1. Algebra One
Math Vocabulary

2. A number’s distance from zero on a number line.
Absolute Value
A number’s distance from zero on a number line.
Examples: 3

3. Algebraic expression
A mathematical phrase that can include numbers, variables, and operation symbols
Examples:
3x2 + 2y + 7xy + 5
3x + 12 – x + 2
or 2x + 14
Write an algebraic expression
For the sum of six and a number:
6 + x
Evaluate the algebraic expression
if x = 2:

4. Coefficient The numerical factor of a variable term
A number that multiplies a variable in a term
Examples:
The coefficients are in red
coefficient
variable
exponent

5. Combinations An arrangement of the elements of a set
without regard to order
Examples
In how many different ways can three letters be chosen from the letters A, B, C, D, and E?
( The order of the three letters is not important:
so, {A,B,C} and {C,B,A} are the same)
{A, B, C} {A, B, E} {A, C, E} {B, C, D} {B, D, E}
{A, B, D} {A, C, D} {A, D, E} {B, C, E} {C, D, E}

6. A term that has no variable factor
Constant
A term that has no variable factor
Examples
Constant
Constant
Constant
Coefficient
Variable
Constant

7. Coordinate Plane A plane formed by a horizontal number line (x-axis)
and a vertical number line (y-axis)
Example:

8. Distance Formula The distance d between any two points and is Examples
The distance between
(-3,2) and (0,-2) is:
(-3,2)
(0,-2) 4 3 5

9. Domain and Range
Domain: The set of all x-coordinates in the ordered pairs (x,y) of a relation
Range: The set of all the y-coordinates in the ordered pairs (x,y) of a relation
Examples x y 1 -1
Domain: {1,2,3,4}
Range: {2.4,6,8}
Domain:
{1,0,-1}
Range:
{1,0}

10. Equations (solving) An equation is a mathematical sentence
containing an equal sign
To solve an equation, find a value for the variable
that makes the sentence true
Examples

11. Equations (graphing) The graph of an equation contains ordered pairs
that make the equation true
Examples x
Y=2-x 2 1 -2 4 x
y=x-3 -3 3 -2 -5

12. Equations (slope-intercept)
The slope-intercept form of an equation is y = mx + b
Where m is the slope of the line and b is its y-intercept
Examples
slope = -1
y-int = 2
slope = 1
y-int = -3
slope = 2
y-int = -3

13. Factoring
To write an expression (or number) as a product of two or more expressions (or numbers )
Examples
Factor
3x+6 = 3(x+2)
x2-2x-15 =
(x-5)(x+3)
Factor tree
Factor x2 + 3x + 2
(x + 1)
(x + 2)
(x + 1)(x + 2)

14. Function notation
A way to write an equation or rule that is a function,
use the symbol f (x) in place of y
f(x) is read “f of x” and means that the value of the function depends on the value of x
f(x) is the output of the function with input x
(Given an x, you get f(x) or y)
Examples
f(x) = x+3
f(2) = 2+3= 5
when x=2, y=5
(2,5)
f(x) = x2
f(-3)=(-3)2
= 9

15. using <, >, <, >, or
Inequalities
(number line)
The graph of a mathematical sentence showing the relationship between quantities that are not equal,
using <, >, <, >, or
Examples

16. Inverse Examples Addition and subtraction are inverse operations
Operations that undo each other
Examples
Addition and subtraction are inverse operations
(undo adding 3 by subtracting 3)
Multiplication and division are inverse operations
(undo multiplying by 2 by dividing by 2)
To solve an equation:
x + 3 = 5
x + 3 – 3 = 5 – 3
x = 2

17. Irrational Numbers A number that cannot be written
as a ratio of two integers
Numbers in decimal form that
are non-terminating and non-repeating
Examples
Real Numbers
Rational Numbers
Irrational
numbers
Integers
Whole
Natural

18. Line of best fit
A straight line that best fits the data on a scatter plot
(This line may pass through some, none,
or all of the points)
Examples

19. Linear systems: Elimination A method of solving a system of equations
with two variables to reduce it to an equation
with only one variable
by eliminating one of the variables
by addition/multiplication
Examples

20. Linear systems: Substitution
Example
To solve a system by substitution, solve one equation
for one variable in terms of the other,
Substitute into the other equation to obtain
an equation with only one variable

21. The midpoint of a line segment with endpoints and
Midpoint formula
The midpoint of a line segment with endpoints and is
Examples A B
A: (-4,3) and B(2,-5)

22. Permutations An arrangement of elements in which order is important
Examples
MATH: how many ways can two letters be arranged from the four letters M, A, T, and H?
12 possible permutations:
MA, AM, MT, TM, MH, HM,
AT, TA, AH, HA, TH, HT
CAT: How many permutations
are there of the letters C A T ?
6 possible permutations:
CAT, CTA, ATC, ACT, TAC, TCA

23. Polynomial
An expression that is the sum (or difference) of more than one term, each of these having variables with whole number exponents
(A quotient with a variable in the denominator
is not a polynomial)
Some polynomials have special names
Examples
Not a polynomial

24. Pythagorean Theorem In a right triangle, the sum of the squares of the
length of the legs is equal to the square of the length
of the hypotenuse: 5 3 4 5 13 15 8 17 12

25. An equation of degree two: ax2 + bx + c = 0
Quadratic Equation
An equation of degree two: ax2 + bx + c = 0
Example
To solve:

26. Discriminant Quadratic formula The part of the quadratic formula
Examples
The part of the quadratic formula
that is under the radical:
It tells the nature of the roots: how many
and whether they are real (D>0) or not (D<0)

27. Ratio, Proportion Ratio: A comparison of two numbers by division.
Proportion: An equation stating
that two ratios are equal.
If the cross products of the two ratios are equal,
then the pair forms a proportion
Examples
is a proportion because 12x1 = 3x4
do not form a proportion
because 15x2 5x7

28. The ratio used to enlarge or reduce
Scale Factor
The ratio used to enlarge or reduce
similar figures
Examples
Drawings: if the Eiffel Tower
is 1000 feet tall and the drawing of it
was 1 foot tall, the scale factor would be
Models: if a car is 204” in length and
the length of a model of the car is 12” long,
the scale factor would be

29. Real Number A number that is either rational or irrational.
Real numbers include natural numbers, whole numbers,
integers, rational numbers and irrational numbers
Examples
Real Numbers
Rational Numbers
Irrational
numbers
Integers
Whole
Natural

30. Slope A measure of the steepness of a line
The ratio of the vertical change (rise)
to the horizontal change (run)
The change in y over the change in x
Slope = = = where
The symbol for slope is m
rise = -2
run
= 4
(-2,3)

31. Subset A set whose elements are all elements of another set
A set contained within a another set
The symbol for subset is
Examples
The set {a,b,c} has subsets:
{a}, {b}, {c}, {ab}, {ac},
{bc},{a,b,c} and { }
The set of Rational numbers
is a subset of the set of Real numbers,
All Rational numbers are Real numbers