Algebra Ch. 1 Definitions

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Algebra Ch. 1 Definitions
2010-12-14 20:43:41
algebra chapter one definitions

Chapter one Vocab
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  1. Absolute value
    The distance that a number is from zero on a number line
  2. Additive inverse
    The opposite of a number. Additive inverses sum to zero
  3. Algebraic expression
    The mathematical phrase that can include numbers, variables, and operation symbols
  4. Base
    A number that is multiplied repeatedly
  5. Coefficient
    Numerical factor when a term has a variable
  6. Constant
    A term that has no variable factor
  7. Coordinate plane
    A plane formed by two number lines that intersect at right angles
  8. Coordinates
    The numbers that make a ordered pair and identify the location of a point
  9. Counterexample
    Any example that proves a statement false
  10. Deductive reasoning
    A process of reasoning, logically from given facts to a conclusion
  11. Element
    An item in a matrix
  12. Equation
    Mathematical sentence that uses an equal sign
  13. Evaluate
    Substitute a given number for each variable and then simplify
  14. Exponent
    A number that shows repeated multiplication
  15. Inequality
    A mathematical sentence that compares the values of two expressions using an inequality symbol
  16. Integers
    Whole numbers and their opposites
  17. Irrational numbers
    A number that cannot be written as a ratio of two integers. Irrational numbers in decimal form is non-terminating and non-repeating
  18. Like terms
    Terms with exactly the same variable factors in a variable expression
  19. Matrix
    A rectangular arrangement of numbers. The number of rows and columns in the matrix determines its size
  20. Multiplicative inverse/reciprocal
    Given a nonzero rational number, a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero number and its multiplicative inverse is always one
  21. Natural numbers
    The counting numbers (-1, 0, 1, 2, 3...)
  22. Open sentence
    An equation that contains one or more variables
  23. Ordered pair
    Two numbers that identify the location of a point
  24. Origin
    The point at which the axis of the coordinate plane intercept
  25. Quadrants
    The four parts into which the coordinate plane is divided by its axis
  26. Rational numbers
    A real number that can be written as a ration of two integers. Rational numbers in decimal form are terminating or repeating
  27. Real numbers
    A number that is either rational or irrational
  28. Scatter plot
    A graph that relates data of two different sets. The two sets of data are displayed as ordered pairs
  29. Simplify
    Replace an expression with its simplest name of form
  30. Term
    A number, variable, or the product or quotient of a number and one or more variables
  31. Trend line
    A line on a scatter plot drawn near the points. It shows a correlation
  32. Variable
    A symbol, usually a letter, that represents one or more numbers
  33. Whole numbers
    Nonnegative integers (0, 1, 2, 3...)
  34. x-axis and y-axis
    horizontal (x) and vertical (y) axis of the coordinate plane
  35. x-coordinate and y-coordinate
    location of an x-axis and y-axis of a point on the coordinate plane.
  36. Consecutive integers
    Integers that differ by one (-2, -1, 0, 1, 2…)
  37. Equivalent equations
    Equations that have the same solutions
  38. Identity
    Equation that is true for every value
  39. Inverse operations
    Operations that undo one another
  40. Literal equation
    An equation involving two or more variables
  41. Measures of central tendency
    Mean, median, and mode. They are used to organize/summarize a set of data
  42. Outlier
    A data value that is much higher or lower than the other data values in the set
  43. Solution of an equation
    Any value(s) that make an equation true
  44. Stem-and-leaf plot
    A display of data made by using the digits of the values
  45. Uniform motion
    The motion of an object moving at a constant rate
  46. Range = x or y?
    Domain = x or y?
    • Range = y
    • Domain = x
  47. Compound inequalities
    Two inequalities that are joined by and/or
  48. Equivalent inequalities
    Equivalent inequalities have the same set of solutions
  49. Solution of an inequality
    One variable – any value of values of a variable in the inequality that makes an inequality true
  50. Arithmetic sequence
    A number sequence formed by adding a fixed number to each previous term
  51. Common difference
    The fixed number added to each term of an arithmetic sequence
  52. Conjecture
    Conclusion reached by inductive reasoning
  53. Constant of variation
    Direct variation – nonzero constant k in the function y = kx
  54. Dependent variable
    A variable that provides the output values of a function (y on the graph)
  55. Direct variation
    A linear function that can be expressed in the form y = kx, where k is not 0
  56. Function
    A relation that assigns exactly one value in the range to each value of the domain
  57. Function notation
    To write a rule in function notation, you use the symbol f(x) in place of y
  58. Function rule
    An equation that describes a function
  59. Independent variable
    A variable that provides the imput values of a function (x in the graph)
  60. Inductive reasoning
    Making conclusions based on observed patterns
  61. Relation
    Any set of ordered pairs
  62. Sequence
    A number pattern
  63. Term
    A number, variable, or the product or quotient of a number and one of more variables Ex: 5x + (y/2) – 8 has three terms – 5x, y/2, -8
  64. Vertical-line test
    A method used to determine if a relation is a function or not. If the line passes through a graph more than once, the graph is NOT a function
  65. Correlation Coefficient
    A number that tells how closely the equation of best fit models the data. The value r of the correlation coefficient is in the range -1 < r < 1
  66. Absolute value equation
    Equation whose graph forms a V that opens up or down
  67. Line of best fit
    The most accurate trend line on a scatter plot showing the relationship between two sets of data
  68. Linear equation
    An equation whose graph forms a straight line
  69. Negative reciprocal
    A number of the form –b/a, where a/b is a nonzero rational number. The product of a number and its negative reciprocal is -1
  70. Parallel lines
    Two lines in the same plane that never intersect. Parallel lines have the same slope.
  71. Perpendicular lines
    Lines that intersect to form right angles. 2 lines are perpendicular if the product of their slopes is -1
  72. Point-slope form
    y-y₁ = m(x – x₁)
  73. Rate of change
    • Change in the dependent variable
    • Change in the independent variable
  74. Slope
    • Ratio of the vertical change to horizontal change
    • Vertical change = y₂ – y₁
    • Horizontal change = x₂ – x₁
    • Where x₂ – x₁ is not zero
  75. Slope-intercept form
    A linear equation of a nonvertical line written as y = mx + b, where m = slope & b = y-intercept
  76. Standard form of a linear equation
    The form of a linear equation Ax + By = C, where A, B, and C are real numbers and A and B are not zero
  77. Translation
    A transformation that shifts a graph horizontally, vertically, or both
  78. x-intercept/y-intercept
    • x-coordinate of the point where a line crosses the x-axis
    • y-coordinate of the point where a line crosses the y-axis
  79. Inputs - x or y?
    Outputs - x or y?
    • Inputs - x
    • Outputs - y
  80. How to solve 3r2?
    3 * r2