Eighth Grade Algebra Essential Knowledge
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Algebraic Expression – an expression that includes at least one variable
Power – an expression that represents repeated multiplication of the same factor
Exponent – represents the number of times the base is used as a factor
Base of a power – the number or expression that is used as a factor is a repeated multiplication
Equation – a mathematical sentence formed by placing the symbol = between 2 expressions
Inequality – a mathematical sentence formed by placing one of the symbols <, >, <,or > between 2
expressions
7. Integers – the numbers…..-3, -2, -1, 0, 1, 2, 3, etc., consisting of the negative integers, zero, and the
positive integers
8. Opposites – two numbers that are the same distance from 0 on a number line but are on opposite sides
of 0
9. Absolute Value – the absolute value of a number a is the distance between a and 0 on a number line.
The symbol /a/ represent the absolute value of a
10. Distributive Property – a property that can be used to find the product of a number and a sum or
difference, examples: a(b+c) = ab+ac, or (b-c)a = ba - ca
11. Terms of an Expression – the parts of the expression that are connected by plus and minus signs
12. Simplified Expression – an expression that is in simplest terms
13. Equivalent Equations – equations that have the same solutions
14. Inverse Operations – two operations that undo each other
15. Cross Product – in a proportion, a cross product is the product of the numerator on 1 ratio and the
denominator of the other ratio.
16. Cross Products property – the cross products of a proportion are equal
17. Percent – out of 100
18. Coordinate Plane – a plane crossed by the x and y axis
19. Ordered Pair – 2 quantities written in order to be found on a coordinate plane (x,y)
20. Linear Equation – an equation whose graph is a line
21. Y-Intercept – the y-coordinate of a point where a graph crosses the y-axis
22. X-intercept – the x-coordinate of a point where a graph crosses the x-axis
23. Slope – the slope m of a nonvertical line is the ratio of the vertical change(the rise) to the horizontal
change(the run) between any two points (x1,y1) and (x2,y2) on the line m=y2-y1/x2-x1
24. Slope-Intercept Form – a linear equation written in the form y = mx + b where m is the slope and b is the
y-intercept of the equation’s graph
25. Point-Slope Form – an equation of a nonvertical line written in the form y - y1=m(x - x1) where the line
passes through a given point (x1,y1) and has a slope of m
26. Standard Form of a Linear Equation – Ax + By = C , where A, B, and C are real numbers and A and B are
not both zero
27. Correlation – the relationship between paired data. The paired data have positive correlation if y tends
to increase as x increases, negative correlation if y tends to decrease as x decreases, and relatively no
correlation if x and y have no apparent relationship
28. Line of Fit – a line used to model the trend in data having a positive or negative correlation
29. Compound Inequality – two inequalities joined by and or or
30. Half-plane – in a coordinate plane, the region on either side of a boundary line
31. Exponential Growth – when a > 0 and b > 1, the function y = abx represents exponential growth. When
a quantity grows exponentially, it increases by the same percent over equal time intervals. The
exponential growth model is y = a(1 + r)t
32. Growth Factor – the expression 1 + r in the exponential growth model y = a(1 + r)t
33. Exponential Decay – when a > 0 and 0 < b < 1, the function y = abx represents exponential decay. When
a quantity decays exponentially, it decreases by the same percent over equal time periods
34. Decay Factor – the expression 1 – r in the exponential decay model y = a(1 - r)t
35. Polynomial – a monomial or a sum of monomials, each called a term of polynomial
36. FOIL Pattern – order of multiplying, firsts, outers, inners, lasts
37. Factored Completely – continued factoring until no further factors can be found
38. Parabola – the U-shaped graph of a quadratic function
39. Vertex of a parabola – the lowest or highest point on a parabola
40. Axis of Symmetry – the line that passes through the vertex and divides the parabola into 2 symmetric
parts
41. Quadratic Equation – an equation that can be written in the standard form ax2+ bx+ c=0, where a does
not equal zero
42. Quadratic Formula – the formula below that can be used to find the solutions of the quadratic equation
ax2+ bx+ c=0, where a does not equal zero and b2 -4ac > 0
x = -b + b2 – 4ac
2a
43. Square Root Function – a radical function whose equation contains a square root with the independent
variable in the radicand
44. Hypotenuse – the hypotenuse of a right triangle is the side opposite the right angle
45. Pythagorean Theorem – if a triangle is a right triangle then the sum of the squares of the lengths a and b
of the legs equals the square of the length c of the hypotenuse a2 + b2=c2
46. Rational Number – a number that can be written as a simple fraction
47. Hyperbola – has 2 symmetrical parts called branches; approaches but doesn’t intersect lines called
asymptotes
48. Box-and-Whisper Plot – A data display that organizes data values into 4 groups using the minimum
value, lower quartile, median, upper quartile and maximum value.
