equal.
- A linear equation in one variable is expressed in the form ax + b = 0.
- The solution of an equation in one variable produces a true statement when a number replaces the variable.
- Equivalent equations have the same solution set.
- A formula expresses the relationship between quantities, often using variables.
- To solve for a variable, rewrite an equation to isolate the variable on one side.
- A verbal model is a narrative representation of a real-life mathematical problem.
- A linear inequality in one variable may be expressed as ax + b < 0, ≤ 0, > 0, ≥ 0.
- A solution of an inequality in one variable produces a true statement when substituted into the inequality.
- The graph of an inequality in one variable spans all points on a number line that satisfy the inequality.
- A compound inequality combines two inequalities linked by "and" or "or".
- Equivalent inequalities demonstrate the same solution set.
- Absolute value |x| measures the distance of x from zero on a number line.
- An extraneous solution appears valid but does not satisfy the original equation.
- A relation maps input values to output values.
- The domain is the set of input values for a relation.
- The range is the set of output values for a relation.
- A function ensures each input has one unique output.
- An equation in two variables contains two variables.
- The solution of an equation in two variables is an ordered pair (x, y) making the equation true.
- The graph of an equation in two variables is the set of all points (x, y) that satisfy the equation.
- An independent variable denotes the input in an equation, while the dependent variable denotes the output.
- A linear function takes the form y = mx + b where m and b are constants.
- Function notation uses symbols like f(x) to denote the dependent variable of a function.
- The slope is determined by the ratio of vertical change (rise) to horizontal change (run) between points on a line.
- Parallel lines do not intersect within the same plane.
- Perpendicular lines intersect at right angles within the same plane.
- Rate of change compares how much one quantity changes relative to another.
- A parent function is the simplest form within a function family.
- The y-intercept is where a graph intersects the y-axis.
- Slope-intercept form of a linear equation is y = mx + b, establishing slope m and y-intercept b.
- The x-intercept is where a graph intersects the x-axis.
- The standard form of a linear equation is Ax + By = C where A and B are not both zero.
- Point-slope form of a line is y - y₁ = m(x - x₁), defined around a specific point (x₁, y₁).
- Direct variation indicates y = ax when two variables, x and y, are directly proportional, with a as a nonzero constant.
- The constant of variation a is essential in variations (direct, inverse, or joint).
- A scatter plot graphs pairs of data points (x, y) to evaluate variable relationships.
- Positive correlation occurs if y increases as x increases, while negative correlation means y decreases as x increases.
- The correlation coefficient r (between -1 and 1) measures how well a line fits data pairs.
- The best fitting line closely aligns with all data points in a scatter plot.
- An absolute value function incorporates an absolute value expression.
- The vertex of an absolute value graph indicates the peak or trough of the function.
- A transformation modifies a graph's size, shape, or position.
- A translation shifts a graph without altering size or shape.
- A reflection flips a graph or figure across a line.
- A linear inequality in two variables states Ax + By < C, ≤ C, > C, or ≥ C.
- The solution of a linear inequality in two variables is an ordered pair satisfying each inequality.
- The graph of a linear inequality depicts all viable solutions on a coordinate plane.
- Half-planes emerge as regions created by a linear inequality's boundary line.
- A system of two linear equations consists of equations in the forms Ax + By = C and Dx + Ey = F.
- The solution of a system of linear equations is an ordered pair satisfying all equations.
- A consistent system has at least one solution, while an inconsistent system lacks a solution.
- An independent system has exactly one solution, while a dependent system contains infinitely many solutions.
- The substitution method solves a system by substituting one variable into another equation.
- The elimination method eliminates variables by manipulating equations then combining them.
- A system of linear inequalities includes two or more inequalities.
- The solution of a system of linear inequalities consists of ordered pairs meeting all conditions.
- The graph of a system of linear inequalities represents all solutions graphically.
- A linear equation in three variables is expressed as ax + by + cz = d, with a, b, c not all zero.
- A system of three linear equations features three linear equations in three variables.
- The solution of a system of linear equations in three variables is an ordered triple (x, y, z) that satisfies all equations.
- An ordered triple is a set of three numbers (x, y, z) representing a point in a three-dimensional space.
- A matrix is a rectangular array of numbers organized in rows and columns.
- The dimensions of a matrix are defined by the number of rows and columns, noted as m × n.
- Each number in a matrix is termed an element.
- Equal matrices have matching dimensions and corresponding elements.
- A scalar refers to a real number.
- Scalar multiplication involves multiplying each matrix element by a scalar.
- The determinant is a real number tied to square matrices, denoted as det A or |A|, calculated as ad - cb for specific 2x2 matrices.
- Cramer's rule uses determinants to solve systems of linear equations under certain conditions.
- The coefficient matrix for the system ax + by = e, cx + dy = f is structured as |a b| |c d|.
- An identity matrix has ones along its main diagonal and zeros elsewhere.
- An inverse matrix exists if the product of two n × n matrices returns the identity matrix.
- The matrix of variables in a linear system includes variables expressed as a matrix.
- The matrix of constants includes constants from the linear equation systems presented as a matrix.
- A quadratic function takes the form y = ax² + bx + c, where a cannot equal zero.
- The standard form of a quadratic equation is also y = ax² + bx + c with a not equal to zero.
- A parabola is the set of points equidistant from a focus and a directrix, visible in the graph of a quadratic function.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of key Algebra 2 definitions with this set of flashcards. Each card features important terms like 'opposite', 'reciprocal', 'numerical expression', and 'power' with clear definitions. Perfect for reviewing and reinforcing your algebra vocabulary!
