{
 "source": "https://peabody.kids/flashcards/math-algebra-terms",
 "id": "math-algebra-terms",
 "title": "Algebra Terms",
 "category": "math",
 "subject": "Math",
 "levels": [
  "6-8",
  "9-12"
 ],
 "description": "The vocabulary of algebra: expressions, equations, functions, graphing and polynomials.",
 "tags": [
  "algebra",
  "vocabulary"
 ],
 "frontLabel": "Term",
 "backLabel": "Meaning",
 "cards": [
  [
   "Variable",
   "A letter that stands for a number"
  ],
  [
   "Constant",
   "A fixed number that does not change"
  ],
  [
   "Coefficient",
   "The number multiplying a variable",
   "In −4y, it is −4"
  ],
  [
   "Term",
   "A part of an expression separated by + or −"
  ],
  [
   "Like terms",
   "Terms with the same variables raised to the same powers"
  ],
  [
   "Expression",
   "A combination of numbers, variables and operations without an equals sign"
  ],
  [
   "Equation",
   "A statement that two expressions are equal"
  ],
  [
   "Inequality",
   "A statement comparing two expressions using <, >, ≤ or ≥"
  ],
  [
   "Solve",
   "Find the value of the variable that makes the statement true"
  ],
  [
   "Evaluate",
   "Replace variables with numbers and compute the result"
  ],
  [
   "Simplify",
   "Combine like terms and reduce an expression"
  ],
  [
   "Factor",
   "Write an expression as a product of simpler expressions"
  ],
  [
   "Expand",
   "Multiply out brackets to remove them"
  ],
  [
   "Substitution",
   "Replacing a variable with a value or another expression"
  ],
  [
   "Linear equation",
   "An equation whose graph is a straight line; the variable has degree 1"
  ],
  [
   "Slope-intercept form",
   "y = mx + b"
  ],
  [
   "Point-slope form",
   "y − y₁ = m(x − x₁)"
  ],
  [
   "Standard form of a line",
   "Ax + By = C"
  ],
  [
   "Slope",
   "Rise over run; change in y divided by change in x"
  ],
  [
   "Rise",
   "The vertical change between two points"
  ],
  [
   "Run",
   "The horizontal change between two points"
  ],
  [
   "Y-intercept",
   "Where a graph crosses the y-axis (x = 0)"
  ],
  [
   "X-intercept",
   "Where a graph crosses the x-axis (y = 0)"
  ],
  [
   "Parallel lines (slopes)",
   "Have equal slopes"
  ],
  [
   "Perpendicular lines (slopes)",
   "Slopes are negative reciprocals; their product is −1"
  ],
  [
   "Slope of a horizontal line",
   "0"
  ],
  [
   "Slope of a vertical line",
   "Undefined"
  ],
  [
   "Function",
   "A rule that gives each input exactly one output"
  ],
  [
   "Function notation",
   "f(x) is read 'f of x'; the output for input x"
  ],
  [
   "Domain",
   "All allowed input values"
  ],
  [
   "Range",
   "All resulting output values"
  ],
  [
   "Independent variable",
   "The input variable, usually x"
  ],
  [
   "Dependent variable",
   "The output variable, usually y; it depends on x"
  ],
  [
   "Vertical line test",
   "A graph is a function if no vertical line crosses it twice"
  ],
  [
   "Absolute value",
   "The distance of a number from zero, written |x|"
  ],
  [
   "System of equations",
   "Two or more equations solved together"
  ],
  [
   "Substitution method",
   "Solve one equation for a variable and substitute into the other"
  ],
  [
   "Elimination method",
   "Add or subtract equations to cancel a variable"
  ],
  [
   "Consistent system",
   "A system with at least one solution"
  ],
  [
   "Inconsistent system",
   "A system with no solution, such as parallel lines"
  ],
  [
   "Dependent system",
   "A system with infinitely many solutions; the same line"
  ],
  [
   "Polynomial",
   "An expression of terms with whole-number powers of variables"
  ],
  [
   "Degree",
   "The highest power of the variable in a polynomial"
  ],
  [
   "Standard form of a polynomial",
   "Terms written from the highest power to the lowest"
  ],
  [
   "Quadratic equation",
   "An equation of the form ax² + bx + c = 0"
  ],
  [
   "Quadratic formula",
   "x = (−b ± √(b² − 4ac)) / 2a"
  ],
  [
   "Completing the square",
   "Rewriting a quadratic so a perfect square trinomial appears"
  ],
  [
   "Vertex form",
   "y = a(x − h)² + k"
  ],
  [
   "Difference of squares",
   "a² − b² = (a − b)(a + b)"
  ],
  [
   "Perfect square trinomial",
   "a² + 2ab + b² = (a + b)²"
  ],
  [
   "Greatest common factor (GCF)",
   "The largest factor shared by all the terms"
  ],
  [
   "Zero product property",
   "If ab = 0, then a = 0 or b = 0"
  ],
  [
   "Root, zero or solution",
   "An x value where the function equals 0"
  ],
  [
   "Radical",
   "A root symbol, such as √"
  ],
  [
   "Rationalize the denominator",
   "Rewrite a fraction so the denominator has no radical"
  ],
  [
   "Rational expression",
   "A fraction whose numerator and denominator are polynomials"
  ],
  [
   "Inverse variation",
   "y = k/x; as one quantity goes up, the other goes down"
  ],
  [
   "Direct variation",
   "y = kx; the ratio y/x is constant"
  ],
  [
   "Constant of variation",
   "The constant k in a variation equation"
  ],
  [
   "Arithmetic sequence formula",
   "aₙ = a₁ + (n − 1)d"
  ],
  [
   "Geometric sequence formula",
   "aₙ = a₁ · rⁿ⁻¹"
  ],
  [
   "Exponential growth",
   "y = a(1 + r)^t with r > 0"
  ],
  [
   "Exponential decay",
   "y = a(1 − r)^t with 0 < r < 1"
  ],
  [
   "Compound interest formula",
   "A = P(1 + r/n)^(nt)"
  ],
  [
   "Continuous compounding formula",
   "A = Pe^(rt)"
  ]
 ]
}