49. Median – the median of a numerical data set is the middle number when the values are written in
numerical order
50. Lower Quartile – the median of the lowest half of an ordered data set
51. Upper Quartile – the median of the upper half of an ordered data set
52. Numerator – top number in a fraction
53. Denominator – bottom number in a fraction
54. Perimeter – total distance around a shape
55. Area of a rectangle – base times height units squared
56. Variable – a letter that is used to represent one or more numbers
57. Order of Operations – rules for evaluating an expression involving more than one operations,
Parenthesis, Exponents, Multiply/Divide, Add/Subtract
58. Verbal Model – describes a real-world situation using words as labels and using math symbols to relate
to the words
59. Rate – a fraction that compares 2 quantities measured in different units
60. Unit Rate – a rate in which the denominator of the fraction is 1 unit
61. Formula – an equation that relates 2 or more quantities
62. Function – a function consists of: a set called the domain containing numbers called inputs and a set
called the range containing numbers called outputs
63. Domain – the set of all inputs of a function
64. Range – the difference of the greatest value and the least value
65. Independent Variable – the input variable of a function
66. Dependent Variable – the output variable of a function
67. Least Common Denominator – the product of the factors of the denominators of the rational
expressions with each common factor used only once
68. Absolute Value – the absolute value of a number a is the distance between a and 0 on a number line.
The symbol |a| represents the absolute value of a
69. Conditional Statement – a statement with a hypothesis and a conclusion
70. Additive Identity – the number 0 is the additive identity; because the sum of any number and 0 is the
number; a+0=a
71. Additive Inverse – the additive inverse of a number a is its opposite, -a The sum of a number and its
additive inverse is 0
72. Multiplicative Identity – the number 1 is the multiplicative identity because the product of any number
and 1 is the number, a*1=a
73. Equivalent Expressions – two expressions that have the same value for all values of the variable
74. Term – a single number or variable in an expression
75. Coefficient – the number part of a term with a variable part
76. Constant term - a term with a number part but no variable part
77. Like Terms - terms that have the same variable parts. Constant terms are also like terms
78. Multiplicative Inverse – multiplicative inverse of a nonzero number a is its reciprocal 1/a, the product of
a nonzero number and its multiplicative number is 1
79. Square Root – if b2 = a, then b is the square root of a
80. Radicand – the number or expression inside a radical symbol
81. Perfect Square – a number that is the square if an integer
82. Irrational Number – a number that cannot be written as a quotient of 2 integers. The decimal form of
an irrational number neither terminates nor repeats
83. Real Numbers – the set of all rational and irrational numbers
84. Inverse Operations – 2 operations that undo each other
85. Ratio – a comparison of 2 numbers using division. The ratio of a and b, where b can be written as a to b,
a:b or as a/b
86. Proportion – an equation that states that 2 ratios are equivalent: a/b = c/d where b = 0 and d = 0
87. Scale Drawing – a 2-dimensional drawing of an object in which the dimensions of the drawing are
proportional to the dimensions of the object
88. Scale Model – a 3-dimensional model of an object in which the dimensions of the model are in
proportion to the dimensions of the object
89. Scale – a ratio that relates the dimensions of a scale drawing or scale model and the actual dimensions
90. Literal Equation – an equation in which letters are used to replace the coefficients and constants of
another equation
91. Reciprocal – divide 1 by the number, interchange the numerator and denominator
92. Quadrant – the 4 regions into the coordinate plane is divided by the x-axis and the y-axis
93. Linear Function – the equation Ax + By=C represents a linear function provided B does not equal zero
94. Rate of Change – a comparison of a change in 1 quantity with a change in another quantity. In realworld situations, you can interpret the slope of a line as a rate of change
95. Parallel lines – 2 lines in the same plane that do not intersect
96. Direct Variation – the relationship of 2 variables x and y if there is a nonzero number a such that y=ax.
If y=ax, then y is said to vary directly with x
97. Constant of Variation – the nonzero constant a in a direct variation equation y=ax or in an inverse
variation equation y=a/x
98. Function Notation – a way to name a function using the symbol f(x) instead of y. the symbol is read as
“the value of f at x” or “f of x”
99. Family of Functions – a group of functions with similar characteristics
100.Parent Linear Function – the function f(x) = x, which is the most basic function in the family of linear
functions
101.Converse of a conditional – a statement formed by interchanging the hypothesis and the conclusion of
a conditional. The converse of a true statement is not necessarily true
102.Perpendicular – 2 lines in the same plane that intersect to form a right angle
103.Scatter Plot – a graph used to determine whether there is a relationship or trend between paired data
104.Best fitting line – the line that most closely follows the trend of the data, found using technology
105.Zero of a Function – an x value for which f(x) = 0 (or y=0)
106.Least Common Multiple – the smallest number that is a multiple of 2 or more numbers
107.Order of Magnitude – a number rounded to the nearest power of 10
108.Scientific Notation – a way to represent numbers to large or too small to be written as a standard
number
109.Compound Interest – interest is added to the principal so that the new amount can also have interest
added
110.Factor By Grouping – finding patterns of common factors
111.Quadratic Function – a nonlinear function that can be written in standard form y=ax2+bx+c where a is
not 0
112.Axis of Symmetry – a line of symmetry for a graph
113.Minimum Value – smallest number
114.Maximum Value – largest number